Test Bank Statistics Learning from Data 3rd Edition By Roxy Peck, Catherine Case

Test Bank

Name:

Class:

Date:

Chapter 01 - Collecting Data 1. The entire collection of individuals or objects about which information is desired is called a sample. a. True b. False ANSWER: False 2. A study is observational if the investigator observes the behavior of a response variable when one or more factors are manipulated. a. True b. False ANSWER: False 3. Suppose you are part of a gardening club with fifty members, all of whom are growing a particular variety of tomatoes on a shared garden plot. Early in the growing season, you notice that tomatoes tended by some members were noticeably redder than the tomatoes tended by other club members. You recall that, at the start of the growing season, a new fertilizer became available and that some of the gardening club members started to use it on their tomatoes. Which of the following studies could enable you to determine whether the new fertilizer contributed to the redder tomatoes? a. Survey six of the fifty club members asking them if they used the new fertilizer and rate their tomato color. b. Survey all fifty club members asking them if they used the new fertilizer and rate their tomato color. c. Ask a group of six club members to plant more tomatoes with three members using only the new fertilizer and three members using only the old fertilizer. d. Survey the ten club members with the reddest tomatoes and ask them which fertilizer they used.

ANSWER: c 4. Which of the following statistical studies is observational? a. A group of students is surveyed to determine the percentage who believe in reincarnation. b. A random sample of students is shown a documentary on the evolution of reincarnation beliefs throughout human history. A second random sample is not shown in the documentary. The object of the study is to determine whether viewing the documentary affects belief in reincarnation. c. To determine whether vitamin C has any effectiveness at lessening the duration of the common cold, one set of cold sufferers is given no vitamin C, a second set is given 2 grams per day, and a third set is given 5 grams of vitamin C per day. d. To determine if a new regenerative injection therapy is effective for reducing knee arthritis pain, a randomly selected group of arthritis patients were randomly assigned to two groups. In one group, the patients received physical therapy plus the new regenerative injection therapy. In the other group, the patients received only physical therapy.

ANSWER: a 5. Which of the following statistical studies is an experimental study?

I) A researcher observes the effect of alcohol consumption on reaction time by administering various quantities of alcohol to randomly selected subjects.

II) A study is conducted to see if exposure to increased carbon dioxide levels increases tomato yield. Tomato plants are selected at random and then exposed to various doses of carbon dioxide.

III) Two random samples of senior adults are selected. The first group watches a 30-minute presentation on Medicare fraud, while the other group does not watch the presentation. A survey is then administered to measure the level of confidence that subjects have in their healthcare providers. a. I and II only b. II and III only

Name:

Class:

Date:

Chapter 01 - Collecting Data c. I and III only d. I, II, and III ANSWER: d 6. Suppose you would like to know the flavor of ice cream preferred by the students at your university. Which of the following studies would help you learn the preferred ice cream flavor of your university student population? a. Survey a random sample of fifty students asking them their favorite ice cream flavor. b. Conduct an experiment on fifty student volunteers where the volunteers are randomly assigned to different groups, each of which is asked to try a single flavor of ice cream and report how well they like it. c. Survey a sample of fifty students from the freshman class asking them their favorite ice cream flavor. d. Conduct an experiment on fifty students randomly selected students from the senior class. In the experiment, the participants are randomly assigned to different groups, each of which is asked to try a single flavor of ice cream and report how well they like it.

ANSWER: a 7. You’re the owner of a bakery that produces cakes for special events. You’re considering investing in new equipment that would enable you to create larger cakes with more elaborate decorations. Before investing in the new equipment, it is essential that you know whether or not your clients would pay more money for the larger, more elaborate cakes. You have 100 clients, all of whom would respond to an inquiry within the time frame in which you must decide whether or not to purchase the new equipment. Which of the following studies would give you the best insight into whether or not your client population would purchase the larger, more elaborately decorated cakes? a. A survey of the next ten clients who contact you to order cakes b. A survey of ten clients selected at random from a list of all your clients c. A survey of the ten clients who placed the largest number of cake orders over the past year d. A census of your clients ANSWER: d 8. You’re a veterinarian interested in the effect of brisk, daily walks on the health of large dogs. You take a survey of 100 dog owners and find that dogs taken for one or more brisk walks each day become ill less frequently. Which of the following describes this finding? a. A statistic because it reflects data taken from the entire population of large dogs b. A population parameter because it reflects data taken from a sample c. A statistic because it reflects data taken from a sample d. A population characteristic because the study was based on a census.

ANSWER: c 9. You live in an apartment building with 50 residents. You’re investigating the effect of a new bus stop on the ability of your building’s residents to arrive at work on time. You survey all 50 of the building’s residents and ask them questions about their work arrival time since the new bus stop became available. Which of the following accurately describes the results of your survey? a. A population characteristic because it was based on a census b. A statistic because the sample did not include residents from buildings in other neighborhoods c. A statistic because the sample was drawn from an easily available group d. A population parameter because it was based on a sample of residents from the building ANSWER: a

Name:

Class:

Date:

Chapter 01 - Collecting Data 10. You’re concerned about the concentration of nitrates in the drinking water wells in your city. There are 200 wells in your city. You take water from 58 of these wells and analyze the water to determine nitrate concentration. The average nitrate concentration from the 58 wells is 5 milligrams per liter. Which of the following accurately describes your 5 milligrams per liter average concentration? a. A statistic because it is based on a sample of the city’s wells. b. A population characteristic because it is based on a sample from the city’s wells. c. A statistic because it was based on a census of the city’s wells. d. A population characteristic because it is based on a census of the city’s wells.

ANSWER: a 11. Suppose you’re the owner of a sewing supplies shop. You have an inventory of 50 thread packages in your store, some of which contain nylon fiber. You’re interested in learning how many of the thread packages in your inventory contain nylon fiber. You perform a simple test for nylon fiber on all 50 packages of thread in your store and find that 10 of the 50 contain nylon fiber. Which of the following accurately describes the results of your survey? a. A statistic because it is based on a sample of the shop’s thread packages b. A population parameter because it is based on a census of the shop’s thread packages c. A statistic because it was based on a census of the shop’s thread packages d. A population parameter because it is based on a sample of the shop’s thread packages.

ANSWER: b 12. You’re interested in learning about the typical body weight of residents in the small town where you live. The town has only 200 residents. You send out a questionnaire to all 200 residents asking them for their body weight in kilograms.

All 200 residents reply with the requested data. You use the data supplied by all 200 residents to determine the typical body weight of your town’s residents. Which of the following accurately describes the typical body weight you just determined? a. A statistic because it was based on a sample of your town’s residents b. A population characteristic because it was based on a sample of your town’s residents c. A statistic because it was based on a census of your town’s residents d. A population parameter because it was based on a census of your town’s residents ANSWER: d 13. Which of the following are the advantages of a simple random sample in an observational study? a. The sample can be drawn from an easily available group. b. The sample statistics will be distinctly different from the population parameters. c. All individuals in the population need not have the same chance of being included in the sample. d. Your sample statistics will reflect the population characteristics.

ANSWER: d 14. A simple random sample of size n is a sample selected from a population in such a way that every different possible sample of this same size n has an equal chance of being selected. a. True b. False ANSWER: True 15. As long as the sample size is small relative to the population, there is little practical difference between sampling with replacement and sampling without replacement.

Name:

Class:

Date:

Chapter 01 - Collecting Data a. True b. False ANSWER: True 16. Many people have speculated that high school students who eat a meal before attending classes earn better grades than those who fast before class. You decide to evaluate this claim by surveying 20 high-school senior-year history students from each school in your city. Will the results of your survey predict the effect of pre-class meals on student grades? a. Yes, because the survey data was based on a census b. Yes, because the samples were drawn from easily available groups c. No, because every student did not have an equal chance of being selected to participate in the survey d. No, because the sample size was too small ANSWER: c 17. Suppose you’re an arborist responsible for the health of pine trees in the 20 public parks located throughout your city.

Pine trees are present in all of the city’s parks, and each neighborhood of your city contains a park. A colleague tells you that he suspects the pine trees for which you are responsible may have a disease. The disease can be accurately diagnosed by examining the color of the pine tree’s needle leaves. You sample leaves from the 3 city parks nearest the waterfront.

Will the results of your survey predict the health of the city parks’ pine trees? a. Yes, because the survey data was based on a census. b. Yes, because the samples were drawn from easily available groups c. No, because each of the city’s parks did not have an equal chance of having its pine tree needles examined. d. No, because the sample size was too small.

ANSWER: c 18. Suppose you’re sampling with replacement from a population size of 100. How small must your sample size be for sampling without replacement to be viewed as equivalent? a. 20 b. 1 c. 10 d. 2 ANSWER: c 19. Stratified sampling is a sampling method that involved no random sampling. a. True b. False ANSWER: False 20. Clusters are non-overlapping sub-groups of a population consisting of diverse individuals. a. True b. False ANSWER: True 21. In stratified random sampling, a population is first divided into non-overlapping, non-random sub-groups. Random samples are then selected from each subgroup. a. True

Name:

Class:

Date:

Chapter 01 - Collecting Data b. False ANSWER: True 22. Which of the following sampling methods best describes the one used in the following study?

To analyze the level of employee satisfaction at stores in a certain large city, a grocery store chain selects eight store locations at random and surveys all employees at these locations. a. Simple random sampling b. Stratified random sampling c. Cluster sampling d. Systematic sampling ANSWER: c 23. Which of the following sampling methods best describes the one used in the following study?

To analyze the hair length of fashion models at a large modeling agency, models’ names were selected from the employee directory for a hair-length measurement. One model was selected randomly from the first 15 models listed in the directory, then every 15th model after that in the employee directory was also selected. a. Simple random sampling b. Stratified random sampling c. Cluster sampling d. Systematic sampling ANSWER: d 24. Nonresponse bias can occur when responses are not obtained from all individuals selected for inclusion in the sample. a. True b. False ANSWER: True 25. Increasing sample size will generally eliminate bias in a sample. a. True b. False ANSWER: False 26. Selection bias can occur if a study consists exclusively of volunteers. a. True b. False ANSWER: True 27. Measurement (response) bias could result from which of the following?

I) An improperly calibrated assessment tool used to weigh survey responses II) A survey that includes leading questions III) Appearance or behavior of the person asking the survey questions a. I and II only b. II and III only c. I and III only d. I, II, and III

Name:

Class:

Date:

Chapter 01 - Collecting Data ANSWER: d 28. Which of the following best summarizes “nonresponse bias”? a. A tendency for samples to differ from the corresponding population as a result of systematic exclusion of some part of the population b. A tendency for samples to differ from the corresponding population because data are not obtained from all individuals selected for inclusion in the samples c. A tendency for samples to differ from the corresponding population because the method of observation tends to produce values that differ from true values d. A bias on the part of the researcher towards those who chose not to participate in the survey ANSWER: b 29. A question in a survey on consumer food preferences asks respondents to select their favorite flavor of ice cream from a list that only includes “chocolate” and “vanilla”. Which of the following types of bias does this question include? a. Selection bias b. Measurement bias c. Nonresponse bias d. Response bias ANSWER: c 30. To estimate the proportions of students who plan to purchase tickets to an upcoming school fundraiser, a high school decides to sample 100 students as they register for the spring semester. There are 2000 students at the school. Which of the following sampling plans would result in a simple random sample? a. Number the students from 1 to 2000 and then use random numbers to select 100 students. b. Survey the first 100 students to register c. Randomly select 100 students from a list of 950 female students at the school d. Select one of the first 20 students to register using a random number table and then select every 20th student thereafter ANSWER: a 31. Which of the following actions should be used to create a simple, random sample?

I) Create a sampling frame which is essentially a list of objects or individuals in the population II) Identify each object or individual in the sample frame with a unique number III) Use a random number generator to select the sample a. I and II only b. II and III only c. I and III only d. I, II, and III ANSWER: d 32. The owner of a dress shop wants to learn which customers would be interested in an upcoming sale event. The dress shop has 622 customers, but it is only practical to contact 20 regarding their interest in the sale event. The customer names and contact information are stored in a database that permits the assignment of unique numbers for each customer. Which of the following methods could be used to select a simple random sample for the survey? a. Select the first 20 customers in the database b. Sort the customers by age and select the first 20

Name:

Class:

Date:

Chapter 01 - Collecting Data c. Use a random number generator to request 20 integers between 1 and 622 and use the customers corresponding to those numbers in the survey d. Sort the customers by the date of their first purchase and select the first 20.

ANSWER: c 33. You have a population of 5000 objects which require quality testing. . Which of the following sample sizes is the largest sample size for which there would be little practical difference between sampling with replacement and sampling without replacement? a. n = 2500 b. n = 1000 c. n = 500 d. n = 5 e. n – 10 ANSWER: c 34. Suppose you’re responsible for measuring the length of juvenile fish in a fish hatchery. Your standard procedure requires that you base your measurement on the average of five fish selected from each tank. In order to avoid traumatizing the fish, your procedure further dictates that you select fish one at a time from each tank, measure the fish, and then immediately return it to the tank from which it was drawn. Your supervisor directs you to use a new procedure in which each sampled fish is returned to a different tank so that it cannot be re-sampled. You are concerned that the change in sampling will cause a difference in results. How many fish would need to be in each tank in order for the two sampling methods to be equivalent? a. At least 50 fish b. At least 500 fish c. No more than 1000 fish d. No more than 100 fish ANSWER: a 35. Suppose you want to learn how often chemistry students attending a local college visit the student fitness center on campus. You interviewed students from the chemistry department who have an athletic build. Is the sample likely to be representative of the population of interest? a. Yes, since every individual in the population has an equal chance of being selected for the sample. b. No, since only students with an athletic build visit the gym. c. No, since you did not interview students outside of the chemistry department. d. No, since not every individual in the population has an equal chance of being selected for the sample.

ANSWER: d 36. Suppose you want to know how many times per month the people of Portland go shopping. You interview 50 people.

You restrict your sampling to residents of a neighborhood adjacent to the downtown shopping district but select them randomly from residences within that district. Is your sample likely to be representative of the population of interest? a. No, since the sample size is too small. b. Yes, since every individual in the population has an equal chance of being selected into the sample. c. No, since you did not interview people from other cities. d. No, since not every individual in the population has an equal chance of being selected for the sample.

ANSWER: d

Name:

Class:

Date:

Chapter 01 - Collecting Data 37. Suppose you want to know the effect of vitamin C supplementation on the frequency and severity of seasonal colds for students living in dormitories on a particular large university campus. You use a computerized survey which is presented randomly to 50 of the 1000 dormitory residents when they log onto their computers each day. All dormitory residents have computers and all of them log onto their computers daily. Is your sample likely to be representative of the population of interest? a. No, since the sample size is too small. b. Yes, since every individual in the population has an equal chance of being selected into the sample. c. Yes, because the sample size is large. d. No, since not every individual in the population has an equal chance of being selected for the sample ANSWER: b 38. Suppose you want to know how many of the students at your elementary school prefer dark chocolate over milk chocolate. There are 88 total students at your elementary school including those in kindergarten through fifth grade. In order to assess student chocolate-type preference, you conduct a survey of twenty students randomly selected from the third, fourth, and fifth-grade classes. Is your sample likely to be representative of the population of interest? a. No, since the sample size is too small. b. Yes, since every individual in the population has an equal chance of being selected into the sample. c. Yes, because the sample size is large. d. No, since not every individual in the population has an equal chance of being selected for the sample.

ANSWER: d 39. Suppose you own a coffee shop and are considering whether to feature a peppermint or a spearmint coffee drink for the winter holidays. You would like to survey your 150 regular customers to see what they prefer. You have a database of your regular customers, so you randomly select 50 customers and offer them a free coffee in return for answering the survey. All 50 of your sampled customers respond with their mint preference. Was your sample likely to have been representative of the population of interest? a. No, since the sample size is too small. b. Yes, since every individual in the population has an equal chance of being selected into the sample. c. Yes, because the sample size is large. d. No, since not every individual in the population has an equal chance of being selected for the sample.

ANSWER: b 40. Random assignment to treatments will guarantee groups that are exactly alike for experimental purposes. a. True b. False ANSWER: True 41. Suppose you’re evaluating the effect of using duck vs. chicken eggs on the cooking time of a cake made using a standard recipe. You’ll be making four cakes with chicken eggs and four cakes with duck eggs and comparing the average of the four cooking times for each egg type. You have two different types of flour and two different sizes of cake pans.

You know that both flour type and pan size can affect cooking time. Which of the following approaches would prevent the flour type and pan size from acting as confounding variables?

I) Use one flour type to make all the chicken egg cakes and the other flour type to make all the duck egg cakes.

II) Use the larger pans to make all the duck egg cakes and the smaller pans to make all the chicken egg cakes.

III) Ensure that both flour types and pan sizes are used to make both the chicken egg cakes and the duck egg cakes. a. I only b. II only

Name:

Class:

Date:

Chapter 01 - Collecting Data c. II and III only d. III only ANSWER: d 42. You’re evaluating the effect of three different bicycle tire brands (A, B, and C) on cycling speed for an average human commuter. You measure the time required for three different cyclists to ride a fixed route. The riding time is measured six times for each tire brand. Potentially confounding variables include rider strength, wind speed, and air temperature. Which of the following approaches would reduce the confounding effects of wind and rider strength?

I) Create a sequence of 18 trials and randomly assign each tire brand to one of the 18 trials.

II) Ensure that one rider completes all six of the timed rides for each tire brand.

III) Complete all six timed rides for tire brand A, then all six timed rides for tire brand B, and then all six timed rides for tire brand C. a. I only b. II only c. I and II only d. I, II and III ANSWER: a 43. Suppose you’re evaluating the effect of compost types on the growth rate of ornamental trees in a public garden. The growth rate of the ornamental trees varies with sunlight, soil drainage, and compost quality. You have batches of 3 different types of compost and 48 ornamental trees ready for planting. You have three available planting areas, one with plentiful sunlight and well-drained soil, one with shade and well-drained soil, one with shade and poorly-drained soil, and one with shade and well-drained soil. Which of the following experimental approaches would prevent sunlight and soil drainage from confounding the effects of the compost type?

I) Use each of the 3 compost types in a different planting area II) Use all of the compost types in one of the planting areas III) Use all three compost types in all 4 planting areas a. I and II only b. I only c. II and III only d. III only ANSWER: d 44. Suppose you’re evaluating the performance of two new styles of solar panels for residential electricity generation.

You have twenty available panels of each style that you plan to use to run an experiment in which you’ll compare the amount of electricity each panel style generates over a one-month period. The amount of electricity solar panels generate depends on the direction they face (orientation) and the amount of shading they receive. You have two sites available to install your test panels, including a south-facing roof with no shading and a north-facing field with partial shading. Which of the following solar panel installation plans will prevent the effects of orientation and shading from confounding the effects of solar panel type?

I) Install both types of panels at both of the sites II) Install one type of solar panel at each of the two sites III) Install both types of panels at either one or the two sites a. I only b. II and III only c. III only d. I and III only

Name:

Class:

Date:

Chapter 01 - Collecting Data ANSWER: a 45. A placebo is identical in appearance to the treatment of interest, but contains no active ingredients. a. True b. False ANSWER: True 46. A control group provides a baseline for comparison to a treatment group. a. True b. False ANSWER: True 47. If both the subjects and the person measuring the response are aware of the assigned treatment, then single blinding is being used. a. True b. False ANSWER: False 48. You’re planning a study in which neither the subject nor the person measuring the response should be aware of the assigned treatment. Which of the following experiments should be used? a. Single-blind b. Double-blind c. Either single-blind or double-blind d. No blinding should be used ANSWER: b 49. You’re planning a study in which the person measuring the response should be aware of the assigned treatment, but the subject should not. Which of the following experiments should be used? a. Single-blind b. Double-blind c. Either single-blind or double-blind d. No blinding should be used ANSWER: a 50. You have 80 volunteer subjects whom you must assign to four treatment groups for an experiment. Of the following methods, which would permit you to make a random assignment of your subjects to treatments?

I) Assign equal numbers of men and women to each treatment group II) Assign subjects to treatment groups in the order in which they volunteered for the study III) Assign subjects by physically drawing from a container containing paper slips with a unique subject name on each slip . a. I only b. I and II only c. II only d. III only ANSWER: d

Name:

Class:

Date:

Chapter 01 - Collecting Data 51. Which of the following should be considered when using a coin toss as a random mechanism for assigning subjects to treatments?

I) The experiment has only two treatments II) The coin is not physically damaged such that it fails to act as a random mechanism III) Unequal treatment group sizes are acceptable a. I only b. I and II only c. I, II, and III d. III only ANSWER: c 52. Suppose you are assigning subjects to treatments in an experimental study. Of the following strategies, which will ensure that subjects are assigned randomly?

I) Physically draw experimental units from a container II) Use a random number generator III) Use a random mechanism such as a coin a. I and II only b. II and III only c. II only d. I, II, and III ANSWER: d 53. Suppose you planned to assign subjects to treatments by physically drawing experimental units from a container. Of the following issues, which could prevent random assignment from being achieved?

I) You fail to assign each subject a unique number II) You fail to mix the paper slips containing subject numbers well a. Both I and II b. I only c. II only d. Neither I nor II ANSWER: a 54. You have 30 subjects whom you need to randomly assign to three treatment groups. You plan to use a random number generator to randomly assign subjects to treatments. Of the following issues, which could prevent random assignment even though a random number generator is being used?

I) You fail to assign each subject a unique number II) You ignore random numbers that correspond to already-assigned subjects a. Neither I nor II b. I only c. II only d. Both I and II ANSWER: b 55. In a well-designed experiment, the factors are confounded whenever possible. a. True b. False

Name:

Class:

Date:

Chapter 01 - Collecting Data ANSWER: True 56. Random assignment of volunteers should result in comparable experimental groups. a. True b. False ANSWER: True 57. A group of physical therapists investigated the effect of home exercise on back pain reduction in females aged 45-65 years. The study recruited 100 volunteers who chose to perform either a 20-minute or a 40-minute exercise routine daily for one month and then reported the effect on their back pain using a standard scale. At the end of one month, participants who exercised for 20 minutes had a significantly higher pain reduction than those who exercised for 40 minutes. The therapists conducting the study concluded that a 20-minute exercise routine would reduce back pain for females aged 4565 years. Based on the study design, do you think that the conclusions are reasonable? a. The conclusions are reasonable because this was an experiment with a control group. b. The conclusions are not reasonable because this was not an experiment with random assignment of subjects to experimental groups. c. The conclusions are not reasonable because this was an observational study. d. The conclusions are reasonable because this was an experiment with random assignment of subjects to experimental groups.

ANSWER: b 58. Suppose you’re conducting an experiment to determine whether drinking a particular herbal tea every morning improves afternoon alertness. You recruit 50 volunteers and randomly assign 25 each to a group that drinks the herbal tea and a control group that drinks plain water. At the end of the one-month study, subjects in the herbal tea group report greater afternoon alertness compared to the control group. Based on the study design, do you think that the conclusion that the particular herbal tea improves afternoon alertness is reasonable? a. The conclusion is reasonable because this was an experiment with a control group. b. The conclusion is not reasonable because a placebo group was not included. c. The conclusion is not reasonable because this was an observational study. d. The conclusion is reasonable because this was an experiment with random assignment of subjects to experimental groups.

ANSWER: b 59. A group of dieticians conducted a study to determine whether grapefruit juice or cranberry juice was more effective for preventing seasonal flu. The dieticians randomly sampled 200 people from their local community and asked if they would like to participate in a study about the benefits of juice for flu prevention. The participants were randomly assigned to three treatment groups. In the first group, participants were asked to drink three glasses of grapefruit juice per day, in the second group participants were asked to drink three glasses of cranberry juice per day, and in the third group, participants were asked to avoid both grapefruit and cranberry juice. The study ran for three months corresponding to the flu season in the area. At the end of the study, subjects reported the frequency with which they contracted the flu. There were no significant differences between the cranberry juice group and the grapefruit juice group, and neither was there any difference between either juice group and the no-juice group. Based on these results, the dieticians concluded that neither grapefruit juice nor cranberry juice was effective in preventing seasonal flu. Do you think this conclusion is reasonable? a. The conclusion is not reasonable because this was an observational study. b. The conclusion is reasonable because a placebo group was included. c. The conclusion is reasonable because this was an experiment with random assignment of subjects to

Name:

Class:

Date:

Chapter 01 - Collecting Data experimental groups. d. The conclusion is not reasonable because the study did not include a control group.

ANSWER: c 60. One hundred and fifty people who live in a large city in the United States volunteered to participate in a statistical study. The volunteers were divided into two groups, with people who had children in group 1 and people without children in group 2. Those in group 1 were asked to eat a lemon slice daily for five months. Those in group 2 were asked not to eat lemon for five months. At the end of the study, it was found that on average, people in group 1 were sick less often than those in group 2. Did the study use a random selection process from some populations? Did the study use random assignment to experimental groups? a. The study used both random selection and random assignment. b. The study used neither random selection nor random assignment. c. The study used random selection but did not use random assignment. d. The study used random assignment but did not use random selection.

ANSWER: b 61. You’re a math educational researcher interested in the effectiveness of a new undergraduate math curriculum on the graduation rates of engineering students worldwide. You conduct a study in which you recruit volunteers from five elite universities in the United States. You assign your female volunteers to a group that uses the new math curriculum and your male volunteers to a group that uses a traditional math curriculum. At the end of the study, you find no effect of the new math curriculum on graduation rates. Did the study use a random selection process from the population of interest?

Did the study use random assignment to experimental groups? a. The study used random assignment but did not use random selection. b. The study used random selection but did not use random assignment. c. The study used neither random selection nor random assignment. d. The study used both random selection and random assignment.

ANSWER: c 62. Five hundred randomly selected Seattle residents participated in a survey to assess the effects of daily exercise on the severity of seasonal depression resulting from reduced daylight hours during the winter months. The participants completed a survey asking if they engaged in daily exercise as well as the frequency with which they experienced depression during the months of November, December, and January compared to the other nine months of the year. Part of the introductory survey information included references to prior studies which concluded that frequent exercise was very effective for reducing seasonal depression. Could the study result be used to draw conclusions regarding the effects of daily exercise on seasonal depression in the general population? a. Yes, because the study included participants from an area that experiences seasonally reduced daylight hours. b. Yes, because study participants were randomly selected. c. No, because the study did not include participants from areas that do not experience seasonally reduced daylight hours. d. No, because the survey’s introductory information could influence the participants’ responses.

ANSWER: d 63. Coaches for a college track team conducted a study regarding the effectiveness of barefoot training for injury prevention in college track athletes. Surveys were sent to 50 male freshman track athletes randomly selected from ten major universities at the end of their first competitive season asking them to report the footwear (or lack thereof) they used for training as well as the number of lower body injuries they sustained during both training and competition. The survey results showed that the use of shoes during training and competition significantly increased the incidence of lower

Name:

Class:

Date:

Chapter 01 - Collecting Data body injuries among the study participants. Can the results of this study be used to conclude that barefoot training is effective for preventing injury in the population of college track athletes? a. No, because the sample size was too small. b. Yes, because participants were randomly selected. c. No, since not every individual in the population had an equal chance of being selected for the sample. d. Yes, because the study was observational.

ANSWER: c 64. You’re a pain management specialist interested in the effect of a new treatment on back pain reduction in males aged 40-60 years. You conduct a study in which you recruit 100 men between the ages of 40 and 60 years, all of whom are of normal weight. The men aged 40 to 50 years receive the new treatment, while the men aged 50 to 60 years do not receive the treatment. At the end of the study, you ask all the study participants to assess their back pain. You find that the group that received the treatment had a significantly greater back pain reduction than the group that did not receive the treatment. Did the study use a random selection process from the population of males aged 40-60 years? Did the study use random assignment to experimental groups? a. The study used both random selection and random assignment. b. The study used neither random selection nor random assignment. c. The study used random selection but did not use random assignment. d. The study used random assignment but did not use random selection.

ANSWER: b 65. Two hundred people who live in San Francisco volunteered to participate in a statistical study. The volunteers were divided into two groups by age, with people under 40 years of age in group 1 and people 40 years of age and older in group 2. Those in group 1 were asked to participate in sports once a day for 1 month. Those in group 2 were asked to abstain from participating in sports for 1 month. At the end of the month, progress in weight reduction was significantly higher for group 1 than for group 2. From the resulting data, the researchers concluded that daily sports exercises would help every San Francisco resident lose weight faster. Based on the study design, do you think that the conclusions are reasonable? a. The conclusions are reasonable because the study was an experiment. b. The conclusions are not reasonable because this was not an experiment with random assignment of subjects to experimental groups. c. The conclusions are not reasonable because this was an observational study. d. The conclusions are reasonable because this was an experiment with random assignment of subjects to experimental groups.

ANSWER: b 66. In August 1994, wildlife biologists compared daytime and nighttime counts of wild brook trout, brown trout, and rainbow trout by the same snorkelers in five streams. Overall, the snorkelers counted 109 trout in the daytime and 333 trout at night. From these counts, biologists concluded that trout migrated to deep portions of the stream during the daytime. Based on the study design, do you think that this conclusion is correct? a. The conclusions are reasonable because the study was an experiment. b. The conclusions are not reasonable because this was not an experiment with random assignment of subjects to experimental groups. c. The conclusions are not reasonable because this was an observational study. d. The conclusions are reasonable because this was an experiment with random assignment of subjects to experimental groups.

ANSWER: c

Name:

Class:

Date:

Chapter 01 - Collecting Data 67. A group of psychology students conducted a study to determine whether wearing brightly colored shirts to class improved scores on graded in-class exercises. They randomly selected 100 students to participate in the study and allowed each participant to choose whether to wear a neutral-colored shirt or brightly colored shirt to class during a week in which several graded in-class exercises were conducted. The results showed no significant differences in the grades for the neutral vs. brightly colored shirt groups. The students conclude that wearing bright shirt colors to class does not improve assignment scores. Based on the study design, do you think that this conclusion is reasonable? a. The conclusions are reasonable because the study was an experiment. b. The conclusions are not reasonable because this was not an experiment with random assignment of subjects to experimental groups. c. The conclusions are not reasonable because this was an observational study. d. The conclusions are reasonable because this was an experiment with a random selection of study participants.

ANSWER: b 68. Suppose you’re interested in determining if a particular medical treatment is effective in reducing knee pain in women aged 50 years and over with a confirmed diagnosis of kneecap arthritis. Your study participants consisted of 500 volunteers, all of whom are women aged 50 years or older, regularly attend supervised knee exercise training classes, and have confirmed diagnoses of kneecap arthritis. You randomly assign 250 of your selected subjects into two groups including a group that receives the medical treatment and a group that does not. After the treatments have been completed, you assess the 500 study participants to determine whether or not their knee pain has changed. You find that the group which received the treatment showed a significant reduction in knee pain vs. the group which did not receive the treatment. Which of the following can you conclude? a. The medical treatment was effective in reducing knee pain in the study participants. b. The medical treatment is effective for reducing knee pain in women aged 50 years and over with kneecap arthritis. c. It is not possible to conclude whether or not the medical treatment had an effect on kneecap arthritis pain. d. It is not possible to conclude whether the medical treatment had an effect on kneecap arthritis pain in the study participants.

ANSWER: a 69. Suppose you are a physician interested in the effect of diet on arthritis pain in women over the age of 60 years. You conduct a study in which 500 women from your local area over 60 years of age with arthritis volunteer to participate. You randomly assign the volunteers to two groups. Each group is given a different diet they are asked to follow for six months. At the end of the study, the participants are asked to report the severity of their arthritis pain compared to their pain prior to starting the study. Participants following one of the two diets report a significant reduction in their arthritis pain while participants following the other diet report no reduction in their arthritis pain. From the study results, you can conclude that diet reduced arthritis pain in the study participants but you cannot conclude whether diet reduces arthritis pain in women over 60 years of age. Based on the study design, do you think these conclusions are reasonable? a. The conclusions are reasonable because the study was an observation with random selection of study participants. b. The conclusions are reasonable because the study was an experiment which included random selection of subjects and random assignment of subjects to experimental conditions. c. The conclusions are reasonable because the study was an experiment which did not include random selection of subjects, but did include random assignment of subjects to experimental conditions. d. The conclusions are not reasonable because the study was an observation without random selection of study participants.

ANSWER: c

Name:

Chapter 01 - Collecting Data

Class:

Date:

Name:

Class:

Date:

Chapter 02 - Graphical Methods 1. Your laboratory procedure asks you to record the following information about each sample you analyze: I) Sample weight in grams II) Name of the customer who submitted the sample III) Age of the customer who submitted the sample IV) Sample temperature at the time of submission Which of these represents numerical data? a. I only b. I and II only c. I and III only d. I, III, and IV only ANSWER: d 2. A survey form regarding preferred breakfast food choices solicits the following responses: I) Preferred hot beverage (coffee, tea, or cocoa) II) Preferred entrée (omelet, pancakes, or sausages) III) Amount of hot beverage consumed (cups) IV) Age of the respondent Which of these represents categorical data? a. IV only b. I and II only c. II and III only d. II and IV only ANSWER: b 3. You are a wildlife biologist planning to gather field data on a rare bird species. For each study location, you will record the following data: I) Prevalent vegetation (pine forest, grassland, or deciduous forest) II) Distance in miles from the nearest city III) Elevation above mean sea level in feet IV) Maximum daytime temperature in degrees Fahrenheit Which of the following accurately describes your data? a. I and II are categorical, while III and IV are numerical b. I, III, and IV are categorical, while II is numerical c. I is categorical, while II, III, and IV are numerical d. I and IV are categorical, while II and III are numerical ANSWER: c 4. You are creating a survey to assess the political involvement of students at your university. Your survey questions ask respondents for the following: I) What is your age?

II) What is your residence location (on-campus vs. off-campus)?

III) What is your political party?

IV) How many elections have you voted in over your lifetime?

Which of the following accurately describes the data you are gathering? a. I and IV are numerical, while II and III are categorical b. II and III are numerical, while I and IV are categorical c. I II, and III are numerical, while IV is categorical

Name:

Class:

Date:

Chapter 02 - Graphical Methods d. IV is numerical, while I, II, and III are categorical ANSWER: a 5. A consumer information survey form solicits the following responses: I) Age of the respondent II) Gender of the respondent III) Level of job satisfaction (satisfied, somewhat satisfied, dissatisfied) IV) Annual income Which of the responses represents categorical data? a. I only b. II only c. III only d. II and III only ANSWER: d 6. The following variables are commonly used to describe human appearance: I) Eye color (blue, green, brown, grey) II) Hair color (brown, black, blond, grey) III) Hair length IV) Waist circumference Which of these variables are categorical? a. I only b. II only c. II and III only d. I and II only ANSWER: d 7. A data set is discrete if the possible values are isolated points on the number line. a. True b. False ANSWER: True 8. You are gathering data on the sales of packaged hard candies sold in a hotel gift shop. Your variables of interest include: I) The type of container in which the candies are packaged (glass jar, cardboard box, or plastic bag) II) The weight of the container III) The number of candies in the container IV) The height above the floor at which the candy-filled container was displayed Which of the variables of interest are numerical and discrete? a. I only b. II only c. III only d. II and III only ANSWER: c 9. In a psychological study of distance perception, introductory psychology class volunteers were given 5, 10, or 15 extra credit points depending on their level of participation in the experiment. The volunteers walked along paths laid out along

Name:

Class:

Date:

Chapter 02 - Graphical Methods hallways in the psychology building and were asked to judge the distance they had walked. Each path distance was between 100 and 200 feet in length and contained from two to seven 90-degree turns. The investigators also kept track of class standing (freshman, sophomore, junior, or senior). For each of the variables in this study, determine whether it is categorical or numerical. If the variable is numerical, determine whether it is continuous or discrete. a) the true length of the path b) the amount of extra credit given to the volunteers c) the length of the path as judged by the students d) the number of 90-degree turns e) the class standing of the volunteers ANSWER: a) numerical, continuous; b) numerical, discrete; c) numerical, continuous; d) numerical, discrete; e) categorical 10. Which of the following variables are discrete?

I) The volume of liquid in a 16-ounce bottle of soda pop II) The percentage of males aged 18-25 years who participate in a contact sport III) The number of broken eggs in a package of a dozen eggs IV) A count of the statistics majors at a certain university a. II only b. II and III only c. III and IV only d. I only ANSWER: c 11. In a study of how college students give directions from maps, 40 volunteers from an Introductory Psychology class, including 20 sophomores and 20 juniors, were given the task of giving directions to another person. Observations were made of the subjects’ direction-giving behavior in the experiment including: a) Whether the subject referred to the map or gave directions from memory b) Whether the direction-giver was a sophomore or a junior c) Whether distances were given as part of the directions d) The number of times compass orientation (north, south, east, west) was used e) The frequency of errors in the directions given For each of the variables in this experiment, determine whether it is categorical or numerical. If the variable is numerical, determine whether it is continuous or discrete. Variables include: (a) Were directions given from memory or with reference to a map? (b) Class of direction giver (sophomore vs. junior) (c) Distances given as part of directions (d) Number of times compass directions were used (e) Frequency of errors in the directions ANSWER: (a) categorical; (b) categorical; (c) numerical, continuous; (d) numerical, discrete; (e)numerical, discrete 12. Which of the following graphical displays would permit you to compare the behavior of a single variable for categorical data from two different groups?

I) Bar Chart II) Comparative Bar Chart III) Comparative Dot Plot a. I only b. II only c. I and II only d. III only

Name:

Class:

Date:

Chapter 02 - Graphical Methods ANSWER: b 13. Which of the following graphical displays would permit you to display the distribution of categorical data for one variable from a single group?

I) Bar Chart II) Stem-and-Leaf Display III) Dotplot IV) Histogram a. I only b. I, II, and III only c. III and IV only d. III only ANSWER: a 14. Which of the following graphical displays would permit you to display the distribution of numerical data for one variable from a single group?

I) Dotplot II) Stem-and-Leaf Display III) Histogram IV) Scatterplot a. I and IV only b. II and III only c. I, II, and IV only d. I, II, and III only ANSWER: d 15. Which of the following displays would permit you to see the relationship between two variables? a. Scatterplot b. Time Series Plot c. Comparative Dotplot d. Comparative Stem-and-Leaf Display ANSWER: a 16. Bar charts should be used with categorial data. a. True b. False ANSWER: True 17. Which of the following data displays would permit you to compare the behavior of two different groups for single variable representing numerical data?

I) Comparative Dotplot II) Comparative Stem-and-Leaf Display III) Comparative Bar Chart IV) Scatterplot a. I and II only b. II and III only

Name:

Class:

Date:

Chapter 02 - Graphical Methods c. IV only d. I and III only ANSWER: a 18. Which of the following displays is best for displaying trends over time for numerical data from a single variable? a. Scatterplot b. Time Series Plot c. Histogram d. Dotplot ANSWER: b 19. The tourism board of a resort location conducted a survey of visiting tourists to determine which of four local restaurants served the best dessert. The results from the survey are summarized in the Table below.

Restaurant # Respondents Restaurant A 25 Restaurant B 207 Restaurant C 363 Restaurant D 159 Which of the following graphical displays could you use to display the distribution of tourists who thought each restaurant served the best dessert? a. Bar Chart b. Dotplot c. Stem-and-Leaf Display d. Comparative Bar Chart ANSWER: a 20. A regional restaurant guide surveyed residents to determine which of their community’s restaurants served the best desserts. The survey included 55 people aged 20-30 years and 58 people aged 40-50 years. The survey results are shown in the table below.

Restaurant % Respondents Aged 20% Respondents Aged 4030 Years 50 Years Restaurant A 10 42 Restaurant B 33 22 Restaurant C 20 21 Restaurant D 37 15 Which of the following graphical displays could you use to compare the restaurant dessert preferences for the 20–30-yearold vs. 40–50-year-old groups? a. Comparative Bar Chart b. Comparative Dotplot c. Comparative Stem-and-Leaf Display d. Scatterplot ANSWER: a 21. Suppose you conduct a survey of your colleagues at work to assess their transportation preferences. You ask each survey participant to estimate the number of miles they travel on foot and by car, respectively, each day. The results of your survey are shown in the Table below.

Name:

Class:

Date:

Chapter 02 - Graphical Methods Participant Miles On Foot Miles By Car Colleague 1 0 42 Colleague 2 1.5 12 Colleague 3 6.8 0 Colleague 4 2.1 44 Colleague 5 4.3 89 Colleague 6 0.5 37 Colleague 7 0.6 42 If you wanted to display the distribution of miles traveled on foot, which of the following graphical displays could you use? a. Stem-and-Leaf Display b. Comparative Dotplot c. Comparative Stem-and-Leaf Display d. Scatterplot ANSWER: a 22. Suppose you conduct a survey of your neighbors to assess how often they walk for transportation. You are particularly interested in age-dependent differences in transportation preferences. The results of your survey are shown in the Table below.

15-30 years 50-75 years participant Miles Walked Participant Miles Walked Neighbor #1 0 Neighbor #8 6.6 Neighbor #2 1.2 Neighbor #9 3.1 Neighbor #3 1.8 Neighbor #10 1.2 Neighbor #4 2.2 Neighbor #11 0.8 Neighbor #5 0.5 Neighbor #12 4.7 Neighbor #6 0.3 Neighbor #13 5.1 Neighbor #7 0.9 Neighbor #14 6.3 If you wanted to compare the miles walked by the 15–30-year-olds vs. the 50–75-year-olds in your neighborhood, which display could you use?

I) Histogram II) Comparative Dotplot III) Comparative Bar Chart IV) Comparative Stem-and-Leaf Display a. I only b. I and III only c. I, II, and III only d. I, II, and IV ANSWER: d 23. A local bird-watching club gathers field data on the number of different bird species sighted in their study area. The Table below gives the number of species sighted in the study area as a function of the day of the study. # Bird Species Day of the Study 2 1 6 2 7 3 7 4

Name:

Class:

Date:

Chapter 02 - Graphical Methods 4 5 2 6 2 7 Which of the following graphical displays would work best to show the trend in the number of bird species as a function of time from the start of the study? a. Histogram b. Dotplot c. Time Series Plot d. Bar Chart ANSWER: c 24. You conducted a field study in which you measured water clarity at several locations at a particular beach. You have the geographical coordinates of each measurement location, so you can easily determine the distance from each measurement location to any address near the beach. You suspect that one of the beach hotels is discharging sewage to the ocean, thereby worsening water clarity with sewage solids suspended in the water. Which of the following graphical displays would help show the relationship between water clarity in percent sewage solids and distance from the suspect hotel? a. Histogram b. Dotplot c. Stem-and-Leaf Display d. Scatterplot ANSWER: d 25. The Table below shows the results of a survey of preferred desserts for passengers on a cruise ship. What is the relative frequency for chocolate fondue?

Dessert Butterscotch Sundae Cheesecake Pound Cake Chocolate Fondue Vanilla Crème

Counts 100 281 332 460 580

a. 26.2% b. 18.9% c. 33.1% d. 16.0% ANSWER: a 26. Frequency distributions cannot be used with categorical data. a. True b. False ANSWER: False 27. The relative frequency of a particular category is the number of times the category appears in the data. a. True b. False

Name:

Class:

Date:

Chapter 02 - Graphical Methods ANSWER: False 28. The relative frequency distribution displayed in the Table below summarizes student responses to the question “If you could make your college choice over, would you still choose to enroll at your current college?”

Response Relative Frequency Definitely yes 0.45 Probably yes 0.33 Probably no 0.13 Definitely no 0.09 Which of the following graphical displays is the correct bar chart for the response data? a.

b.

Name:

Class:

Date:

Chapter 02 - Graphical Methods c.

d.

ANSWER: d 29. A survey asked adult respondents how dependent they were on various electronic devices. The table below summarizes the responses.

Relative Frequency Response Personal Computer Cell Phone DVD Player Cannot imagine living 0.25 0.42 0.15 without Would miss, but could do 0.45 0.20 0.35 without 0.30 0.38 0.50 Could definitely live without Which of the following comparative bar charts displays the distribution of responses for the three electronic devices?

Name:

Chapter 02 - Graphical Methods a.

b.

c.

d.

ANSWER: b

Class:

Date:

Name:

Class:

Date:

Chapter 02 - Graphical Methods 30. Artificial nests have often been used when biologists study predation on birds. It is usually assumed that predators will respond to artificial nests in the same way they do to real birds’ nests. A recent experiment was performed to check this assumption for predators of the American robin by comparing the egg loss in three experimental treatments: (1) natural robin’s nests, (2) artificial wicker basket nests placed 30 meters in random directions from natural robin’s nests, and (3) artificial wicker-basket nests placed in a 180 m by 240 m grid around robin’s nests. The data in the Table below are the number of eggs predated (stolen or broken and eaten) within the following time intervals throughout the experiment: start of the experiment to the day-5 check, from the 5-day check to the 10-day check, and from the 10-day check to the 15-day check.

Total Number of Eggs Predated Nest Type Day 5 Check Day 10 Check Day 15 Check Natural robin nest 12 17 19 Wicker basket 30 meter from natural nest 3 12 18 Wicker basket in grid around natural nest 7 32 44 (a) Construct a bar chart to display the total number of predated eggs for the natural robin nests at their 5-, 10-, and 15-day checks. (b) Fill in the relative frequency distribution table representing the total number of predated for the natural robin nests, artificial nests in the 30-meter radius, and the artificial nests in the grid.

Nest Type Start to Day 5 Day 5 Check to Day 10 Check to Check Day 10 Check Day 15 Check Natural robin nest Wicker basket 30 meter from natural nest Wicker basket in grid around natural nest ANSWER: (a)

(b) Nest Type Natural robin nest Wicker basket 30 meter from natural nest Wicker basket in grid around natural nest

Start to Day 5 Check 0.250 0.091 0.084

Day 5 Check to Day 10 Check 0.354 0.364 0.386

Day 10 Check to Day 15 Check 0.396 0.545 0.530

31. Collisions between birds and airplanes are a major problem, threatening passenger safety and bird species viability.

During the years 1990-1994, researchers gathered bird remains from runways at Lihue Airport on the island of Kauai, Hawaii. The data in the Table below are counts of birds found on the runway used for takeoffs and the runway used for landings from the 4 most frequently involved bird species.

Species Takeoff Landing Zebra dove 49 68 Mannikin spp.

33 82

Name:

Class:

Date:

Chapter 02 - Graphical Methods Plover 29 51 Barn-owl 6 39 (a) Construct a bar chart to display the bird species data for the landing runway. (b) Construct a relative frequency distribution table representing the bird species for both the landing and takeoff runways.

ANSWER: (a)

(b)

Species Zebra dove Mannikin spp.

Plover Barn-owl

Relative Frequency Takeoff 0.4188 0.2821 0.2479 0.0513

Relative Frequency Landing 0.2833 0.3417 0.2125 0.1625

32. A statewide survey released by the University of Iowa Injury Prevention Research Center was designed to assess compliance with Iowa seatbelt law. The Table below shows the results for 5 Iowa cities.

City % Age 2-5 properly restrained % Age 6-10 properly restrained Belle Plaine 84 93 Cedar Rapids 79 94 Guttenberg 58 68 Iowa City 92 99 Manchester 59 82 (a) Do the values in the Table represent total counts or relative frequency?Would total counts or relative frequency allow for easier comparison between data groups in a bar chart, why? (b) Display these data in a comparative bar chart so that the different ages can be compared for the different cities.

ANSWER: (a) The values in the Table represent relative frequency. The use of relative frequency is preferred for the construction of comparative bar charts since it ensures a uniform y-scale for all groups being compared.

Name:

Class:

Date:

Chapter 02 - Graphical Methods

(b)

33. In an international survey of adults summarized in the Reuters Institute Digital News Report 2020, each person was asked whether they prefer to get their news from sources that share their point of view, have no point of view, or challenge their point of view. Each survey respondent was classified by age into one of five groups (18-24 years, 25-34 years, 35-44 years, 45-54 years, and 55+ years). The resulting data were used to construct the comparative bar chart shown below.

Based on the data displayed in the comparative bar chart, which of the following trends do we see in news source preference of the 35-44, 45-54, and 55+ age groups?

I) Increasing preference for “No point of view” with increasing age II) Increasing preference for “Share point of view” with increasing age III) Decreasing preference for “No point of view” a. I only b. II only c. II and III only d. I and II only ANSWER: a

Name:

Class:

Date:

Chapter 02 - Graphical Methods 34. In an international survey of adults summarized in the Reuters Institute Digital News Report 2020, each person was asked whether they prefer to get their news from sources that share their point of view, have no point of view, or challenge their point of view. Each survey respondent was classified by age into one of five groups (18-24 years, 25-34 years, 35-44 years, 45-54 years, and 55+ years). The resulting data were used to construct the comparative bar chart shown below.

Based on the data in the bar chart above, which of the following interpretations can be made?

I) In every age group, a “No point of view” source was the most popular way to get news.

II) In every age group, a “Challenge point of view” was the least popular way to get news.

III) The “Challenge point of view” becomes less popular with increasing age of respondents. a. I and II only b. II and III only c. I and III only d. I, II, and III ANSWER: d 35. A statewide survey released by the University of Iowa Injury Prevention Research Center was designed to assess compliance with Iowa seatbelt law. The survey results are summarized in the bar chart below.

Name:

Class:

Date:

Chapter 02 - Graphical Methods Which of the following patterns are displayed in the bar chart?

I) Lower levels of compliance for the 2–5-year age group compared to the 6-10 year age group for all cities II) Lower levels of compliance for cities “G” and “M” compared to cities “BP”, “CR”, and “IC” III) Consistent levels of compliance for the 6-10-year age group for cities “G”, “IC”, and “M” IV) Consistent levels of compliance for the 6-10-year age group for cities “BP” and “CR” a. I only b. II only c. III and IV only d. I, II, and IV only ANSWER: d 36. The most important right and responsibility of citizens in a democratic society is voting. The bar chart below shows, for different age groups in the 2000 United States presidential election, the percentage of individuals in that age group who were registered to vote.

(a) Describe in a few sentences the registration pattern shown in the data above. (b) One argument for the low level of registration in the 18-24-year-old group is that many of them were college students and would have had to vote absentee. Does the need to vote via absentee ballot explain the voter registration level for the 18-24 year age group? Why or why not?

ANSWER: (a) The percentage of people registered to vote is the smallest for the 18-24-year-old group.The percentage rises steadily with age through the 65-74-year-old group, then declines in the over 75-year-old group. (b) While voting by absentee ballot could be seen as more difficult due to the need to request a ballot, the need for absentee voting does not explain the lack of registration, which can be done by a college student at home prior to or following their stay at the university.

37. One interesting aspect of surveys is that the order of the questions can affect the results. This is thought to occur because one question can alter the response to a subsequent question. In 1948 many people in the United States were concerned about the spread of communism as a political and economic philosophy. A survey given that year contained both of the following questions: Question 1: Do you think the United States should let Communist newspaper reporters from other countries come in here and send back to their papers the news as they see it?

Question 2: Do you think a Communist country like Russia should let American newspaper reporters come in and send back to America the news as they see it?

The following bar chart contains the percentages of Yes/No answers given by respondents when asked these questions in different orders.

Name:

Class:

Date:

Chapter 02 - Graphical Methods

Interpret the results of the 1948 survey. Do you think that the order of the questions made a difference in the responses?

Explain.

ANSWER: Yes, the order made a difference. The rate of “Yes” responses to Question 1 was nearly doubled if it was asked after the question about American reporters in Russia.

38. In an international survey of adults summarized in the Reuters Institute Digital News Report 2020, each person was asked whether they prefer to get their news from sources that share their point of view, have no point of view, or challenge their point of view. Each survey respondent was classified by age into one of five groups (18-24 years, 25-34 years, 35-44 years, 45-54 years, and 55+ years). The resulting data were used to construct the comparative bar chart shown below.

Based on the data displayed in the comparative bar chart, which of the following trends do we see in news source preference of the two youngest age groups?

I) Increasing preference for “share point of view” with increasing age II) Decreasing preference for “challenge point of view” with increasing age III) Similar preference for “no point of view” for both age groups a. I and III only b. II only c. I and II only d. I, II, and III ANSWER: d 39. Dotplots work best when the data set is not too large.

Name:

Class:

Date:

Chapter 02 - Graphical Methods a. True b. False ANSWER: True 40. Which of the following are characteristics of dotplots?

I. II. III. IV.

The horizontal axis corresponds to the numerical value for the variable of interest Each observation is represented by a dot above the location on the horizontal axis corresponding to its value Includes a dot for every observation in the data set If two or more observations share the same value, the dots are stacked corresponding to each observation vertically.

a. I, II, and III only b. II, III, and IV only c. III and IV only d. I, II, III, and IV ANSWER: d 41. The density of a histogram class interval can be calculated by dividing the relative frequency of the class interval by the class interval width. a. True b. False ANSWER: True 42. Biologists know that bats have different flight characteristics. Some bats exhibit fast, straight, and long flights; while others are moderately slow and highly maneuverable. The flight capabilities of bats are presumably a function of (a) the characteristics of the bat wings, and (b) the laws of physics. The data presented below are wing weights in grams for certain species of bats from Nicaragua and Costa Rica categorized by the bats’ diet of fruit vs. insects.

Fruit-eaters: 9.9, 11.5, 47.0, 59.6, 18.2, 22.1, 22.9, 15.0, 15.4, 13.3, 38.3, 42.2, 114.3, 105.4, 80.9 Insect-eaters: 23.8, 16.1, 4.2, 3.9, 7.5, 3.5, 3.9 Construct a comparative dotplot that will allow you to compare the distributions of wing weights for the fruit-eating bats vs. the insect-eating bats.

ANSWER: a) Fruit-eaters Wing-Weight

b) Insect-eaters Wing-Weight

43. Biologists know that bats have different flight characteristics. Some bats exhibit fast, straight, and long flights, while

Name:

Class:

Date:

Chapter 02 - Graphical Methods others are moderately slow and highly maneuverable. The flight capabilities of bats are presumably a function of (a) the characteristics of the bat wings, and (b) the laws of physics. The data presented below are wing spans in centimeters for certain species of bats from Nicaragua and Costa Rica categorized by the bats’ diet of fruit vs. insects: Fruit-eaters: 25.2, 27.2, 42.0, 44.8, 31.3, 32.5, 32.0, 28.1, 30.7, 27.0, 41.1, 41.6, 58.4, 58.7, 53.9 Insect-eaters: 32.8, 27.4, 21.0, 23.9, 27.5, 22.4, 18.7 Construct a comparative dot plot that will allow you to compare the distributions of wing spans for the fruit-eating bats vs. the insect-eating bats.

ANSWER: a) Fruit-eaters wingspan

b) Insect-eaters wingspan

44. For stem and leaf plots with single-digit leaves, commas must be used to separate the leaves. a. True b. False ANSWER: False 45. Which of the following are the steps in constructing a stem-and-leaf display?

I) Determine the number of leading digits in your data to use for stem values.

II) List all stem values in a vertical column in increasing order from the stem associated with the smallest data value to the stem associated with the largest data value.

III) Record the leaf for every observation beside the corresponding stem value in ascending order of value from left to right IV) In cases where leaf values include two or more digits, separate the leaf values with commas a. I, II, and III only b. I, II, III, and IV c. I and IV only d. II and III only ANSWER: b 46. An experiment was performed to determine which brand of comparably priced light bulbs, A or B, lasted longer on average. Ten bulbs of each brand were tested, and their lifetimes in hours were recorded. The data are shown below.

Bulb A: 88, 97, 110, 122, 128, 129, 135, 141, 150, 165 Bulb B: 23, 55, 93, 106, 111, 115, 123, 128, 153, 171 Display these data using a comparative (back-to-back) stem-and-leaf display.

ANSWER: Bulb A (hrs) Bulb B (hrs)

Name:

Class:

Date:

Chapter 02 - Graphical Methods

8 7 0 982 5 1 0 5

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Stem: tens Leaf: one

3 6 15 38 3 1

47. One advantage of histograms is that they may be used for large data sets. a. True b. False ANSWER: True 48. In a story written in December 2022, the Des Moines Register reported on the average number of years of teaching experience for elementary schools in Des Moines, Iowa. The data, by elementary school, appears in the table below.

Years School Experience Adams 13.8 Capitol View 9.7 Cattell 8.5 Douglas 13.8 Downtown 7.0 Edmunds 8.4 Findley 14.9 Garton 9.3 Granger 17.2 Greenwood 14

School Hanawalt Hillis Howe Hubbell Jackson Jefferson King Longfellow Lovejoy Madison

Years Experience 12.7 17 14.9 15.1 16.8 19.2 7.0 9.8 9.9 20.8

Years School Experience McKee 17.5 McKinley 5.6 Mitchell 6.2 Monroe 16.2 Moore 16.6 Morris 9.9 Moulton 8.6 Oak Park 11.4 Park Avenue 11.4 Perkins 11.2

Years School Experience Phillips 10.5 Pleasant Hill 12.8 River Woods 5.9 Stowe 16.5 Studebaker 18.4 Wallace 4.8 Willard 9.7 Windson 17.7 Woodlawn 17 Wright 12.9

Construct a histogram for these data, using the following class intervals: 0 to <4,4 to <8, etc.

ANSWER:

Name:

Class:

Date:

Chapter 02 - Graphical Methods 49. The quantity

is sometimes used as an estimate of the appropriate number of intervals in a

histogram. a. True b. False ANSWER: True 50. According to the stem-and-leaf display below, how many times does the number 58 appear in the data set?

a. 0 b. 1 c. 2 d. 5 ANSWER: c 51. The histogram below displays the average number of years of teaching experience for elementary schools in Des Moines, Iowa.

Which of the following conclusions could you draw from the data distribution in the histogram? a. The typical value for the average number of teaching years is between 4 and 8 years b. Relatively few schools have more than 20 average years of teaching experience c. The range for the average number of teaching years is no more than 8 years to 24 years. d. The range for the average number of teaching years is 8 years to 20 years.

ANSWER: b 52. In a story written in December 2002, the Des Moines Register reported on the percentages of students who qualify for Free/Reduced (% F/R) lunch programs in elementary schools in Des Moines, Iowa. The data, by elementary school, is shown in the Table below: School

% F/R

School

% F/R

School

% F/R

School

% F/R

Name:

Class:

Date:

Chapter 02 - Graphical Methods Adams Capitol View Cattell Douglas Downtown Edmunds Findley Garton Granger Greenwood

64 78 55 45 8 83 64 53 52 38

Hanawalt Hillis Howe Hubbell Jackson Jefferson King Longfellow Lovejoy Madison

14 35 49 31 60 5 71 84 66 58

McKee McKinley Mitchell Monroe Moore Morris Moulton Oak Park Park Avenue Perkins

55 78 64 52 42 54 88 59 38 54

Phillips Pleasant Hill River Woods Stowe Studebaker Wallace Willard Windson Woodlawn Wright

27 17 48 56 30 80 82 37 40 29

(a) Construct a histogram for these data using the class intervals 0 to < 20, 20 to < 40, etc. (b) From your histogram, what is the typical value for the percent of students qualifying for free/reduced lunch at any given elementary school?

ANSWER:

(a)

(b) The typical value is given by the center of the distribution, which is 40-60%.

53. The annual household incomes, in thousands of dollars, for 150 households in a small community are summarized in the histogram below.

What proportion of households has annual incomes of $90,000 or more? a. 0.85 b. 0.67 c. 0.23 d. 0.15 ANSWER: d 54. The annual household incomes, in thousands of dollars, for 500 households in a small community are summarized in the histogram below.

Name:

Class:

Date:

Chapter 02 - Graphical Methods

Which of the following values best describes a typical household income for this community? a. $20,000 b. $40,000 c. $60,000 d. $80,000 ANSWER: c 55. The frequency distribution shown below summarizes data on the percentage of college students enrolled in public institutions for the 50 U.S. states.

Percentage Enrolled 40 to < 50 50 to < 60 60 to < 70 70 to < 80 80 to < 90 90 to < 100

Frequency 1 5 2 11 25 6

What is the relative frequency for the 70 to <80 percent interval? a. 0.05 b. 0.10 c. 0.22 d. 11 ANSWER: c 56. An outlier is an unusually small or large data value. a. True b. False ANSWER: True 57. Which of the following stem and leaf plots corresponds to a positively (right) skewed data distribution?

Name:

Class:

Date:

Chapter 02 - Graphical Methods

I.

II.

III.

a. II only b. I and III only c. I, II, and III d. III only ANSWER: a 58. If the upper tail of the distribution stretches out farther than the lower tail, the distribution is negatively (left) skewed. a. True b. False ANSWER: False 59. Ruminants are hoofed animals such as cattle and sheep. Some biologists believe that the curvature of the incisor arcade, that part of the mouth between incisors, is shaped differently depending on the type of food the ruminant eats.

The stem-and-leaf display below shows the distribution of incisor arcade curvature for a group of sheep known to graze on two distinctly different food types. The biologists who support the hypothesis that incisor arcade curvature is determined by ruminant diet anticipated a bimodal data distribution reflecting the adaptation of the sheep to the two different available foods.

1L 1H 2L 3L

| |9 |1 | 22244

Name:

Class:

Date:

Chapter 02 - Graphical Methods

3H 4L 4H 5L 5H 6L 6H 7L 7H

| 55566667778999999 | 022223 | 55556666677778889 | 03 |9 |0 | | |

(a) Briefly describe the shape of the data distribution in the stem-and-leaf display and note any unusual features such as skewness and the presence of outliers. (b) Does the data distribution support the biologist’s expectation of a bimodal distribution of incisor arcade curvature for sheep grazing on two different food types? Why or why not.

ANSWER: (a) The data distribution is unimodal and centered in the low-40 range with no skewness or outliers. (b) Given that the data distribution is unimodal rather than bimodal it does not support the hypothesis that sheep grazing on two different food types would develop two different incisor arcade curvatures.

60. The stem-and-leaf plot below displays the weights (in ounces) of a random sample of tomatoes grown on a local farm.

2L |4 2H | 3L |2 3H |89

stem: ones

4L |13

leaf: tenths

4H |5589 5L |11122334 5H |668999 6L |223344 6H |5556 Briefly describe the distribution of tomato weights.

What is the weight of the heaviest tomato in the sample?

ANSWER: The distribution is unimodal and slightly skewed in the negative direction. Most of the weights are in the higher five categories with relatively few in the lower five categories.

The heaviest tomato weighs 6.6 ounces.

61. The histogram below represents the average number of years of teaching experience for teachers at elementary schools in Des Moines, Iowa in 2022.

Name:

Class:

Date:

Chapter 02 - Graphical Methods

Describe the distribution in terms of shape, skewness, and the presence of outliers (if any).

ANSWER: The distribution is reasonably symmetric with no outliers. The distribution is slightly positive (right) skewed.

62. The histogram below displays data on the hourly wage needed in order for a full-time worker to afford a two-bedroom rental in a particular area.

Which of the following accurately describes the data distribution?

I) Unimodal II) Bimodal III) Positive (right) skewed IV) Negative (left) skewed a. I and IV only b. I and III only c. II and III only d. II and IV only ANSWER: b 63. The comparative dotplots below represent the wing weights of Nicaraguan and Costa Rican bats categorized by the bat’s diet. a) Fruit-eaters Wing-Weight

Name:

Class:

Date:

Chapter 02 - Graphical Methods

b) Insect-eaters Wing-Weight

What do these dotplots tell us about the difference in the typical wing weight and variability in wing weight for the fruiteaters vs. the insect-eaters: ANSWER: Fruit-eating bats have higher typical wing weights compared to insect-eating bats. Additionally, the variability in wing weights for fruit-eating bats is higher than that of insect-eating bats. The wing weights of the fruit-eating bats range from less than 10 grams to just under 115 grams, while the wing-weights for the insect-eating bats range from less than 5 grams to just under 25 grams.

64. The comparative dotplots below represent the wing span of Nicaraguan and Costa Rican bats categorized by the bat’s diet. a) Fruit-eaters wingspan

b) Insect-eaters wingspan

What do these dotplots tell us about the difference in the typical wing span and variability in wing span for the fruit-eaters vs. the insect-eaters: ANSWER: Fruit-eating bats have higher typical wing spans compared to insect-eating bats. Additionally, the variability in wing spans for fruit-eating bats is higher than that of insect-eating bats. The wing spans for fruit-eating bats range from around 25 cm to just under 60 cm, while the wing spans for insect-eating bats range from just under 20 cm to just over 30 cm.

65. The histograms below display sleep deficit in hours for students enrolled in school with morning vs. afternoon start times. Positive values on the horizontal axis indicate sleep deficit, while negative values on the horizontal axis indicate sleep surplus.

Name:

Class:

Date:

Chapter 02 - Graphical Methods

Which of the following can we conclude based on the histogram displays?

I) Students with afternoon start tended to have fewer hours of sleep deficit compared to students with morning start.

II) The variability in hours of sleep deficit or surplus was similar for both morning start and afternoon start students. a. I only b. Both I and II c. II only d. Neither I nor II ANSWER: b 66. The comparative stem-and-leaf display below shows the results of a test comparing the life of two different brands of light bulbs. The test included ten bulbs from each brand and recorded the life (in hours) for similar use conditions.

Bulb A (hrs) Bulb B (hrs) 0 1 2 Stem: tens 3 Leaf: one 4 5 6 7 8 8 7 9 3 10 6 0 11 15 982 12 38 5 13 1 14 0 15 3 5 16 17 1 (a) Briefly describe the data distribution for light bulb brands A and B. (b) Using the data in the stem-and-leaf plot, which bulb brand would you choose to buy and why?

ANSWER: (a) The distributions for brands A and B are both reasonably symmetric. The values for brand A are slightly

Name:

Class:

Date:

Chapter 02 - Graphical Methods higher than those for brand B, and the variability for brand A is lower than for brand B. (b) Brand A would be the better choice to purchase given the longer life and lower variability in life.

67. Ruminants are hoofed animals such as cattle and sheep. Two categories of ruminants are browsers (leaf eaters) and grazers (grass eaters). Some biologists believe that the incisor arcade, that part of the mouth between incisors, is shaped differently for browsers vs. grazers, and that might explain their food preferences. The “curvature” of an incisor arcade is a measure of its shape, with large values indicating a long, thin mouth, and small values indicating a shorter, wider mouth. The back-to-back comparative stem-and-leaf display below compares the curvatures of incisor arcades of a sample of species including both browsers and grazers in the ruminant family.

Browsers Grazers N = 18 N = 54 | 1L | | 1H |9 | 2L |1 4| 3L | 22244 99885 | 3H | 55566667778999999 410 | 4L | 022223 99987 | 4H | 55556666677778889 321 | 5L | 03 | 5H |9 | 6L |0 | 6H | | 7L | 0| 7H | Some biologists believe that browsers have thinner mouths because they browse thorny plants, so browsers have evolved thinner mouths to access leaves between thorns. Does the data in the back-to-back stem-and-leaf plot support this theory? What aspects of the data would you consider when answering the question?

ANSWER: The data distribution does not support this theory. The typical value for browser curvature is only slightly higher than that of the grazers, and both distributions overlap significantly, indicating minimal differences.

68. In the article, “Dimensional Relationships for Flying Animals”, the wing areas in square centimeters of gliding birds of prey are reported. Night hunters are distinguished from the birds that hunt during daylight hours. The back-to-back comparative stem-and-leaf display below shows the distribution of wing area for day vs. night hunters for birds in a given study area.

Day hunter wings (cm2) stem: thousands leaf: units

Night hunter wings (cm2)

3H 715 3L 2H 3212L 1H 317,2851L 082,163,304,396 822,708,703,558,5300H 4380L 405,459 Biologists speculate that, since birds could be detected at a distance by their prey during the day, the species that hunt during the day should be smaller on average than those that hunt at night. Do the data shown in the comparative stemand-leaf display support this theory? What specific aspects of the stem-and-leaf display support your answer?

ANSWER: Yes, the majority of the day hunters have wing areas below 1000 cm2, while for night hunters, the majority

Name:

Class:

Date:

Chapter 02 - Graphical Methods were above 1000 cm2.

69. A college professor wants to identify the relationship between test scores in her class and the number of hours students spend preparing for the test. She collected information about preparation time (hours) and test scores (points out of 100 points max) for ten students in her class. The Table below shows the preparation time and test score for each student.

Student Preparation Time (h) Test Score (points out of 100 max) Student #1 1.5 62 Student #2 5.5 75 Student #3 5.0 91 Student #4 6.5 74 Student #5 0.5 45 Student #6 1.5 71 Student #7 7.5 81 Student #8 4.0 98 Student #9 3.0 91 Student #10 2. 0 91 Choose the most appropriate graphical display to allow the professor to determine the relationship between student preparation and test scores. a. Histogram b. Stem-and-Leaf Display c. Bar Chart d. Scatterplot ANSWER: d 70. In a scatterplot, both the horizontal and vertical axes must be set to zero. a. True b. False ANSWER: False 71. Consumer Reports rated the customer satisfaction for 20 different fitness trackers on a scale from 0 to 100. The Table below shows the price of the rated fitness trackers as well as their customer satisfaction score.

If you wanted to construct a scatterplot to help you determine the relationship between fitness tracker price and rated customer satisfaction, which of the following would you do?

Name:

Class:

Date:

Chapter 02 - Graphical Methods I) Draw horizontal and vertical axes and label one “price” and the other “satisfaction score” II) Scale each axis so that all the values for the variable represented by that axis can be plotted.

III) Ensure that the graph origin includes the point (0,0) IV) For each pair in the data set, add a dot corresponding to its and location a. I and II only b. I, II, and III only c. I, II, and IV only d. III and IV only ANSWER: c 72. A researcher took the following measurements correlating daily low temperatures with elevation above mean sea level.

Daily Low Temperature (°F) 12 17 22 29 30 32 25 14

Elevation (feet above mean sea level) 4,947 5,555 6,577 5,922 6,333 6,874 4,866 5,325

Which of the following are features of an effective scatterplot displaying temperature vs. elevation from the data in the Table above?

I) An x-axis scale that ranges from 10°F to 40°F II) A y-axis scale that ranges from 2,000 feet to 7,000 feet III) An x-axis scale that ranges from 0°F to 100°F IV) A y-axis scale that ranges from 0 feet to 10,000 feet a. I only b. I and II only c. III only d. III and IV only ANSWER: b 73. A field technician took the following measurements correlating signal strength in dB with distance from a transmitter in kilometers.

Signal Strength (dB) 1.1 1.5 2.4 2.0 1.8 2.1 1.3 1.7

Distance From Transmitter (km) 19 17 12 14 15 13 18 15

Which of the following are features of an effective scatterplot displaying signal strength vs. distance to the transmitter from the data in the Table above?

Name:

Class:

Date:

Chapter 02 - Graphical Methods I) An x-axis scale that ranges from 0 to 100 km II) A y-axis scale that ranges from 0 to 50 dB III) An x-axis scale that ranges from 10 to 20 km IV) A y-axis scale that ranges from 1 to 2.5 dB a. I only b. I and II only c. III only d. III and IV only ANSWER: d 74. The scatterplot below displays cost in dollars vs. reported customer satisfaction (score out of 100 max) for 20 fitness tracking devices.

Based on the data displayed in the scatterplot, which of the following are reasonable conclusions? a. Devices that cost more than $200 generally have higher customer satisfaction than devices that cost less than $200. b. Of the devices which cost more than $200, increased cost leads to increased customer satisfaction. c. Of the devices which cost less than $50, increasing cost leads to increased customer satisfaction. d. Of the devices which cost between $100 and $150, increasing cost leads to increased customer satisfaction ANSWER: c 75. A concern was raised in the Des Moines, Iowa school system that the least experienced teachers typically teach students from low-income families. The scatterplot below relates years of teaching experience to the percentage of students receiving free or reduced lunch (an indicator of family income).

Name:

Class:

Date:

Chapter 02 - Graphical Methods

Do the data in the scatterplot support the concern raised regarding the least experienced teachers typically teaching lowincome students?

ANSWER: Yes, the data in the scatterplot supports the concern. Schools with more than 75% of students eligible for free or reduced lunches have less experience (< 10 years) while schools that have less than 75% free or reduced lunch eligibility have average teacher experience values of up to10 or more years.

76. Investigators writing in the Journal of Early Adolescence were interested in the communication about sex and related topics between parents and 12–14-year-olds. The investigators asked students and parents whether or not they had communicated with their child/parent about topics such as pregnancy, how to say “no”, and methods of contraception. A scatterplot of their data is presented below.

Name:

Class:

Date:

Chapter 02 - Graphical Methods

Each point on the scatterplot represents one topic listed by the investigators. For example, 72.4% of parents and 57.6% of adolescents said that parents had discussed childbirth. This would be recorded as the point (57.6, 72.4). If parents and adolescents are in “perfect agreement”, points will lie on a straight-line y = x. Explain whether the placement of the points on the scatterplot indicates (1) or (2) below and provide the rationale for your choice: 1) parents are generally saying that they have talked about topics more so than indicated by the adolescents’ response 2) adolescents are generally saying that they have talked about topics more so than indicated by the parents’ response ANSWER: Since the majority of points lie above the y = x line, parents are generally saying that they have talked about topics more so than indicated by the adolescents’ response.

77. Investigators studying the relationship between gender and the interests of early adolescents asked both boys and girls in grades 5-9 to indicate on a 7-point scale their degree of interest in topics such as Life, Sports, Cars, and Opposite Sex. The data in the scatterplot below represent average levels of interest for boys and girls in grades 5-9.

Name:

Class:

Date:

Chapter 02 - Graphical Methods

Each point represents one topic listed by the investigators. For example, boys’ average rating for “Opposite sex” is 6.2, while girls on average rated their interest in this topic as 6.0 on the 7-point interest scale. This is recorded as the point (6.2, 6.0). If boys and girls responded identically, the points would all lie on a straight-line y = x. Explain whether the placement of the points on the scatterplot indicates (1) or (2) below, and provide the rationale for your choice.

(1) Boys generally showed greater interest than girls (2) Boys and girls show generally equal interest ANSWER: The points generally seem to scatter around the line y = x indicating equal interest for both boys and girls.

78. Investigators studying the relationship between gender and the interests of early adolescents asked boys and girls in grades 5-9 to indicate on a 7-point scale their degree of interest in topics such as Life, Sports, Cars, and Opposite Sex. The data in the scatterplot below represent average levels of interest for boys and girls in grades 5-9.

Name:

Class:

Date:

Chapter 02 - Graphical Methods

Each point represents one topic listed by the investigators. For example, boys’ average rating for “Opposite sex” is 6.2, while girls on average rated their interest in this topic as 6.0 on the 7-point interest scale. This is recorded as the point (6.2, 6.0). If boys and girls responded identically, the points would all lie on a straight-line y = x. In the case of the two points indicated by the arrows on the scatterplot, do girls or boys show more interest in the topics? Explain your choice.

ANSWER: Points that lie above the line y = x indicate higher interest of females (girls) compared to males (boys) for the given topic. Points that lie below the line y = x indicate higher interest of males (boys) compared to female (girls) for the given topic. Since the points indicated by the arrows lie below the line y = x, they indicate higher interest of boys compared to girls.

79. Each year, Cal Fire reports the number of wildfires occurring in California. Data from the yearly reports for 2010 to 2019 are shown in the time series plot below.

Which of the following best describes the trend shown in the time-series plot above?

Name:

Class:

Date:

Chapter 02 - Graphical Methods a. Steady increase year-to-year b. Steady decrease year-to-year c. General upward trend d. General downward trend ANSWER: c 80. The monthly occurrence of California wildfires from 2010 to 2019 is shown in the time-series plot below.

Which of the following best describes the trend shown in the time-series plot above? a. Steady increase month-to-month b. Periodic increase and decrease within each year c. General upward trend d. Steady decrease month-to-month ANSWER: b 81. The average cost of particular Christmas gifts from 1985 to 2020 is shown in the time-series plot below.

Name:

Class:

Date:

Chapter 02 - Graphical Methods

Which of the following accurately describes the trend shown in the time-series plot above?

I) General upward trend from 1995 to 2020 II) Steady increase from 1990 to 1994 a. I only b. Both I and II c. Neither I nor II d. II only ANSWER: b 82. Records of the missions of Baja California provide trends in baptism rates during the late 1700s. The data below are two time series of the numbers of baptisms at two Central Baja missions, San Jose de Comondu and San Gertrudis.

How would you generally describe the trend of baptisms for the two missions over this period? Do they show similar trends?

ANSWER: Generally, the trends for the two missions are similar as shown by the roughly parallel curves from the year 1773 and forward. An exception to this similarity is the greater variability in the San Gertrudis mission baptism rates from 1770 to 1773.

Name:

Class:

Date:

Chapter 02 - Graphical Methods 83. The time-series plot below shows changes in median annual earnings by education level.

Which of the trends are shown in the time-series plot above?

I) General lack of consistent upward or downward trend in median annual income for the “Associate’s degree” and the “Some college, no degree” II) Greater variability in the “Master’s or higher degree” compared to the “High school completion” III) Large, sustained gap between the “Bachelor’s degree” compared to the “High School completion” a. I and II only b. II and III only c. I and III only d. I, II, and III ANSWER: d 84. A pie chart is most useful for numeric data. a. True b. False ANSWER: False 85. The pie chart below summarizes the results of a survey of 300 randomly selected students at a particular high school regarding their soft drink preferences.

Name:

Class:

Date:

Chapter 02 - Graphical Methods

Describe the preference for colas (Coke and Pepsi) compared to other soft drinks.

ANSWER: Over half (55%) of respondents preferred colas vs. other soft drinks.

86. The relative frequency bar chart below summarizes the results of a survey of 300 randomly selected students at a particular high school regarding their soft drink preference.

Which are the most popular and least popular soft drinks? What is the difference between the number of students who opted for the most popular soft drink and the number of students who opted for the least popular soft drink?

ANSWER: The most popular soft drink was Coke, while the least popular was Sprite. 90 students opted for Coke, while 30 students opted for Sprite, so the difference between them is 60 students.

87. The comparative bar chart below summarizes the results of a year-long study on the nature of television commercials for cosmetics and personal care products. The comments are made by males (M) and are classified by the gender of the recipient (M or F).

Name:

Class:

Date:

Chapter 02 - Graphical Methods

What conclusion can we draw regarding the effect of the recipient’s gender on the nature (complimentary, neutral, or insulting) of the comment?

ANSWER: Based on the data in the comparative bar chart, males are more likely to offer complimentary comments to females than to other males.

88. The segmented bar chart below summarizes the results of a year-long study on the nature of television commercials for cosmetics and personal care products. The comments are made by females and are classified by the gender of the recipient.

What conclusion can we draw regarding the effect of the recipient’s gender on the nature (complimentary, neutral, or insulting) of the comment?

ANSWER: Based on the data in the segmented bar chart, female commenters do not alter the nature of their comments significantly based on the gender of the recipient.

89. In a survey of 30 working adults who earn less than $6,000 per year, investigators asked about job satisfaction. The survey results are summarized in the pie chart below.

Name:

Class:

Date:

Chapter 02 - Graphical Methods

How does the number of respondents who were positive regarding their job satisfaction (very satisfied or moderately satisfied) compare to those who were negative regarding their job satisfaction (very dissatisfied or a little dissatisfied)?

ANSWER: The combination of very satisfied and moderately satisfied respondents amounted to slightly more than half of the total responses, so slightly more respondents were positive vs. negative regarding job satisfaction.

90. As part of the United States Census, data is also collected on the number of persons in each household. The census data for four decades is summarized below.

(a) Briefly describe how the proportion of households with 4 people has changed from 1970 to 2000. (b) What sizes of households appear to have decreased and increased the most, respectively, from 1970 to 2000?

ANSWER: (a) The proportion of households with 4 people has decreased slightly from 15.8% of households to 14.6% of households. (b) The household size which decreased the most from 1970 to 2000 was the 5 or more-member household with a drop from 20.9% to 10.4%. The household size which increased the most over that same time period was the 1-member household with a rise from 17.1% to 25.5.

91. The graphical display below shows the change in the geographical distribution of UNESCO (United Nations Educational, Scientific, and Cultural Organization) World Heritage sites from 1978 to 2020.

Name:

Class:

Date:

Chapter 02 - Graphical Methods

Which of the following trends does the graphical display show? a. The number of sites has increased at roughly the same rate for all six regions displayed. b. Of the six regions displayed, the number of sites in North America has changed the most from 1978 to 2020. c. The number of sites in the Arab world and sub-Saharan Africa have increased at a higher rate than those in Latin America and the Asia Pacific region. d. The number of sites in Europe has increased more over the 1978 to 2020 period than those for the other five regions displayed.

ANSWER: d 92. The scatterplot below summarizes data on the Women, Business, and Law (WBL) Index, which is an index of societal factors affecting women’s empowerment, as well as the female labor force participation rate for several countries.

Name:

Class:

Date:

Chapter 02 - Graphical Methods

Source: Women, Business, and the Law (WBL) database; World Development Indicators (WDI) database, World Bank, https://databank.worldbank.org/source/world-development-indicators; International Labour Organization (ILO), https://ilostat.ilo.org/.

Which of the following trends is the most clearly discernable from the scatterplot? a. The difference in female labor force participation rate vs. WBL index for the OECD high income countries vs. that of Latin America & Caribbean Countries b. The difference in female labor force participation rate vs. WBL index for South Asian countries vs. that of Middle East & North African Countries c. The trend in female labor force participation rate vs. WBL index for East Asia & Pacific Countries d. The overall trend in female labor participation rate vs. WBL ANSWER: d 93. The map graphic below displays the hourly wage required to afford a two-bedroom dwelling. A higher hourly wage indicates higher housing prices.

Name:

Class:

Date:

Chapter 02 - Graphical Methods

Which of the following trends are easily discernable from the map graphic?

I) Housing prices are generally highest on the West Coast, Florida, Virginia, and the mid-Atlantic states.

II) Housing prices are generally low for the Dakotas and other plains states (Nebraska, Kansas, Oklahoma) III) Despite the fact that they are both islands, housing prices vary considerably for Puerto Rico vs. Hawaii a. I and II b. II and III c. I and III d. I, II, and III ANSWER: d 94. The graph below is excerpted from the article “The Gaps Between White and Black in America, in Charts” published in The New York Times, June 19, 2020. The graph displays the median household income for different metropolitan areas for majority-white and majority-black communities within each metropolitan area.

Name:

Class:

Date:

Chapter 02 - Graphical Methods

Which of the following trends can be seen from the graph?

I) Significantly greater variability in median household income for majority-white vs. majority-black communities.

II) Consistent gap between majority-white and majority-black communities for different metropolitan areas. a. I only b. Both I and II c. II only d. Neither I nor II ANSWER: d 95. Many Americans believe that vehicles that are expensive to purchase and operate also have high greenhouse gas emissions. To what extent does the scatterplot below of vehicle emissions and costs for 2021 vehicles support this belief?

I) Greenhouse gas emissions are higher for higher-cost vehicles regardless of the vehicle type.

II) Greenhouse gas emissions are higher for higher-cost vehicles in the case of internal combustion engine vehicles III) Greenhous gas emissions are higher for higher-cost vehicles in the case of hybrid and plug-in hybrid vehicles IV) Greenhouse gas emissions don’t change significantly with vehicle cost in the case of battery electric vehicles. a. I only b. II and III only c. II, III, and IV only

Name:

Chapter 02 - Graphical Methods d. III and IV only ANSWER: c

Class:

Date:

Name:

Class:

Date:

Chapter 03 - Numerical Methods 1. Suppose you’re reviewing the results of quality assurance tests for a batch of 50 manufactured items. You’re interested in the typical values for the tests. Which of the following approaches is appropriate?

I) Plot your data with a dotplot to determine the distribution shape. If the shape is symmetric, then use the mean to indicate the typical value for the tests.

II) Plot your data with a stem-and-leaf display to determine distribution shape. If the shape is negatively skewed, then use the median to indicate the typical value for the tests.

III) Plot your data with a stem-and-leaf display to determine the distribution shape. If the shape is positively skewed, then use the median to indicate the typical value for the tests. a. I and II only b. II and III only c. I and III only d. I, II, and III ANSWER: d 2. Suppose you’re designing an automated door to allow dogs to access their owner’s homes unattended. You need to make the dog-door width as small as possible while still being large enough to accommodate the head and shoulders of most large dogs. You have a survey of over 5,000 dog head and shoulder widths. Which of the following steps would help you determine the minimum dog-door width you should recommend for your design?

I) Plot your survey data using a histogram in order to determine the shape of the data distribution.

II) If your data distribution is symmetric, use the median in order to determine the typical dog width.

III) If your data is skewed, use the mean in order to determine the typical dog width.

IV) If your data is symmetric, use the standard deviation to determine the variability in dog widths. a. I only b. I and II only c. I and III only d. I and IV only ANSWER: d 3. You have a data distribution that is skewed, but contains no outliers. Which of the following summary measures is appropriate for describing the center (typical value) and variability of your data? a. Use the mean to describe the center and the standard deviation to describe the variability b. Use the mean to describe the center and the interquartile range to describe the variability c. Use the median to describe the center and the interquartile range to describe the variability d. Use the median to describe the center and the standard deviation to describe the variability ANSWER: c 4. You’re reviewing the data from a survey on fruit production from a particular region. You’ve plotted the data in a dotplot and are reviewing the distribution shape in order to determine the best summary statistics to use to describe the distribution’s center and variability. At first glance, the distribution appears to be symmetric, so you decide to use the mean to describe the distribution center and the standard deviation to describe the distribution variability. On closer examination, you notice several outliers on the positive (high fruit production) side of the distribution. How should you respond to the presence of these outliers? a. The presence of outliers should not change your choice of summary measures. Use the mean and standard deviation as originally planned. b. Change your choice of variability measure from standard deviation to interquartile range, but continue to use the mean to describe your distribution’s center. c. Change your choice of center measure from mean to median, but continue to use standard deviation to

Name:

Class:

Date:

Chapter 03 - Numerical Methods describe your distribution’s variability. d. Change your center measure to median and your variability measure to interquartile range.

ANSWER: d 5. You’re reviewing the data from some tests your colleague performed in the lab. There are 15 data points, so you plot them with a dotplot in order to assess the shape of the data distribution. You find that three of the fifteen data points are outliers, so you decide to use median and interquartile range, respectively, to report the center and variability of the data.

Later, your colleague informs you that the three outlier points belonged to a different batch of test data and should not have been included in the set they gave you to review. How will this new information affect your choice of summary measures for the data set? a. Consider the shape of the remaining distribution. If it is skewed, then change your summary measures to mean and standard deviation b. Change your center summary measure to mean, but continue to use interquartile range for variability. c. Change your variability summary measure to standard deviation, but continue to use median for center. d. Consider the shape of the remaining distribution. If it is skewed, then continue to use median and interquartile range.

ANSWER: d 6. You have a data distribution that is skewed and has several outliers. Which of the following summary measures is appropriate for describing the center (typical value) and variability of your data? a. Use the mean to describe the center and the standard deviation to describe the variability b. Use the median to describe the center and the interquartile range to describe the variability c. Use the median to describe the center and the standard deviation to describe the variability d. Use the mean to describe the center and the interquartile range to describe the variability ANSWER: b 7. The dotplot below represents the surface germ concentration measured on 41 credit and debit cards. The germ concentration is reported in germ-scores with higher values indicating a higher germ concentration.

Which summary measures would you choose for the center and variability of the data distribution shown in the dotplot above? a. Use the mean for center and standard deviation for variability. b. Use the median for center and standard deviation for variability. c. Use median for center and interquartile range for variability. d. Use the mean for center and interquartile range for variability.

ANSWER: c 8. The dotplot below represents the surface germ concentration measured on 41 credit and debit cards. The germ concentration is reported in germ-scores with higher values indicating a higher germ concentration.

Name:

Class:

Date:

Chapter 03 - Numerical Methods

Suppose you found that the test used to produce all the germ scores of 200 and higher was performed incorrectly and you must discard all data points with germ scores above 200. Which summary measures would you choose for the center and variability of the data distribution that only includes germ scores from zero to 200? a. Use the mean for center and standard deviation for variability. b. Use the median for center and standard deviation for variability. c. Use median for center and interquartile range for variability. d. Use the mean for center and interquartile range for variability.

ANSWER: c 9. The dot plot below shows the annual salaries, in thousands of dollars, of a sample of non-management staff who work for a small banking company.

Which of the following summary measures would be appropriate for describing the typical salary and variability in salaries for the data shown in the dotplot? a. Use the median for center and standard deviation for variability. b. Use median for center and interquartile range for variability. c. Use the mean for center and interquartile range for variability. d. Use the mean for center and standard deviation for variability.

ANSWER: b 10. The table below summarizes the number of minutes spent exercising each day for a sample of 30 female college students.

Construct a graphical display of the data distribution and use it to determine the data distribution’s shape. Based on the shape of the data distribution, select which of the following summary measures you would use to describe center and variability. a. Use the mean for center and standard deviation for variability. b. Use the median for center and standard deviation for variability. c. Use median for center and interquartile range for variability. d. Use the mean for center and interquartile range for variability.

Name:

Class:

Date:

Chapter 03 - Numerical Methods ANSWER: c 11. The histogram below displays the distribution of the number of mating partners of queen honey bees.

Could the mean and standard deviation be used to describe the center and variability of mating partner distribution? a. No, because the distribution is positively skewed. b. No, because the distribution is negatively skewed. c. No, because the distribution contains outliers. d. Yes, because the distribution is symmetric with no outliers.

ANSWER: d 12. Given the data distributions A and B represented by the dotplots below, for which would the mean and standard deviation be appropriate choices for measures of center and variability?

Distribution A

Distribution B a. Mean and standard deviation are appropriate for distribution A b. Mean and standard deviation are appropriate for distribution B c. Mean and standard deviation are appropriate for both distribution A and distribution B d. Mean and standard deviation are appropriate for neither distribution A nor distribution B ANSWER: a 13. Given the data distribution represented by the dotplot below, would the mean and standard deviation be appropriate choices for measures of center and variability?

Name:

Class:

Date:

Chapter 03 - Numerical Methods

a. No, because the distribution is negatively skewed b. No, because the distribution is positively skewed c. No, because there are outliers d. Yes, because the distribution is symmetric with no outliers ANSWER: d 14. The two dotplots below represent Math and Verbal SAT scores for 50 first-year college students. For which would the mean and standard deviation be appropriate choices for measures of center and variability?

a. Mean and standard deviation are appropriate for Math scores distribution b. Mean and standard deviation are appropriate for Verbal scores distribution c. Mean and standard deviation are appropriate for both Math and Verbal scores distributions d. Mean and standard deviation are appropriate for neither Math nor Verbal scores distributions ANSWER: b 15. Given the data distribution represented by the dotplot below, would the mean and standard deviation be appropriate choices for measures of center and variability? Note the single data point at 1000.

Name:

Class:

Date:

Chapter 03 - Numerical Methods

a. No, because the distribution is positively skewed b. No, because there are outliers c. No, because the distribution is both positively skewed and has outliers d. Yes, because the distribution is symmetric ANSWER: c 16. Given the data distributions A and B represented by the histograms below, for which would the mean and standard deviation be appropriate choices for measures of center and variability?

Distribution A Distribution B

a. Mean and standard deviation are appropriate for distribution A b. Mean and standard deviation are appropriate for distribution B c. Mean and standard deviation are appropriate for both distribution A and distribution B d. Mean and standard deviation are appropriate for neither distribution A nor distribution B ANSWER: c 17. Data sets represented by graphical displays typically represent samples rather than populations. The centers of both

Name:

Class:

Date:

Chapter 03 - Numerical Methods populations and samples from those populations can be described by means. In which of the following ways does the sample mean differ from the population mean?

I) The sample mean can be higher or lower than the population mean II) The sample mean can change from sample-to-sample, while the population mean does not vary with sampling a. I only b. Both I and II c. II only d. Neither I nor II ANSWER: b 18. Which measures of the numerical data distribution are commonly used to describe the variability of the distribution? a. Interquartile range and standard deviation b. Mean and standard deviation c. Median and interquartile range d. Mean and mean ANSWER: a 19. Which measures of the numerical data distribution are commonly used to describe the center of a distribution? a. Mean and standard deviation b. Interquartile range and median c. Mean and Median d. Interquartile range and standard deviation ANSWER: c 20. Variance and standard deviation both include the concept of deviation from the mean. Which of the following are true of the deviation from the mean for a data set?

I) Is based on all the observations in the data set II) Calculated for each observation by subtracting the sample mean from the value of that particular observation a. I only b. Both I and II c. II only d. Neither I nor II ANSWER: b 21. Sample variance incorporates the concept of deviation from the mean, but has which of the following important differences?

I. II. III. IV.

Includes only the extreme values of the data set Can only be a positive number Includes contributions from all observations in the data set Is expressed in different units a. I and II only b. II and III only c. I, II, and III only d. II, III, and IV only

Name:

Class:

Date:

Chapter 03 - Numerical Methods ANSWER: d 22. Which of the following are the advantages of variance and standard deviation for characterizing the variability of data distributions?

I) Both include the contributions of all points in the data set II) Both include the square of the deviation from the mean, making them sensitive to the distance of individual points from the mean a. I only b. Both I and II c. II only d. Neither I nor II ANSWER: b 23. The variance is the positive square root of the standard deviation. a. True b. False ANSWER: False 24. Which of the following are reasons why people may find standard deviation to be a more natural measure of variability than variance? a. Standard deviation is based on only the extreme values of a data set. b. Standard deviation can be either positive or negative depending on the values of the points in the data set. c. Standard deviation is insensitive to the distance of individual points from the mean. d. Standard deviation is expressed in the same units as the data points.

ANSWER: d 25. The following questions refer to important aspects of variance and standard deviation which make them useful for describing variability in a data distribution. (a) Why was rather than chosen to be used in building the formulas for variance? (b) Why is s more commonly used than s2 as a more useful measure of variability? (c) Why was ANSWER: (a) Because

chosen over

when using s2 to estimate 2?

will always be zero

(b) Because it is in the same units as the original observations (c) Because, on average, dividing by n-1 tends to give a value closer to 2 than dividing by n 26. The Table below gives the calories consumed by three different groups in a study on the effects of exercise on appetite.

Name:

Class:

Date:

Chapter 03 - Numerical Methods

What is the value of the sample mean for each group? a. Control Group = 335, Fun Group = 617, Exercise Group = 744 b. Control Group = 331, Fun Group = 612, Exercise Group = 738 c. Control Group = 359, Fun Group = 662, Exercise Group = 797 d. Control Group = 314, Fun Group = 579, Exercise Group = 697 ANSWER: a 27. Given the three data sets below: Data Set 1: 50, 60, 70, 80, 90, 100 Data Set 2: 50, 75, 75, 75, 75, 100 Data Set 3: 70, 75, 75, 75, 75, 80 Calculate the standard deviation for each of the three data sets. a. Data Set 1 = 18.7, Data Set 2 = 15.8, Data Set 3 = 2.9 b. Data Set 1 = 17.1, Data Set 2 = 15.8, Data Set 3 = 3.2 c. Data Set 1 = 18.7, Data Set 2 = 15.8, Data Set 3 = 3.2 d. Data Set 1 = 17.1, Data Set 2 = 14.4, Data Set 3 = 2.9 ANSWER: c 28. The following data set represents hours of community service performed by ten students during the spring semester:

What are the mean and standard deviation for the data set. a. Mean = 20, Standard Deviation = 27 b. Mean = 27, Standard Deviation = 20 c. Mean = 13, Standard Deviation = 20 d. Mean = 23, Standard Deviation = 25 ANSWER: a

Name:

Class:

Date:

Chapter 03 - Numerical Methods 29. The data set below was part of a study investigating the effect of the shape of drinking glasses. The data are the actual volume (ml) poured into a tall, slender glass by study subjects asked to pour 44.3 ml (1.5 ounces). Calculate the values of the mean and standard deviation for the data set.

a. b. c. d.

ANSWER: b 30. Costs per serving (in cents) for 16 high-fiber cereals rated good by Consumer Reports are shown below: 40 48 60 46 20 78 70 31 50 54 69 45 50 30 60 20 Calculate the mean and standard deviation for the data set above. a. b. c. d.

ANSWER: a 31. The data below represent the number of high school basketball players from each school in a particular school district who graduated with their class in a given year.

50 86 86 75 100 92 92 93 83 What is the mean and standard deviation for data set above? a. b. c. d.

ANSWER: a 32. The following data set represents surface germ concentrations on credit cards sampled from 27 holiday shoppers in a major American city. The concentrations are expressed as germ scores (unitless). Leading zeros have been added to the germ scores that were less than 100 so that all the scores are represented as 3-digit numbers.

032 035 039 041 054 055 056 068 074 078 098 104 105 108 119 119 126 129 143 163 200 242 259 273 349 609 633 What is the mean and standard deviation for data set above? a. b. c. d.

ANSWER: c

Name:

Class:

Date:

Chapter 03 - Numerical Methods 33. The National U.S. Bureau of Labor Statistics published the average unemployment rate for November 2017 by state (see Table below). Find the center of this data. Use a graphical data display if needed to determine the shape of the data distribution.

State Rate State Rate State Rate Hawaii 2.0 Okkahoma 4.2 North Dakota 2.6 Oregon 4.2 Nebraska 2.7 Arizona 4.3 New Hampshire 2.7 Georgia 4.3 Colorado 2.9 North Carolina 4.3 Idaho 2.9 Rhode Island 4.3 Iowa 2.9 Wyoming 4.3 Vermont 2.9 Washington 4.5 Minnesota 3.1 California 4.6 Tennessee 3.1 Connecticut 4.6 Utah 3.2 Michigan 4.6 Wisconsin 3.2 Pennsylvania 4.6 Maine 3.3 Delaware 4.7 Missouri 3.4 Kentucky 4.7 Alabama 3.5 Louisiana 4.7 Kansas 3.5 New York 4.7 South Dakota 3.5 Mississippi 4.8 Florida 3.6 Ohio 4.8 Massachusetts 3.6 Illinois 4.9 Arkansas 3.7 Nevada 5.0 Indiana 3.7 New Jersey 5.1 Virginia 3.7 West Virginia 5.3 Texas 3.8 New Mexico 6.1 Maryland 3.9 District of Columbia 6.4 Montan 4.0 Alaska 7.2 South Carolina 4.0 Choose the most appropriate description for the center of this data. a. On average, the unemployment rate is 4.1% because the mean of the data set is 4.1. This means that the unemployment rate for each state is 4.1%. b. On average, the unemployment rate is 3.2% because the mean of the data set is 3.2. This means the 3.2% is the typical value of unemployment rate for the states. c. On average, the unemployment rate is 4.1% because the mean of the data set is 4.1. This means that 4.1% is the typical value of unemployment rate for the states. d. On average, the unemployment rate is 3.2% because the median of the data set is 3.2. This means that 3.2% is the typical value of unemployment rate for the states.

ANSWER: c 34. The Spotrac organization publishes professional football players’ salaries. The Table below contains information about base salaries for fifteen randomly selected players from the Buffalo Bills team in the year 2016.

Name:

Class:

Date:

Chapter 03 - Numerical Methods

Choose the most appropriate description for the center of this data. Use a graphical data display if needed to determine the shape of the data distribution. a. The mean of the data set is 3.5 million, so the base salary for each player in the Buffalo Bills is 3.5 million dollars. b. The mean of the data set is 2.6 million, so the typical base salary for Buffalo Bills players is 2.6 million dollars. c. The mean of the data set is 3.5 million, so the base salary for each player in the Buffalo Bills is 2.6 million of dollars. d. The data distribution is not symmetric, so the mean cannot be used to describe the typical value of base salaries for the Buffalo Bills players.

ANSWER: d 35. The dot plot below represents surface germ concentration on credit cards used by college students for on-campus purchases. A review of the data collection and testing procedures showed that errors were made in the testing for samples with germ scores above 1000.

With the removal of the data points above 1000, which of the following measures could be used to describe center and variability? a. Center: median, Variability: standard deviation b. Center: mean, Variability: standard deviation c. Center: mean, Variability: interquartile range d. Center: median, Variability: interquartile range ANSWER: d

Name:

Class:

Date:

Chapter 03 - Numerical Methods 36. The data set below represents professional baseball players’ salaries at the beginning of the 2021 season.

Suppose that, by mid-season 2021, the three players with the highest salaries became injured and retired, forfeiting their high salaries. Which of the following best describes the effect of the loss of the three highest salaries on the accuracy with which the calculated mean represents the data distribution center? a. Loss of the three highest salaries makes the calculated mean a poorer measure of the data distribution center. b. Loss of the three highest salaries makes the calculated mean a better measure of the data distribution center. c. Loss of the three highest salaries has no effect on the accuracy with which the calculated mean represents the data distribution center. d. Loss of the three highest salaries would have no effect on the calculated mean for the data set.

ANSWER: b 37. The dotplot below shows the distribution of state gas tax (in cents per gallon) for all fifty U.S. states and Washington D.C.

Which of the following groups of four data points is contributing the most to the variability? a. Data points between 40 and 45 cents per gallon b. Data points below 20 cents per gallon c. Data points above 45 cents per gallon d. Data points between 20 and 25 cents per gallon.

ANSWER: c 38. The data set below represents the survey results investigating the average number of hours residents of 13 U.S. urban areas spend driving in traffic each week.

40 5 1 60 50 55 45 62 59 48 53 61 56 How would elimination of the two lowest values affect the calculated mean and standard deviation for the data set? a. Mean would increase and standard deviation would decrease b. Mean would decrease and standard deviation would increase c. Both the mean and the standard deviation would decrease d. Both the mean and the standard deviation would increase ANSWER: a 39. The data set below represents the survey results investigating the average number of car trips residents of 12 U.S.

Name:

Class:

Date:

Chapter 03 - Numerical Methods suburban towns took each week.

250 316 89 76 92 110 98 115 83 79 114 84 How would elimination of the two highest values affect the calculated mean and standard deviation for the data set? a. Mean would increase and standard deviation would decrease b. Mean would decrease and standard deviation would increase c. Both the mean and the standard deviation would decrease d. Both the mean and the standard deviation would increase ANSWER: c 40. The following data set includes results of a survey of 10 holiday shoppers regarding the number of impulse purchases they had made on the day of the survey.

0 1 1 2 2 2 2 3 3 4 Which of the following are true regarding accurate descriptions of the data set’s center? a. It is necessary to use the median since the distribution is skewed. b. It is possible to use the mean since the distribution is symmetric c. It is necessary to use the median since the distribution contains outliers d. It is possible to use the median since the distribution is symmetric ANSWER: b 41. The following data set includes the results of a survey of 10 online shoppers regarding the dollars (in thousands) spent on holiday gifts in a particular year.

1.5 2.5 1.8 2.4 1.6 1.7 2.1 3.9 4.9 5.6 Which of the following are true regarding accurate descriptions of the data set’s center? a. It is necessary to use the median since the distribution is skewed. b. It is possible to use the mean since the distribution is symmetric c. It is necessary to use the median since the distribution contains outliers d. It is possible to use the median since the distribution is symmetric ANSWER: a 42. The following data set includes the results of a survey of 10 downtown shoppers regarding the frequency with which they purchased chocolate for holiday gifts.

0 1 21 23 30 25 33 40 37 28 Which of the following are true regarding accurate descriptions of the data set’s variability? a. It is necessary to use the interquartile range since the distribution is symmetric. b. It is possible to use the standard deviation since the distribution is symmetric c. It is necessary to use the interquartile range since the distribution contains outliers d. It is possible to use the interquartile range since the distribution is symmetric.

ANSWER: c 43. The following data set includes the results of a survey of 10 residents of a small town regarding the number of evenings they spent with immediate family or close friends during the holiday season in a particular year.

11 12 12 23 23 23 23 30 31 28 Which of the following are true regarding accurate descriptions of the data set’s variability? a. It is necessary to use the interquartile range since the distribution is symmetric. b. It is possible to use the standard deviation since the distribution is symmetric c. It is necessary to use the interquartile range since the distribution contains outliers

Name:

Class:

Date:

Chapter 03 - Numerical Methods d. It is possible to use the interquartile range since the distribution is symmetric ANSWER: b 44. The back-to-back stem-and-leaf display shows the distribution of the proportion of time spent on the nest for worker wasps and queen wasps for twelve colonies. The stem is in tenths and the leaves are in hundredths.

Queen | | 4| | 2| 8| | 98 | 40 | 9875 | 0|

5 5 6 6 7 7 8 8 9 9 10

Worker | 24 | 56789 |3 | 68 | |9 |1 | | 7 | 9 represents 0.79 | |

Which of the following best describes the appropriate summary measures for the distribution centers? a. Use mean for both queen and worker distributions since both distributions are symmetric b. Use median for both queen and worker distributions since both are skewed c. Use the mean for the queen distribution since it is symmetric, but use the median for the worker distribution since it is skewed. d. Use the mean for the worker distribution since it is symmetric, but use the median for the queen distribution since it is skewed.

ANSWER: b 45. The back-to-back stem-and-leaf display shows the distribution of the proportion of time spent on the nest for worker wasps and queen wasps for twelve bee colonies. The stem is in tenths and the leaves are in hundredths.

Queen | | 4| | 2| 8| | 98 | 40 | 9875 | 0|

5 5 6 6 7 7 8 8 9 9 10

Worker | 24 | 56789 |3 | 68 | |9 |1 | | 7 | 9 represents 0.79 | |

Which of the following best describes the appropriate summary measures for the distribution variabilities? a. Use standard deviation for both queen and worker distributions since both distributions are symmetric b. Use interquartile range for both queen and worker distributions since both are skewed c. Use the standard deviation for the queen distribution since it is symmetric, but use interquartile range for the worker distribution since it is skewed.

Name:

Class:

Date:

Chapter 03 - Numerical Methods d. Use the standard deviation for the worker distribution since it is symmetric, but use interquartile range for the queen distribution since it is skewed.

ANSWER: b 46. The interquartile range is resistant to the effect of outliers. a. True b. False ANSWER: True 47. The dotplot below displays the distribution of germ surface concentrations on 41 sampled credit cards. Germ surface concentrations are given in dimensionless germ scores. The data points with germ scores of 600 and higher can be considered outliers.

What effect would the removal of the outliers (germ scores of > 600) have on the mean and standard deviation of the distribution? a. Mean increases and standard deviation decreases b. Mean decreases and standard deviation increases c. Both mean and standard deviation increase d. Both mean and standard deviation decrease ANSWER: d 48. The data set below represent the germ surface concentration on 41 sampled credit cards. Germ surface concentrations are given in dimensionless germ scores. The data points with germ scores of 600 and higher can be considered outliers.

How would the calculated value for the mean change with removal of the outliers? a. Mean drops from 285 to 175 b. Mean drops from 290 to 97 c. Mean drops from 175 to 97 d. Mean does not change with the removal of outliers ANSWER: a 49. The data set below represent the germ surface concentration on 41 sampled credit cards. Germ surface concentrations are given in dimensionless germ scores. The data points with germ scores of 600 and higher can be considered outliers.

Name:

Class:

Date:

Chapter 03 - Numerical Methods

How would the calculated value for the standard deviation change with removal of the outliers? a. Standard deviation drops from 285 to 175 b. Standard deviation drops from 290 to 97 c. Standard deviation drops from 175 to 97 d. Standard deviation does not change with removal of outliers ANSWER: b 50. The data set below represents the reading test scores from an entrance exam for an elementary school.

56 65 25 58 73 55 44 50 75 60 77 60 95 102 105 50 35 73 40 76 72 52 45 37 The school principal is concerned that the students who took the exam are not well prepared for reading classes in the school. The testing center responded to the principal’s concerns by stating that the average test score was above the school’s minimum acceptable score of 60.

Which of the followingare valid reasons for the principal’s concern?

I) The average (mean) score is heavily influenced by the three high outliers 105, 102, and 95 II) The average (mean) score with the three outliers removed is 56, which is below the school’s minimum acceptable score. a. I only b. Both I and II c. II only d. Neither I nor II ANSWER: b 51. Which of the following are valid explanations for why multiple outliers in a data set have a large effect on the variance and standard deviation measures of variability?

I) Both variance and standard deviation include the square of the deviation from the mean for each data point. The squaring operation disproportionately increases the contribution of outliers.

II) Since the deviation from the mean is squared in variance and standard deviation expressions, the contributions of high and low outliers do not cancel each other out. a. I only b. Both I and II c. II only d. Neither I nor II ANSWER: b 52. If a data distribution is perfectly symmetric, which of the following is true for the values of mean and the median of the distribution? a. They will differ by twice the interquartile range b. They will differ by the interquartile range c. They will be the same value d. They will differ by half the interquartile range ANSWER: c

Name:

Class:

Date:

Chapter 03 - Numerical Methods 53. If a distribution is positively (right) skewed, which of the following is true for the relative values of the mean and median of the distribution? a. The mean will be twice the value of the median b. The mean will be larger than the median, and the difference will depend on the specific shape of the distribution. c. The mean will be smaller than the median, and the difference will depend on the specific shape of the distribution. d. The mean and the median will be the same value.

ANSWER: b 54. If a distribution has outliers on the lower (left) side of the distribution, which of the following is true for the relative values of the mean and median of the distribution? a. The mean will be half the value of the median b. The mean will be larger than the median, and the difference will depend on the specific shape of the distribution. c. The mean will be smaller than the median, and the difference will depend on the specific shape of the distribution. d. The mean and the median will be the same value.

ANSWER: c 55. The dotplots below represent the Math SAT scores for college freshmen at a particular school. The distributions represent three different points in time during the gathering of freshman test data. The bottom distribution includes scores from 250 students, the middle distribution includes scores from 500 students, and the upper distribution includes scores from 1000 students.

In all three distributions, the median score is roughly 500. Which of the following is true for the mean scores of the three distributions? a. The mean score is below 500 for all three distributions because the distributions are all negatively (left) skewed. b. The mean score is above 500 for all three distributions because the distributions are all positively (right) skewed. c. The mean score is above 500 for all three distributions because the distributions have high-value outliers. d. The mean score is roughly 500 for all three distributions because all three distributions are reasonably symmetric.

ANSWER: d

Name:

Class:

Date:

Chapter 03 - Numerical Methods 56. The histogram below shows data from a survey on the frequency of impulse purchases based on consumer age.

What can we say about the relationship between the mean and median values of this distribution? a. The mean value is higher than the median b. The mean value is lower than the median c. The mean value is the same as the median d. Cannot tell without actual data point values ANSWER: b 57. The mean is the middle value of an ordered data set. a. True b. False ANSWER: False 58. For any given data set, the median must be greater than or equal to the lower quartile and less than or equal to the upper quartile. a. True b. False ANSWER: True 59. Data on tipping percent for 20 restaurant tables are:

The calculated value for the median of the above data set is: a. 20% b. 22% c. 22.5% d. 23.5% ANSWER: c

Name:

Class:

Date:

Chapter 03 - Numerical Methods 60. Data on weekday exercise time (in minutes) for 20 males are shown below.

What is the value of the interquartile range for this data set? a. 56.5 b. 58.75 c. 64.75 d. 62.25 ANSWER: d 61. Data on weekday exercise time (in minutes) for 20 males are shown below.

What is the value of the median for this data set? a. 26.75 b. 27.50 c. 28.75 d. 29.25 ANSWER: c 62. The following nitrous oxide emissions (in thousands of tons) were recorded for the 48 states in the continental United States.

What is the median, lower quartile, and upper quartile values for this data set? a. Lower quartile = 17.5, median = 34, upper quartile = 65 b. Lower quartile = 18.5, median = 33, upper quartile = 64.5 c. Lower quartile = 17.5, median = 34, upper quartile = 66 d. Lower quartile = 18, median = 33, upper quartile = 66.5 ANSWER: c 63. The two dot plots below represent the fraction of residents of two cities in the northern United States that celebrated the winter holidays locally rather than traveling.

City A

Name:

Class:

Date:

Chapter 03 - Numerical Methods City B

Which of the following choices of summary measures best describe the typical (representative) value of the data set and data distribution’s variability? If a distribution contains outliers, choose a variability measure which describes how much the values in the middle half of the data is spread out. a. For city A use mean for center and standard deviation for variability; for city B use median for center and interquartile range for variability b. For city A use median for center and interquartile range for variability; for city B use mean for center and standard deviation for variability c. Use mean and standard deviation for both cities A and B d. Use median and interquartile range for both cities A and B. ANSWER: b 64. The data set below represent the fraction of residents of cities in the northern United States that celebrated the winter holidays locally rather than traveling.

50 86 86 75 100 92 92 93 83 88 90 100 83 75 71 92 71 73 70 67 89 90 100 82 100 78 70 89 100 77 43 60 83 90 Which of the following best describes the typical fraction of residents who celebrated holidays locally as well as the extent to which the values in the middle half of the data set are spread out? a. Typical value = 85, Extent of spread of the middle half of the data set = 19 b. Typical value = 78, Extent of spread of the middle half of the data set = 28 c. Typical value = 89, Extent of spread of the middle half of the data set = 14 d. Typical value = 80, Extent of spread of the middle half of the data set = 7 ANSWER: a 65. The data set below represents the fraction of residents of towns in the Caribbean islands that celebrated the winter holidays locally rather than traveling.

84 85 94 82 93 93 98 95 93 89 99 92 79 92 75 90 82 84 81 88 90 86 93 94 83 80 88 90 93 85 90 87 93 92 Which of the following best describes the typical fraction of residents who celebrated holidays locally as well as the extent to which the values in the middle half of the data set spread out. a. Typical value = 81, Extent of spread of the middle half of the data set = 15 b. Typical value = 90, Extent of spread of the middle half of the data set = 9 c. Typical value = 95, Extent of spread of the middle half of the data set = 18 d. Typical value = 79, Extent of spread of the middle half of the data set = 4 ANSWER: b 66. Which of the five boxplots below correspond to a data set with the following 5-number summary?

Minimum = 60, Lower Quartile = 69, Median = 76, Upper Quartile = 82, Maximum = 89

Name:

Class:

Date:

Chapter 03 - Numerical Methods

ANSWER: Boxplot 4 67. Suppose you and a colleague are analyzing the results of a survey of weekly earnings of full-time servers in 20 downtown restaurants shown in the data set below. Your colleague created the boxplot below the data set. Your colleague asked you to review the boxplot for accuracy.

752 1008 1200 925 729 760 1044 1161 959 1084 865 1075 1199 898 654 693 955 748 633 698

Which of the following is true regarding the five-number summary (in US dollars) for the restaurant server earnings and the accuracy of your colleague’s boxplot? a. Minimum = 633, lower quartile = 739, median = 912, upper quartile = 1060, maximum = 1200, boxplot is accurate b. Minimum = 633, lower quartile = 739, median = 912, upper quartile = 1060, maximum = 1200, boxplot is not accurate c. Minimum = 633, lower quartile = 729, median = 895, upper quartile = 1020, maximum = 1200, boxplot is accurate d. Minimum = 633, lower quartile = 729, median = 895, upper quartile = 1020, maximum = 1200, boxplot is not accurate ANSWER: a

Name:

Class:

Date:

Chapter 03 - Numerical Methods 68. Suppose you and a colleague are analyzing the results of a survey of weekly earnings of ski instructors at 20 mountain resorts shown in the data set below. Your colleague created the boxplot shown below the data set. Your colleague asked you to review the boxplot for accuracy.

892 618 674 503 450 708 919 610 711 473 652 444 933 811 447 1006 720 586 980 1033

Which of the following is true regarding the five-number summary (in US dollars) for the ski instructor earnings and the accuracy of your colleague’s boxplot? a. Minimum = 444, lower quartile = 524, median = 701, upper quartile = 898, maximum = 1010, boxplot is not accurate b. Minimum = 444, lower quartile = 545, median = 691, upper quartile = 906, maximum = 1033, boxplot is accurate c. Minimum = 444, lower quartile = 524, median = 701, upper quartile = 898, maximum = 1010, boxplot is accurate d. Minimum = 444, lower quartile = 545, median = 691, upper quartile = 906, maximum = 1006, boxplot is not accurate ANSWER: b 69. Scientists studying the interactions of worker and queen wasps in a nest conducted a series of experiments to determine whether the interaction of the queen with workers was required to maintain hive activity, or if the mere presence of the queen in the hive was sufficient to do so. The scientists randomly selected 9 colonies for the study and measured hive activity under three different conditions: • • •

Normal conditions (N) = undisturbed nest where the queen interacts with workers Queen Removed (QR) = the queen is completely removed from the nest for about an hour Queen Cooled (QC) = the queen was removed from the nest and placed in a cool environment, making her inactive, then returned to the nest; thus, she is present in the nest, but not able to interact with the worker wasps.

The table below shows wasp nest activity levels (proportion of time workers were active) for the three conditions described above.

Normal

Queen

Queen Cooled/

Name:

Class:

Date:

Chapter 03 - Numerical Methods

Colony # 1 2 3 4 5 6 7 8 9

(Undisturbed) 0.18 0.16 0.06 0.46 0.11 0.37 0.32 0.59 0.43

Removed 0.06 0.19 0.17 0.33 0.17 0.23 0.25 0.40 0.31

Inactive 0.03 0.18 0.05 0.24 0.14 0.11 0.06 0.29 0.37

Calculate five-number summaries for each of the treatment groups (N, QR, and QC) and use them to create a comparative boxplot.

ANSWER: 5-number summaries: N: 0.06, 0.135, 0.32, 0.445, 0.59; QC: 0.03, 0.055, 0.14, 0.265, 0.37; QR: 0.06, 0.17, 0.23, 0.32, 0.40

70. The summary statistics for the % by weight of lead in ancient Roman coins are shown in the table below:

Statistic N Mean Median St. Dev. Minimum Maximum 1st Quartile 3rd Quartile

Value 21 0.61 0.62 0.25 0.09 1.29 0.41 0.73

Which of the following would be considered outliers for this data set? a. 1.01% b. 1.25% c. 0.05% d. 0.09% ANSWER: b 71. The summary statistics for the carat weight of diamonds in a particular museum exhibition are shown in the table

Name:

Class:

Date:

Chapter 03 - Numerical Methods below:

Statistic N Mean Median St. Dev. Minimum Maximum 1st Quartile 3rd Quartile

Value 54 3.28 4.02 1.25 0.11 8.37 1.67 5.49

Which of the following would be considered outliers for this data set?

I) 10.88 II) 5.48 III) 7.79 IV) 11.57 a. IV) only b. I) and IV) only c. I), III), and IV) only d. I), II), III), and IV) ANSWER: b 72. The summary statistics for the typical inches of overnight snowfall on New Year’s Eve at 12 surveyed ski resorts are shown in the table below:

Statistic N Mean Median St. Dev. Minimum Maximum 1st Quartile 3rd Quartile

Value 12 8.1 6.2 1.25 0.5 26.8 5.6 8.4

Which of the following would be considered outliers for this data set?

I) 0.8 II) 1.2 III) 13.9 IV) 15.1 a. IV) only b. I) and IV) only c. I), III), and IV) only d. I), II), III), and IV) ANSWER: d 73. To compare the average weekly earnings of full-time male and female workers, twenty men and twenty women were selected. The following boxplot displays the data for both male and female workers.

Name:

Class:

Date:

Chapter 03 - Numerical Methods

Which of the following can we conclude regarding the comparative wages of male and female workers? a. From the comparative boxplot, both data distributions appear approximately symmetric, but the distribution for male workers tend to be higher than the one for female workers. From this we can conclude that wages of male workers are greater than wages of female workers. b. From the comparative boxplot, both data distributions appear approximately symmetric, but the distribution for female workers tend to be higher than the one for male workers. From this we can conclude that wages of female workers are greater than wages of male workers. c. From the comparative boxplot, both data distributions appear to be skewed to the left, but the median of the data for the men lies higher than the median of the data for the women. From this we can conclude that wages of male workers are greater than those of female workers. d. From the comparative boxplot, both data distributions appear to be skewed to the left, but the median of the data for women lies higher than the median of the data for the men. From this we can conclude that wages of female workers are higher than those of male workers.

ANSWER: a 74. Scientists studying the interactions of worker and queen wasps in a nest conducted a series of experiments to determine whether the interaction of the queen with workers was required to maintain hive activity, or if the mere presence of the queen in the hive was sufficient to do so. The scientists randomly selected 9 nests for the study and measured hive activity under three different conditions: • • •

Normal conditions (N) = undisturbed nest where the queen interacts with workers Queen Removed (QR) = the queen is completely removed from the nest for about an hour Queen Cooled (QC) = the queen was removed from the nest and placed in a cool environment, making her inactive, then returned to the nest; thus, she is present in the nest, but not able to interact with the worker wasps.

The comparative boxplot below shows wasp nest activity levels (proportion of time workers were active) for the three conditions described above.

Name:

Class:

Date:

Chapter 03 - Numerical Methods

Based on the comparative boxplot data, which of the following can we conclude regarding the effect of the wasp queen on nest activity levels?

I) All three data distributions are reasonably symmetric, and the distribution for N group is higher than either the QC or QR groups. From this, we can conclude that the queen must be interacting with workers in order to maintain nest activity.

II) All three data distributions are skewed to the left, but the mean of the QR group is higher than that of the QC group. From this, we can conclude that nest activity is highest if the queen is removed.

III) All three data distributions are skewed to the right, but the upper quartile of the QC group is higher than the median of the QR group. From this, we conclude that the presence of the queen in the hive, not the interaction of the queen with workers, was required to maintain hive activity. a. I only b. II only c. I and II only d. III only ANSWER: a 75. The boxplot below displays comparative data regarding the effectiveness of two different practice priorities (fixed vs. variable) in score improvement for a strategy game.

Which of the following can we conclude from the boxplot?

I) The variable priority leads to a greater range of values compared to the fixed priority II) The middle half of the data has a larger spread in the case of the variable priority compared to that of the fixed priority

Name:

Class:

Date:

Chapter 03 - Numerical Methods III) The median of the variable priority is higher than that of the fixed priority a. I and II only b. II and III only c. I and III only d. I, II, and III ANSWER: d 76. Suppose that the distribution of weekly water usage for single-family homes in a particular city is mound-shaped and approximately symmetric. The mean is 1,300 gallons and the standard deviation is 200 gallons. What is the approximate value of the 95th percentile? a. 1,700 gallons b. 1,100 gallons c. 1,500 gallons d. 1,900 gallons ANSWER: a 77. The mean number of text messages sent per month by customers of a cell phone service provider is 1,850 and the standard deviation is 800. What is the z-score associated with 3,000 messages sent? a. z = 2.75 b. z = 1.44 c. z = -1.44 d. z = 1.19 ANSWER: b 78. In recent years there has been considerable discussion about the appropriateness of the body shapes and proportions of dolls. Some dolls are very popular, and there is concern that the dolls may be viewed as having the “ideal body shape”, potentially leading young children to develop mental health issues regarding body self-image. The data summary below compares the chest circumference (cm) of two different popular dolls (scaled to typical human height) to those of typical humans.

• •

Doll A = 75.0; Doll B = 82.3 Human mean = 90.7; Human standard deviation = 5.2

What is the z-score for doll A and doll B? ANSWER: Doll A z-score = -3.02, Doll B z-score = -1.62; 79. In 1990 the New York Times reported the average number of square feet per standing passenger in 1987 and 1988 for 19 subway stops. Although the sampling methods were not reported, we will presume that these data represent a random sample of days during the morning and evening rush hours. The NYC Transit Authority managers attempted to improve the space problem on subway cars by adding cars to trains during rush hour. They gathered 1988 data to check on their efforts after one year. The data are in the table below.

Morning 1987 3.2 3.1

Sq. Ft. per standing passenger Morning Afternoon Afternoon 1988 1987 1988 2.8 8.8 3.7 2.0 6.7 5.2

Name:

Class:

Date:

Chapter 03 - Numerical Methods

2.9 4.0 4.8 2.2 2.5 3.7 3.4 2.5 6.9 6.9 2.4 2.4 2.3 1.9 2.2 2.4 1.8

2.9 8.6 4.1 2.2 5.5 1.9 4.4 3.3 3.9 3.9 1.5 2.1 1.8 2.1 1.9 2.1 2.2

3.0 9.2 8.4 2.4 6.8 6.8 9.4 3.1 7.7 16.4 3.6 3.6 2.9 2.7 3.6 3.8 3.7

3.3 17.3 11.7 2.9 5.6 5.6 6.2 2.7 13.0 33.3 3.5 3.1 3.5 2.5 3.2 2.7 4.3

a. If the goal of the NYC Transit Authority was to provide at least 3 square feet of space per passenger on the subway trains, how did available space on the 1987 morning rush hour trains compare to this goal? Use the zscore for the value of 3 square feet to express your answer. b. Did the addition of the extra cars help provide the requisite 3 square feet per passenger on the morning rush hour train?

ANSWER: (a) the mean for the 1987 morning data is 3.24 square feet, and the standard deviation is 1.50 square feet, giving a z-score of -0.16. The negative z-score indicates that the Transit Authority was meeting its goal. (b) the mean for the 1988 morning data is 3.12 square feet and the standard deviation is 1.71 square feet, giving a z-score of -0.07. The fact that the z-score is still negative indicates that the NYC Transit Authority is meeting its goal of providing 3 square feet per passenger, but the fact that the negative z-score is lower magnitude means that space per passenger has been reduced, which was likely not the intention.

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data 1. Suppose you conduct a survey of over 10,000 individuals from different regions in your state gathering information regarding family income and their favorite holiday dessert. You find a strong correlation between family income and preference for yam custard. Which of the following can you conclude?

I. II. III.

The families who preferred yam custard had better access to markets with high-quality, fresh yams.

The families who preferred yam custard could afford high-quality milk and egg ingredients needed to make the good-tasting custard.

The families who preferred yam custard could afford to purchase custard from pastry shops that produced highquality products.

a. I and II only b. I, II, and III c. Neither I, nor II, nor III d. II and III only ANSWER: c 2. Which of the following studies is most likely to support a causal relationship between predictor variable A and response variable B? a. An observation with a large sample count and a positive, linear relationship. b. An experiment with rigorous control of predictor variable A? c. A survey whose results show a relationship between A and B with a correlation coefficient of 0.99. d. An experiment that excludes confounding variables.

ANSWER: d 3. Which of the following are reasons why observations with r values close to 1 cannot be used to establish causality? a. The observations may not include a sufficient number of samples. b. The relationship between variables may be nonlinear. c. An unidentified third variable could be influencing both variables under investigation. d. The relationship between variables could be negative.

ANSWER: c 4. Suppose you observe the relationship between average monthly commuting time and days of bus ridership for 220 people in your city. Which of the following characteristics of the relationship indicate that the increased bus ridership causes a reduction in commuting time?

I. II. III.

A positive, linear relationship between days of bus ridership and average monthly commuting time.

A nonlinear relationship between days of bus ridership and average monthly commuting time.

A correlation coefficient of -0.99 between days of bus ridership and average monthly commuting time.

a. I and II only b. I, II, and III c. Neither I, nor II, nor III d. II and III only ANSWER: c 5. You perform a study gathering data on the effect of cacao solids content on the melt temperature of the chocolate used for a particular truffle confection. You collect 50 data points relating melt temperature in degrees Celsius to the cocoa

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data content in percent and find a correlation coefficient of 0.93. Which of these can you conclude?

I) The relationship between melt temperature and cacao content is strongly linear II) The relationsip between melt temperature and cacao content is positive III) Increasing the cacao percentage causes an increase in chocolate melt temperature IV) The relationship between cacao content and melt temperature is non-linear a. I and II only b. I, II, and III only c. II and III only d. II and IV only ANSWER: a 6. Consider the following five scatterplots. All are drawn to the same scale on both the x - and y - axes.

For which of the scatterplots do the variables x and y have a nonlinear relationship? a. Scatterplot B only b. Scatterplots A, B, and C only

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data c. Scatterplots D and E only d. All five scatterplots show a nonlinear relationship ANSWER: c 7. Consider the following five scatterplots. All are drawn to the same scale on both the x - and y- axes.

For which of the scatterplots do the variables x and y have a relationship which is linear and negative? a. Scatterplot A only b. Scatterplots B, and C only c. Scatterplots D and E only d. Scatterplots A and C only ANSWER: a 8. The data below were gathered on a random sample of five basking sharks. Basking sharks swim through the water and passively let the water bring food into their mouths.

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data

Shark Body Length (m) 4.0 4.5 4.0 6.5 5.5

Mean Swimming Speed (m/s) 0.89 0.83 0.76 0.94 0.94

A scatterplot of mean swimming speed (m/s) vs. shark body length (m) is shown below:

Which of the following describes the relationship between mean speed and body length as shown in the scatterplot? a. Strongly linear and negative b. Moderately linear and positive c. Weakly linear and negative d. Strongly linear and positive ANSWER: b 9. Which of the following scatterplots show a strongly linear, negative relationship?

Name:

Class:

Chapter 04 - Describing Bivariate Numerical Data

a. Scatterplot A only b. Scatterplots C only c. Scatterplots A and B only d. Scatterplots C and D only ANSWER: a 10. Which of the following scatterplots show weakly linear relationships?

Date:

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data

a. Scatterplots A and D only b. Scatterplots B and C only c. Scatterplots A, and C only d. Scatterplots A, B, and C only ANSWER: b 11. The following scatterplot shows the relationship between two variables. Which of the following is true for the relationship?

I. II. III.

It is nonlinear It appears to be strong (very little scatter) Includes areas of both positive and negative direction a. I and II

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data b. II and III c. I and III d. I, II, and III ANSWER: d 12. Pearson’s correlation coefficient, r, does not depend on the units of measurement of the two variables. a. True b. False ANSWER: True 13. In order to calculate Pearson’s correlation coefficient, r, which of the following steps should be followed?

I) Calculate the z - score (zx) for the x - value of each data point as well as the z - score (zx) for the x - value of each data point.

II) Sum the zx values III) Sum the zy values IV) Multiply each zx value by the corresponding zy value for that data point a. II and III only b. I and IV only c. I, II, and IV only d. I, III, and IV only ANSWER: b 14. The data below were gathered on a random sample of five basking sharks. Basking sharks swim through the water and passively let the water bring food into their mouths.

Shark Body Length (m) 4.0 4.5 4.0 6.5 5.5

Mean Swimming Speed (m/s) 0.89 0.83 0.76 0.94 0.94

What is the value of the correlation coefficient for this data? a. 0.75 b. 0.65 c. 0.80 d. 0.85 ANSWER: a 15. The data in the table below show the weights and baking times for 15 pastries.

Pastry Weight (g) 85 74 76 88

Pastry Baking Time (min) 12.1 14 10.4 11.8

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data

49 75 70 60 81 54 50 96 60 65 61

6 9.6 8.2 9.9 14.2 6.8 7 15.5 8.3 9.5 11.7

What is the correlation coefficient, r, for the data in the table above? a. 0.83 b. 0.76 c. 0.88 d. 0.92 ANSWER: a 16. Calculate the correlation coefficient for the data in the table below.

x 5 8 9 15 33 9 27 45 18

y 589 601 777 821 601 592 726 845 649

a. 0.49 b. 0.53 c. 0.56 d. 0.45 ANSWER: d 17. The value of Pearson’s r is always between 0 and 1. a. True b. False ANSWER: False 18. Which of the following indicates the range of possible values for Pearson’s correlation coefficient, r? a. 0 < r < 1

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data b. -1 < r < 1 c. -1 ≤ r ≤ 1 d. -1 < r ≤ 1 ANSWER: c 19. If, on average, y increases as x increases, the correlation coefficient is positive. a. True b. False ANSWER: True 20. Of the following, which is true of Pearson’s correlation coefficient, r? a. The value of r does not depend on the units of y and x. b. r = 0 indicates a perfect correlation between x and y c. r cannot be less than 0 or greater than 1 d. |r| is greater than 1.0 unless the points on a scatterplot line up exactly ANSWER: a 21. If r is close to 1, then the data points lie close to a straight line with a positive slope. a. True b. False ANSWER: True 22. What is it that the Pearson correlation coefficient quantifies?

ANSWER: The Pearson correlation coefficient quantifies the degree to which there is a linear relationship between two variables.

23. If a scatterplot exhibits a negative relationship, what can be said about ANSWER: The summation expression is negative.

24. If a scatterplot exhibits a positive relationship, which of the following is true regarding the correlation coefficient r? a. r is negative or zero b. r is positive or zero c. r is positive d. r is negative ANSWER: c 25. Which of the following are essential characteristics of a least squares regression line? a. Has a y - intercept of zero b. Has a positive slope c. Maximizes the sum of squared deviations d. Minimizes the sum of squared deviations ANSWER: d 26. The scatterplot below shows a linear relationship between variables. Which of the following steps would you perform

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data to determine whether Line 1 or line 2 was a better fit?

I) For each line, calculate the deviations, which are the differences between y - values predicted and the actual y values from the data set.

II) For each line, calculate the sum of the deviations.

III) For each line, square each of the deviations.

IV) For each line, calculate the sum of the squares of all the deviations. a. I and II only b. I, III, and IV only c. I and III only d. I only ANSWER: b 27. The scatterplot below shows a linear relationship between variables. You and two colleagues are attempting to find a line equation that fits the data set. One of your colleagues thinks that Line 1 is the better fit, while the other colleague thinks that line 2 is the better fit. Equations for Lines 1 and 2 are shown below with constants a, b, c, and d representing slopes and y-intercepts.

Line 1: y = a + bx Line 2: y = c + dx

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data

If you use a sum of the squared deviations about the fit line as an indication of the fit of the line to the data set, which of the following expressions is accurate? a. If is greater than then Line 1 is a better fit b. If

is greater than

c. If

is greater than

then Line 1 is a better fit

d. If

is greater than

then Line 2 is a better fit

then Line 2 is a better fit

ANSWER: b 28. Which of the following is true for a line y = a + bx that represents the least squares regression line for a particular data set?

I. The constant a, which represents the y - intercept for the line, is chosen such that

is

minimized II. The constant b, which represents the slope of the line, is chosen such that

is minimized

III. Both the slope, b, and the y - intercept, a, of the line are chosen such that

is minimized

a. I only b. II only c. Neither I, nor II, nor III d. III only ANSWER: d 29. When calculating a least squares regression line for a particular data set, you find the slope m and y - intercept b of a line equation y = mx + b that minimizes the sum of the squared deviations. Which of the following accurately describes why the square of the deviations should be used to find the best-fit line equation?

I. II. III.

Deviations are usually all negative, so using the square of the deviations simplifies calculations.

Squaring the deviation values prevents a negative argument of a square root.

Deviations are both negative and positive and, if not squared, could cancel each other out

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data a. Neither I, nor II, nor III b. I only c. II only d. III only ANSWER: a 30. Data on the weight of a pickup truck (pounds) and the distance (feet) required for a pickup truck traveling at 40 miles per hour to come to a complete stop was gathered for 30 trucks and used to fit the regression line = 26 + 0.05x where y = stopping distance in feet and x = weight of the truck Which of the following statements is a correct interpretation of the value 26 in the equation of the regression line? a. On average, the stopping distance increases by 26 feet for each 1-pound increase in truck weight. b. On average the stopping distance is 26 feet when the truck weight is 0. c. On average, the stopping distance goes up 0.05 feet for each 1-pound increase in truck weight. d. It is not reasonable to interpret in this setting because a weight of 0 is outside the range of the data used to fit the regression line.

ANSWER: d 31. The breeding success of ground-nesting birds such as white-tailed Ptarmigans is affected by the depth of winter snow in high-elevation nesting grounds. The scatterplot below relates the percentage of white-tailed Ptarmigan hens hatching at least one egg to the snowfall depth (cm) in the Sierra Nevadas over several winter seasons.

The least squares best-fit line is %NestSuccess = 55.2 – 0.092(SnowDepth). On one exceptional snow year, the Sierra Nevadas recorded a snowfall depth of 580 cm. Which of the following percent of white-tailed Ptarmigans would you expect to hatch at least one egg if the snow depth was 580 cm? a. 1.84 b. 109 c. 53.4 d. The least squares best-fit line cannot be used for a snow depth of 580 cm since that depth is outside the range

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data of data used to fit the line.

ANSWER: d 32. The use of small aircraft with human observers is common in wildlife studies where the goal is to estimate the abundance of different species. Recently, there has been interest in using unmanned aerial vehicles (UAV) to document species abundance. The scatterplot below is from a test run of a UAV over 10 areas in southern Florida using bird decoys to test the reliability of the UAV detection of a particular bird species.

The least squares best-fit line for the data in the scatterplot is given by: actual count = -0.924 + 1.09 (UAVcount) Based on the least squares best-fit line above, if the wildlife UAVcount is 29, which of the following actual wildlife counts would we expect? a. The least squares best-fit line cannot be used to predict actual wildlife counts for a UAV of 29 as that value is beyond the range of data used to construct the best-fit line. b. 30.7 c. 32.5 d. 31.6 ANSWER: a 33. The scatterplot below shows the relationship between wind speed (km/h) and the rate of wildfire spread (km/h). A

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data least squares regression line was fitted to the data (shown in red) with the equation:

= -0.797 + 0.110x

What rate of fire spread would you predict for a wind speed of 40 km/h? a. 3.60 km/h b. 5.20 km/h c. The least squares regression line cannot be used to predict wildfire spread rates for a 40 km/h wind speed since that value is beyond the range of data used to construct the best-fit line. d. 4.40 km/h ANSWER: c 34. You’re working on a wildfire prediction and mapping team for the State of California. You’re comparing the relative wildfire threat for two different neighborhoods based on windspeed and proximity of the wildfires to each neighborhood.

You have the following scatterplot and least squares regression line to use for wildfire speed prediction. If the windspeed near neighborhood A was 20 km/h and the windspeed near neighborhood B was 30 km/h, how much faster is the wildfire near neighborhood B spreading compared to the wildfire near neighborhood A?

Least squares regression line (shown in red):

= -0.797 + 0.110x

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data a. Fire is spreading 2.69 km/h faster at neighborhood B compared to neighborhood A b. Fire is spreading 1.10 km/h faster at neighborhood B compared to neighborhood A c. Fire spreading rates for neighborhoods A and B cannot be compared because the wind speed at neighborhood A would require extrapolation. d. Fire spreading rates for neighborhoods A and B cannot be compared because the wind speed at neighborhood B would require extrapolation.

ANSWER: b 35. You’re working on a wildfire prediction and mapping team for the State of California. You’re comparing the relative wildfire threat in three different neighborhoods based on windspeed and proximity of the wildfires to each neighborhood.

You have the following scatterplot and least squares regression line to use for wildfire speed prediction. The wind speed near neighborhood A was 10 km/h, the windspeed near neighborhood B was 40 km/h, and the windspeed at neighborhood C was 25 km/h. What is the predicted difference in the fire spread rate for the neighborhoods with the fastest and slowest fire spread rates, respectively?

Least squares regression line (shown in red):

= -0.797 + 0.110x

a. Spread rate differences of 3.30 km/h for neighborhood B vs. neighborhood A. b. Spread rate difference of 1.65 km/h for neighborhood B vs. neighborhood C. c. Spread rate difference of 1.65 km/h for neighborhood C vs. neighborhood A d. The fire spreading rate for neighborhoods A and B cannot be predicted since use of a wind speed of 40 km/h would require extrapolation.

ANSWER: d 36. Suppose you’re conducting a study for a health class at your school. You need to find the height and weight of 100 students. Height is difficult to measure, but weight is easy to measure, so you’re interested in determining if students who weigh more will also be taller. You start by creating a scatterplot to relate the two variables. Which of the following is true of your variables and the arrangement of your scatterplot? a. Weight is the predictor variable and should be plotted on the x - axis. Height is the response variable and should be plotted on the y - axis b. Height is the predictor variable and should be plotted on the x - axis. Weight is the response variable and should be plotted on the y - axis c. Weight is the predictor variable and should be plotted on the y - axis. Height is the response variable and

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data should be plotted on the x - axis. d. Height is the predictor variable and should be plotted on the y - axis. Weight is the response variable and should be plotted on the x - axis.

ANSWER: a 37. Is the value of Pearson’s correlation coefficient dependent on which variable is used as the predictor and which variable is used as the response?

ANSWER: No, the Pearson correlation coefficient only shows the degree of linearity between two variables. Linearity is not affected by which variable is x (the predictor) and which variable is y (the response).

38. The scatterplot below relates to a person’s balancing capability (balance score) to the range of motion in their ankle.

Which of the following is true for response and predictor variables and the x and y variables in the least squares linear regression line expression of the form y = mx + b? a. Ankle range of motion is the predictor variable and would be the y-variable in the regression line. b. Balance score is the response variable and would be the x-variable in the regression line. c. Ankle range of motion is the response variable and would be the y-variable in the regression line. d. Balance score is the response variable and would be the y-variable in the regression line.

ANSWER: d 39. Suppose you’re a travel agent tasked with finding the best prices on 20 regional train services in your region during the 6 national holidays. Contacting each of the 20 regional train representatives to inquire about holiday pricing is a timeconsuming job. You notice that prices for regional train services tend to track with those for the single, national train service. One of your colleagues tells you that they already conducted a study and found that prices for all 20 of the regional rail systems have the following linear relationship with prices for the national rail system: y = 2.04 - (0.16)x Which of the following best describes predictor and response variables for this scenario as well as which variables are represented as x and y in the regression line? a. The national rail price is the predictor variable and would be x in the regression line expression. b. The regional train service price is the predictor variable and would be x in the regression line expression. c. The national rail price is the response variable and would be y in the regression line expression.

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data d. The regional train service price is the response variable and would be x in the regression line expression.

ANSWER: a 40. The scatterplot below relates daily high temperatures to the average daily number of outdoor shootings in a particular U.S. city. The least squares linear regression line for the data set is shown in red.

Which of the following is true for response and predictor variables and the x and y variables in the least squares linear regression line expression of the form y = mx + b? a. Average daily number of shootings is the response variable and would be the y-variable in the regression line. b. Average daily number of shootings is the predictor variable and would be the x-variable in the regression line. c. Daily high temperature is the response variable and would be the y-variable in the regression line. d. Daily high temperature is the predictor variable and would be the y-variable in the regression line.

ANSWER: a 41. Suppose you have a data set with two variables A and B. You create a scatterplot of A vs. B and notice a linear relationship. You calculate a least squares regression line y = mx + b which predicts the effect of variable A on variable B. Which of the following is true regarding your variables A and B and their use in your regression line?

I. II. III.

The variable B is the predictor variable and should be used as input for x in the regression line equation.

The variable A is the response variable.

The effect of variable B on variable A can be predicted by using variable B as x in the regression line equation.

a. I only b. II only c. III only d. Neither I, nor II, nor III ANSWER: d 42. The least squares line passes through the point ( a. True b. False

).

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data ANSWER: True 43. Twenty-five assembly line workers participated in a study to investigate the relationship between experience and the time required to complete an assembly task. Assembly time (minutes) and experience (months) were measured for each worker. The resulting data was used to produce the scatterplot below where y = minutes to complete the assembly and x = months of worker experience.

Statistical software was used to determine the following least squares regression line for the data represented in the scatterplot: y = 84.683 - 0.30411 Which of the following is the value of the y-intercept of the least squares regression line? a. -84.683 minutes b. 84.683 minutes c. -0.304 minutes d. 0.304 minutes ANSWER: b 44. The data set in the table below represents the rate of increase in flood water level in feet per day with sustained onshore winds in miles per hour.

Onshore Wind Speed (mph) 32 36 16 21 29 28 27 33

Flood Water Rise Rate (ft/day) 3.36 3.38 1.1 0.8 1.66 0.82 1.31 2.89

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data

16 27 32 28 30 31

1.26 4.82 2.67 2.52 1.76 2.98

Calculate the least squares regression line for the data set. a. flood water rise rate = b. c. d.

flood water rise rate = flood water rise rate = flood water rise rate =

(onshore wind speed) (onshore wind speed) (onshore wind speed)

(onshore wind speed)

ANSWER: a 45. The data set in the table below represents the average cost of dinner for a party of four at a downtown restaurant with the cost of dinner for the least expensive diner in the party of four.

Least Expensive Diner Cost ($) 130 136 116 121 130 128 126 134 117 126 137 122 131 140

Average Cost for Party of Four ($) 332 339 110 80 167 88 111 299 122 488 266 252 176 298

Calculate the least squares regression line for the data set. a. party of four cost = ($806) + (8.04) (least expensive diner cost) b. party of four cost = ($806) - (8.04) (least expensive diner cost) c. party of four cost = (-$806) + (8.04) (least expensive diner cost) d. party of four cost = (8.08)(least expensive diner cost) ANSWER: c

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data 46. The data set in the table below represents the average cost in dollars of airline tickets for extended vacations with the vacation duration in days.

Vacation Duration (days) 21 56 34 44 78 15 49 63

Average Airline Ticket Cost ($) 280 595 330 408 653 193 449 299

Calculate the least squares regression line for the data set. a.

b.

c.

d.

airline ticket cost = ($133) +

(vacation duration)

airline ticket cost = (-$133) +

(vacation duration)

airline ticket cost = ($133) -

(vacation duration)

airline ticket cost = (-$133) -

(vacation duration)

ANSWER: a 47. Lodging prices in ski resort towns usually decrease with increasing distance to the ski slopes. The data set in the table below represents the average cost per night in dollars for a hotel room in a ski resort town in the western United States during Christmas week and distance in miles of the hotel from the ski lifts.

Distance to ski lifts (miles) 20 57 33 45 76 12 48 67

Nightly Hotel Cost ($) 854 520 801 775 389 992 646 299

Calculate the least squares regression line for the data set. a. hotel room cost = ($1120) + (distance to life)

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data b.

c.

d.

hotel room cost = ($1120) -

(distance to life)

hotel room cost = (-$1120) +

(distance to life)

hotel room cost = ($2240) -

(distance to life)

ANSWER: b 48. Marketers for a retail jewelry chain hypothesized that the lower the age of a prospective bride or groom, the less they spent on wedding rings. A quick survey of eight wedding ring shoppers gave the results shown in the table below where the cost of the purchased ring is in dollars and the age of the bride or groom is in years.

Age of bride or groom (years) 20 57 33 45 76 17 48 67

Cost of purchased ring ($) 1708 1040 1602 1550 778 1984 1292 1292

Calculate the least squares regression line for the data set. a. purchased ring cost = ($2166) + (age of bride or groom) b.

c.

d.

purchased ring cost = ($2166) -

(age of bride or groom)

purchased ring cost = (-$2166) +

(age of bride or groom)

purchased ring cost =

(age of bride or groom)

ANSWER: b 49. Twenty-five assembly line workers participated in a study to investigate the relationship between experience and the time required to complete an assembly task. Assembly time (minutes) and experience (months) were measured for each worker. The resulting data was used to produce the scatterplot below where y = minutes to complete the assembly and x = months of worker experience.

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data

Statistical software was used to determine the following least squares regression line for the data represented in the scatterplot: y = 84.683 - 0.30411x Predict the time required to complete the assembly for an employee with 10 months of experience. a. 81.6 minutes b. 90.6 minutes c. 120.7 minutes d. 110.4 minutes ANSWER: a 50. A scatterplot showed a nonlinear relationship between y and an independent variable x. The variable u(x) was defined as u(x) = . A scatterplot of y versus u was approximately linear. The least squares regression line summarizing the relationship between y and u was

= 24 - 3u. What is the predicted value of y when x = 16?

a. -24 b. 16 c. 12 d. 4 ANSWER: c 51. The breeding success of ground-nesting birds such as white-tailed Ptarmigans is affected by the depth of winter snow in high elevation nesting grounds. The scatterplot below relates the percentage of white-tailed Ptarmigan hens hatching at least one egg to the snowfall depth (cm) in the Sierra Nevadas over several winter seasons.

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data

The least squares best-fit line is % NestSuccess = 55.1816 - 0.092 (SnowDepth). Which of the following percent of white-tailed Ptarmigans would you expect to hatch at least one egg if the snow depth was 200 cm? a. 36.782 b. 73.582 c. 55.182 d. The least squares best-fit line cannot be used for a snow depth of 200 cm since that depth is outside the range of data used to fit the line.

ANSWER: a 52. The use of small aircraft with human observers is common in wildlife studies where the goal is to estimate the abundance of different species. Recently there has been interest in using unmanned aerial vehicles (UAV) to document species abundance. The scatterplot below is from a test run of a UAV over 10 areas in southern Florida using bird decoys to test the reliability of the UAV detection of a particular bird species.

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data

The least squares best-fit line for the data in the scatterplot is given by: actual count = -0.924 + 1.09 (UAVcount) Based on the least squares best-fit line above, if the wildlife UAVcount is 15, which of the following actual wildlife counts would we expect? a. The least squares best-fit line cannot be used to predict actual wildlife counts for a UAV of 15 as that value is beyond the range of data used to construct the best-fit line. b. 15.426 c. 17.274 d. 16.350 ANSWER: b 53. The scatterplot below shows the relationship between the average cost per day for long-term lodgings at a popular beach resort vs. the stay duration in days. A least squares linear regression line was calculated for the data: cost per day = $2225 -

(days of stay)

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data

Predict the cost of a 60-day stay. a. $1165 b. $3284 c. $1642 d. $2330 ANSWER: a 54. Suppose you’re looking for an apartment in a new city. The cost for apartments decreases with distance from the city center. A least squares linear regression line for the data set representing apartment cost ($) vs. distance from the city center (miles) is given by: rent = $1120 -

(miles from city center)

Your work location is 40-miles from the city center. What rent would you except for an apartment adjacent to your work location? a. $1080 b. $683 c. $437 d. $537 ANSWER: b 55. The cost of family vacations increases with the distance from home traveled. The scatterplot below gives the vacation cost incurred by eight different families based on their vacation travel distanced. A least squares regression line for the scatterplot data is given by: vacation cost = $133 +

(miles traveled)

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data

A family is planning a vacation 30 miles from their home. Predict their vacation cost. a. $282 b. $252 c. $312 d. $371 ANSWER: c 56. Data on the weight of a pickup truck (lb) and the distance (ft) required for a pickup truck traveling at 40 miles per hour to come to a complete stop was gathered for 30 trucks and used to fit the regression line = 26 + 0.05x where y = stopping distance in feet and x = weight of the truck in pounds. Which of the following statements is a correct interpretation of the value 0.05 in the equation of the regression line? a. On average, the truck weight goes up 0.05 pounds for each additional foot required to stop the truck. b. On average the stopping distance is 0.05 feet when the truck weight is 0. c. On average, the stopping distance goes up 0.05 foot for each 1 pound increase in truck weight. d. The correlation coefficient for this data set is 0.05.

ANSWER: c 57. The slope of the least squares line is the average amount by which y increases as x increases by one unit. a. True b. False ANSWER: True 58. The slopes of the least squares lines for predicting y from x, and the least squares line for predicting x from y, are equal. a. True b. False ANSWER: False 59. If r = 1, then the slope of the least squares regression line is equal to the ratio of the standard deviation of y to the standard deviation of x. a. True b. False ANSWER: True

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data 60. A particular data set for flood insurance cost vs. elevation is strongly linear and can be fitted by a least squares regression line: cost = $10,000 -

(elevation in feet). Which if the following describes the slope of the regression

line?

I. II. III.

The cost of flood insurance increases by $500 for every foot of elevation increase The cost of flood insurance is $10,000 regardless of elevation The cost of flood insurance decreases by $500 for every foot of elevation increase

a. I only b. II only c. Neither I, nor II, nor III d. III only ANSWER: c 61. A particular data set for landslide frequency (events per week) vs. rainfall (inches) is linear and can be fitted by a least squares regression line: frequency = Which of the following describes the slope of the regression line?

I. II. III.

When rainfall is zero, the landslide frequency is 0.06 events per week.

The landslide frequency increases by 15.2 events per week for every inch of rainfall.

The landslide frequency decreases by 15.2 events per week for every inch of rainfall,

a. I only b. Neither I, nor II, nor III c. II only d. III only ANSWER: b 62. Suppose you’re a marine biologist studying the average cruising speed of harbor seals. You would like to be able to predict seal cruising speed to within ±0.08 m/s. You suspect that seals with longer bodies will have faster average cruising speeds. You make measurements of mean cruising speed (m/s) and body length (m) on several harbor seals. The results of your measurements are shown in the scatterplot below with a least squares line: = 0.61 + (0.0534)x.

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data

If the coefficient of determination (r2) is 53%, and the standard deviation about the least squares regression line (se) is 0.048 m/s, which of the following accurately describes whether or not you should use the least squares line to predict seal cruising speed?

I.

Since the data has a linear relationship and se

II.

The correlation coefficient r suggests a very weak linear relationship, so you cannot use the least squares line for your predictions.

Although the se is less than your ±0.08 m/s prediction tolerance, the r2 of 53% indicates that only slightly over half of the variability in seal mean cruising speed can be explained by a linear relationship with body length, so you should not use the least squares line for your predictions.

III.

, you can use the least squares line for your predictions.

a. I only b. II only c. III only d. Neither I, nor II, nor III ANSWER: c 63. The Des Moines Register recently reported the ratings of high school sportsmanship as compiled by the Iowa High School Athletics Association. For each school the spectators and participants were rated by referees, where 1 = superior and 5 = unsatisfactory. A scatterplot of spectator scores vs. participant scores is shown below along with the results of a regression analysis.

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data

Least squares regression line: (WrestSpectators) = 0.667 + 0.701(WrestParticipants) Coefficient of Determination (r2) = 0.467 Standard Deviation About the Least Squares Line (se) = 0.322 a. Describe the linearity of the relationship between spectator and participant sportsmanship scores. b. What proportion of the variability in the sportsmanship scores of the spectators can be explained by the calculated linear relationship in the least squares regression line? c. With what accuracy can the least squares regression line predict the sportsmanship score of wrestling spectators for a given sportsmanship score of the wrestling participants?

ANSWER:

a. The relationship between spectators and participants is moderately linear with a correlation coefficient r of 0.683. b. The linear relationship given by the least squares regression line accounts for approximately 47% of the variability in the spectator sportsmanship scores as given by the coefficient of determination r2 = 0.467. c. The Standard Deviation About the Least Squares Line se gives the tolerance for the least squares regression line prediction of wrestling spectators. So, for any given wrestling participant sportsmanship score would vary by ±0.322.

64. Children and adolescents who have undergone certain medical procedures may require long-term use of a feeding tube which enters the nose and runs down the esophagus and into the stomach. If the patient is growing rapidly, it is difficult to know how far to insert the feeding tube. In an effort to help feeding-tube patients and their parents estimate the proper tube length to use, researchers at a major children’s hospital measured esophageal lengths and children’s heights and performed a regression analysis. The data from this analysis is summarized below: Esophagus Length (E): sample mean = 34 cm, sample standard deviation = 3.5 cm Child Height (H): sample mean = 124.5 cm, sample standard deviation = 19 cm Correlation Coefficient r = 0.995 Standard Deviation About the Least Squares Line = 2.1 cm Least Squares Regression Line: E = 11.476 + 0.181H

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data

a. For a child with a height one standard deviation above the mean, what is the predicted esophageal length? b. What proportion of the variability in esophageal length is accounted for by the linear relationship between height and esophageal length? c. For a child with a height one standard deviation above the mean, what is the range of predicted esophageal lengths?

ANSWER:

a. A height one standard deviation above the mean is given by 124.5 cm + 19 cm = 143.5 cm E = 11.476 + 0.181 (143.5) = 37.4 cm The coefficient of determination, r2, gives the proportion of variability in esophageal length is accounted for by the linear relationship between height and esophageal length. r = 0.995, r2 = 0.990 or about 99% b. The Standard Deviation About the Least Squares Line se gives the tolerance for the least squares regression line prediction. So, a child with a height one standard deviation above the mean would have a predicted esophageal length of 37.4 cm ± 2.1 cm, or 35.3 cm to 39.5 cm.

65. Archaeologists were interested in the effect of toxic metals on the health of the upper-class citizens of ancient Rome.

They conducted a study in which they analyzed the metal content of ancient Roman coins to determine the relative amounts of lead and gold. The table below shows the weight percent of gold and lead in the sampled coins.

Weight % Gold 0.3 0.31 0.28 0.32 0.34 0.29 0.33 0.26 0.3 0.27 0.27

Weight % Lead 0.17 0.19 0.21 0.22 0.28 0.26 0.32 0.17 0.19 0.19 0.17

A regression analysis of the data in the table gave the following results: • • •

Least Squares Regression Line: (wt% lead) = (-0.184 wt%) + 1.34(wt% gold) Correlation Coefficient r = 0.698 Standard Deviation About the Least Squares Line se = 0.038wt%

Which of the following is true regarding predictions of Roman coin lead content based on the coin’s gold content?

I.

The least squares regression line for lead content vs. gold content will predict lead content with a tolerance of ± 0.038 weight%, but the linear relationship between lead content and gold content only accounts for about 49% of the variability in the coin lead content.

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data II. III.

The linear relationship between lead content and gold content accounts for about 70% of the variability in the coin lead content, but the least squares regression line will only predict lead content with a tolerance of ± 0.49 weight percent.

The least squares regression line for lead content vs. gold content will predict lead content with a tolerance of ± 0.038 weight%, and the linear relationship between lead content and gold content accounts for about 70% of the variability in the coin lead content.

a. I only b. II only c. Neither I, nor II, nor III d. III only ANSWER: a 66. Mining engineers have developed a new process for extracting gold from lead ores. The weight % of gold extractable by their new process varies with the ore’s lead content in weight %. The table below shows the weight % gold extracted and the weight % lead of 11 ore samples treated by the new process.

Weight % Gold 0.17 0.19 0.21 0.22 0.28 0.26 0.32 0.17 0.19 0.19 0.17

Weight % Lead 0.3 0.31 0.28 0.32 0.34 0.29 0.33 0.26 0.3 0.27 0.27

A regression analysis of the data in the table gave the following results: • • •

Least Squares Regression Line: (wt% gold) = (0.219 wt%) + 0.363(wt% gold) Correlation Coefficient r = 0.698 Standard Deviation About the Least Squares Line se = 0.020weight%

Which of the following is true regarding predictions of extractable gold (weight %) based on ore lead content (weight %) for the new process?

I. II. III.

The least squares regression line for gold weight % vs. lead weight % will predict gold weight % with a tolerance of ± 0.020 weight %, but the linear relationship between gold weight % and lead weight % only accounts for about 49% of the variability in the gold weight % of the ore.

The linear relationship between gold weight % and lead weight % accounts for about 70% of the variability in the ore’s gold weight %, but the least squares regression line will only predict gold weight % with a tolerance of ± 0.49 weight %.

The least squares regression line for gold weight % vs. lead weight % will predict gold weight % with a tolerance of ± 0.020 weight%, and the linear relationship between gold weight % and lead weight % accounts for about

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data 70% of the variability in the ore gold weight %. a. I only b. Neither I, nor II, nor III c. II only d. III only ANSWER: a 67. Hand therapists assembled data relating the diameter of index finger joints (mm) to the frequency (times per week) which patients performed therapeutic exercise. The table below shows the exercise frequency and the measured joint diameter (mm) from the therapists’ study.

Exercise Frequency 42 60 20 50 24 27 27

Joint Diameter (mm) 1.42 4.75 0.67 2.66 0.52 2.35 1.4

A regression analysis of the data in the table gave the following results: • • •

Least Squares Regression Line: (joint diameter) = (-0.979 mm) + 0.0825 (frequency) Correlation Coefficient r = 0.854 Standard Deviation About the Least Squares Line se = 0.830mm

Which of the following is true regarding predictions of finger joint diameter (mm) based on exercise frequency?

I. II. III.

The linear relationship between joint diameter (mm) vs. exercise frequency accounts for about 85% of the variability in finger joint diameter, but the least squares regression line will predict finger joint diameter with a tolerance of ± 0.689 mm.

The least squares regression line for joint diameter (mm) vs. exercise frequency will predict index finger joint diameter with a tolerance of ± 0.475 mm, and the linear relationship between joint diameter (mm) vs. exercise frequency accounts for about 73% of the variability in finger joint diameter.

The least squares regression line for joint diameter (mm) vs. exercise frequency will predict joint diameter with a tolerance of ± 0.830 mm, and the linear relationship between joint diameter and exercise frequency accounts for about 73% of the variability in finger joint diameter.

a. I only b. II only c. III only d. Neither I, nor II, nor III ANSWER: c 68. The standard deviation about the least squares line is roughly the typical amount by which an observation deviates from the least squares line. a. True b. False

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data ANSWER: True 69. The scatterplot and regression analysis below represent data collected by hand therapists on the effect of therapeutic exercise on index finger joint diameter. One of the goals of the therapists’ study was to determine whether or not therapeutic exercise could reduce finger joint diameter sufficient to allow surgical placement of a high-performance prosthesis. In order for successful surgical placement, the finger joint diameter must be predicted to within 0.500 mm.

• • •

Least Squares Regression Line: (joint diameter) = (-0.979 mm) + 0.0825 (frequency) Correlation Coefficient r = 0.854 Standard Deviation About the Least Squares Line se = 0.830 mm

Which of the following should be considered when determining if exercise frequency can accurately predict finger joint diameter accurately enough to determine suitability of the prosthesis?

I. II.

The tolerance with which the regression line will predict finger joint diameter is more than 0.8 mm, which exceeds the required 0.5 mm.

The linear relationship between exercise frequency only accounts for 73% of the variability in finger joint diameter, so, other factors might result in a finger joint diameter which did not meet the requirements for the prosthesis.

a. I only b. Both I and II c. II only d. Neither I nor II ANSWER: b 70. You run the quality testing lab for a machined parts fabricator. You need to measure the diameter of a drilled hole in a particular part to ± 1 mm. The drilled hole is difficult to access, so you would like to predict the drilled hole diameter from another, more accessible part dimension. You conduct a study correlating the part circumference, which is easy to access and measure, to the drilled hole diameter and conduct a regression analysis on your study results. See summary below:

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data Number of parts measured = 200 Mean part circumference = 27.8 mm, standard deviation of part circumference = 1.3 mm Mean drilled hole diameter = 10.9 mm, standard deviation of mean drilled hole diameter = 1.8 mm Correlation coefficient r = 0.996 Standard Deviation about the Least Squares Regression Line se = 0.2 mm Which of the following describe whether or not you can use the regression line from your analysis to predict the drilled hole diameter from the part circumference accurately enough to meet your needs? a. You cannot, even though the linear relationship described by the regression line captures over 99% of the variability of the drilled hole diameter, and the tolerance of the prediction given by se is greater than the required ± 1 mm maximum. b. You cannot, even though the ± 0.2 mm tolerance of the prediction given by se is less than the required ± 1 mm maximum, and the linear relationship described by the regression line only captures 98% of the variability of the drilled hole c. You can, because the linear relationship described by the regression line captures over 99% of the variability of the drilled hole diameter and the ± 0.2 mm tolerance of the prediction given by se is less than the required ± 1 mm maximum. d. You cannot, because the linear relationship described by the regression line captures only 98% of the variability of the drilled hole diameter and the tolerance of the prediction given by se is greater than the required ± 1 mm maximum.

ANSWER: c 71. You run the water quality testing lab for the county health department. You need to ensure that the lead concentrations in water from municipal wells remain below a target limit of 20.0 parts per million (ppm) with a tolerance of ± 2.0 ppm.

There are 50 municipal drinking water wells in the county, and 5 of them are not easily accessible for testing. You would like to predict the average lead concentration in water from the 5 inaccessible wells using the average lead concentration from the easily accessible 45 wells. You conduct a study correlating the average lead concentration in the 5 inaccessible wells to the average lead concentration in the 45 easily accessible wells and conduct a regression analysis on your study results, see summary below: • • • • •

Number of water samples per well = 6 Mean lead concentration for inaccessible wells = 22.4 ppm, standard deviation for inaccessible wells = 6.6 ppm Mean lead concentration for accessible wells = 38.1 ppm, standard deviation for accessible wells = 8.7 ppm Correlation coefficient r = 0.995 Standard Deviation about the Least Squares Regression Line se = 4.0 ppm

Which of the following describe whether or not you can use the regression line from your analysis to predict average lead concentration in the 5 inaccessible wells using average lead concentration from the 45 accessible wells? a. No, even though the linear relationship described by the regression line captures over 99% of the variability of the inaccessible well lead concentration, the ± 4.0 ppm tolerance of the prediction given by se is greater than the required ± 2.0 ppm maximum. b. Yes, because the linear relationship described by the regression line captures over 99% of the variability of the inaccessible well lead concentration and the ± 4.0 mm tolerance of the prediction given by se is less than the target lead limit of 20.0 ppm. c. Yes, because the linear relationship described by the regression line captures over 99% of the variability of the inaccessible well lead concentration, and the ± 4.0 ppm tolerance of the prediction given by se is less than the standard deviations of the average lead concentrations from both the inaccessible and accessible wells. d. No, even though the linear relationship described by the regression line captures only 95% of the variability of

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data the inaccessible well lead concentration, and the ± 4.0 ppm tolerance of the prediction given by se is greater than the required ± 2.0 ppm maximum.

ANSWER: a 72. You’re a water conservation specialist for a public ornamental garden in a city in an arid region. You’re concerned that the numerous, large decorative ponds in the garden are resulting in excessive water loss due to evaporation. A water savings of as little as 2 gallons per pond per month is significant for your purposes. You study the average monthly water use for each pond in gallons and relate it to the surface area of each pond in square feet. You perform a regression analysis and get the following results: water use = 10 gallons +

(pond area)

Correlation coefficient r = 0.862 Standard Deviation about the Least Squares Regression Line se = 0.6 gallons Which of the following can you conclude about the accuracy with which your regression line can predict pond water usage from pond surface area? a. The regression line would be a good predictor because the tolerance of prediction of ± 0.6 gallons would permit you to detect changes in water use of less than your 2-gallon threshold of concern. b. The regression line would be a good predictor since the correlation coefficient of 0.862 indicates a strong linear relationship between month water use and pond surface area. c. The regression line would be a poor predictor since its coefficient of determination of 0.743 suggests that the linear relationship described by the regression line fails to capture over 25% of the variability in pond water use. d. The regression line would be a good predictor of monthly water use since its coefficient of determination of 0.928 suggests that the linear relationship described by the regression line captures nearly 93% of the variability in pond water use.

ANSWER: c 73. If you perform a regression analysis on bivariate data and calculate a least squares regression line with a high coefficient of determination (r2) and a low standard deviation about your least squares line (se) which of the following can you conclude?

I. II.

It is unlikely that there are other variables contributing significantly to the variation in your response variable since the linear relationship described by your regression line is responsible for most of the variability in your response variable.

The accuracy you can expect when using your least squares regression line to make predictions is high.

a. I only b. Both I and II c. II only d. Neither I nor II ANSWER: b 74. You’re a member of a residential fruit-grower’s cooperative. Many members of your organization believe that the larger the radial distance that certain pitted fruits, such as cherries, grow from the tree trunk, the larger the fruits will be.

In order to assess this hypothesis, you measure several fruits from trees in your orchard, noting the approximate distance from that trunk at which the fruit was located prior to picking. A scatterplot showing your data with a least squares

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data regression line and residual plot are shown below.

Based on the residuals plot, which of the following can you conclude? a. The least squares regression line is appropriate since the residuals plot shows no distinctive patterns, no data points with y-values far from height 0, or whose x - values differ greatly from the rest of the data set. b. The least squares regression line is not appropriate since the residuals plot shows curvature, indicating that the relationship between distance from trunk and fruit diameter is not linear. c. The least squares regress line is not appropriate because four data points have y - values with a height far from the horizontal relative to the rest of the data set. d. The least squares regression line is not appropriate because one data point has an x - values much smaller than the rest of the data set.

ANSWER: a 75. A residuals plot is a scatterplot of the residuals vs. the predictor variable of the original data set. Residual plots are excellent ways to spot which of the following problems, which can render a regression line appropriate?

I. II. III.

Curvature Unusually high or low values of the response variable Unusually high or low values of the predictor variable

a. I and II only b. II and III only c. I and III only d. I, II, and III ANSWER: d 76. The residual plots for 3 different data sets are shown below. Of these residual plots, which one indicates that the regression line is not appropriate?

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data

a. Residual Plot I only b. Residual Plots I and II only c. Residual Plot III only d. Residual Plot II only ANSWER: d 77. You’re analyzing viscosity test data to determine the impact of ambient lab temperature (T) on measured viscosity.

You create a scatterplot of measured viscosity vs. ambient temperature and think that there may be curvature, indicating a non-linear relationship between viscosity and T. You calculate a least squares regression line and plot the residuals (Plot A below). In order to confirm your suspicions of nonlinearity, you create a variable u where u(T) = exp(T), then calculate a least squares regression line for viscosity vs. u and plot the residuals (Plot B below).

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data

Based on the appearance of residuals plots A and B, were you correct in suspecting a non-linear relationship between viscosity and ambient lab temperature?

I. II. III.

No, neither residual plot A nor residual plot B show any patterns or evidence of curvature No, only plot A shows a pattern suggesting curvature, and both plots A and B must show curvature in order to confirm non-linearity of the viscosity vs. T relationship.

Yes, because plot A shows some evidence of curvature and plot B does not.

a. I only b. Neither I, nor II, nor III c. II only d. III only ANSWER: d 78. You are a public health researcher studying the effect of body weight in infants and young children on timely development of verbalization and motor skills. You initially suspected a linear relationship for verbal skills development time and a logarithmic relationship for motor skills development time. You calculate least squares regression lines for both verbal skills onset time vs. body weight and for motor skills onset time vs. body weight. The residual plots for both relationships are shown below.

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data

Based on the appearance of the residual plots, which of the following can you conclude regarding the linearity of the verbal skills onset time vs. body weight and motor skills onset time vs. body weight? a. Both verbal skills onset time and motor skills onset time have linear relationships with body weight. b. Neither verbal skills onset time nor motor skills onset time have linear relationships with body weight. c. Verbal skills onset time has a linear relationship with time, while motor skills onset time has a non-linear relationship with body weight. d. Motor skills onset time has a linear relationship with time, while verbal skills onset time has a non-linear relationship with body weight.

ANSWER: d 79. You’re evaluating a data set of 60 observations of daily home energy use (kWh) with daily low temperature (°F). You perform a regression analysis and calculate the following least squares regression line:

When you review the scatterplot, you notice that, while most daily low temperatures range from 20°F to 31°F, there is one data point with a daily low temperature of -16°F. You suspect that this point is an influential observation. You remove the point and recalculate the regression line and get the following result:

Which of the following is reasonable to conclude regarding the data point with the -16°F daily low temperature?

I) The observation is not an influential observation since its removal did not have a large impact on the regression line’s slope.

II) The observation is not an influential observation since its removal did not have a large impact on the regression line’s y-intercept.

III) The observation is an influential observation since its removal had an effect on the regression line’s slope.

IV) The observation is an influential observation since its removal had an effect on the regression line’s yintercept. a. I only b. I and II only c. III only

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data d. III and IV only ANSWER: b 80. You’re evaluating a data set of 35 observations of the weekly number of home cooked meals eaten by families with annual family income ($). You perform a regression analysis and calculate the following least squares regression line: When you review the scatterplot, you notice that, while most of the observed families had annual incomes between $35,000 to $50,000, there is one data point with an annual income of $88,000. You suspect that this point is an influential observation. You remove the point and recalculate the regression line and get the following result: Which of the following is reasonable to conclude regarding the data point with the $88,000 annual income?

I) The observation is not an influential observation since its removal did not have a large impact on the regression line’s slope.

II) The observation is not an influential observation since its removal did not have a large impact on the regression line’s y - intercept.

III) The observation is an influential observation since its removal had a large effect on the regression line’s slope.

IV) The observation is an influential observation since its removal had a large effect on the regression line’s x values. a. II only b. I and II only c. IV only d. III and IV only ANSWER: c 81. You’re evaluating a data set of 100 observations of recent college graduates with bachelor’s degrees relating the starting salary upon graduation ($) with student debt ($). You perform a regression analysis and calculate the following least squares regression line: When you review the scatterplot, you notice that, while most of the graduates had student debt between $30,000 and $70,000, there is one data point with a student debt of $1,500. You suspect that this point is an influential observation.

You remove the point and recalculate the regression line and get the following result: Which of the following is reasonable to conclude regarding the data point with the $1,500 student debt?

I) The observation is not an influential observation since its removal did not have a large impact on the regression line’s slope.

II) The observation is not an influential observation since its removal did not have a large impact on the regression line’s y - intercept.

III) The observation is an influential observation since its removal had a large effect on the regression line’s slope.

IV) The observation is an influential observation since its removal had a large effect on the regression line’s y intercept. a. I only b. I and II only c. III only d. III and IV only ANSWER: c

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data 82. You’re evaluating a data set of 25 observations of holiday shoppers relating total holiday spending ($) with precipitation (inches). You perform a regression analysis and calculate the following least squares regression line:

When you review the scatterplot, you notice that, while most of the observed precipitation ranged from 0.5 inches to 4.0 inches, there is one data point with 20 inches of precipitations. You remove the point and recalculate the regression line and get the following result:

Which of the following is reasonable to conclude regarding the data point with the $1,500 student debt?

I) The observation is not an influential observation since its removal did not have a large impact on the regression line’s slope.

II) The observation is not an influential observation since its removal did not have a large impact on the regression line’s y - intercept.

III) The observation is an influential observation since its removal had a large effect on the regression line’s slope.

IV) The observation is an influential observation since its removal had a large effect on the regression line’s y intercept. a. I only b. I and II only c. III only d. III and IV only ANSWER: d 83. The plot below shows the points and two different regression lines for a single data set. The blue line is the regression line for all the points in the data set. The red line is the regression line for the data points excluding the circled point which is suspected of being an influential observation.

Which of the following characteristics correctly describes the circled data point?

I) It is an influential observation because it changed the y - intercept of the regression line.

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data II) It is an influential observation because it changed the slope of the regression line III) It is an influential observation because its x - value is far from those of other values IV) It is an influential observation because its y - value is far from those of other values a. I and II only b. III and IV only c. II and III only d. IV only ANSWER: a 84. You’re reviewing data from a study comparing preferences in young children with perceptions of typical gender behavior by parents and guardians. A scatterplot of the data is shown below along with the calculated least squares regression line.

While you are performing your analysis, one of the experimenters notifies you that the circled data point may have been taken incorrectly. You recalculate your least squares regression without the suspect (circled) point and notice that both the y-intercept and slope of the regression line changed.

Which of the following accurately describes the suspect (circled) point?

I. II. III.

The suspect data point had the potential for being an influential observation because its x-value was far away from the majority of the other data points.

The suspect data point was confirmed as an influential observation because its removal changed the regression line slope.

The suspect data point was confirmed as an influential observation because its removal changed the regression line y-intercept.

a. I and II only b. II and III only c. I and III only d. I, II, and III ANSWER: d 85. The coefficient of determination is equal to the positive square root of Pearson’s r. a. True b. False ANSWER: False

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data 86. Which of the following indicates the range of possible values of the coefficient of determination, r2? a. b. c. d.

ANSWER: a 87. Data were collected on the price of cars (in dollars) and the age of cars (in years) for each car in a sample of 60 used Toyota Camrys. A scatterplot showed a negative linear relationship between price and age. The least squares regression line was fit and the r2 value was computed. If which of the following is a correct statement? a. The correlation coefficient equals negative 0.55 b. There is a strong linear relationship between car price and the car’s age. c. For each additional mile driven, car price increases by approximately $0.55 d. Approximately 55% of the variability in car price can be explained by the linear relationship between car price in dollars and car age in years.

ANSWER: d 88. The value of the residual plus

is equal to

a. True b. False ANSWER: True 89. A bivariate numerical data set is shown in the Table below along with the equation for the least squares regression line.

Predictor 20 57 33 45 76 12 48 67 What is the residual for the data set? a. The residual for response value. b. The residual for response value. c. The residual for

Response 854 520 801 775 389 992 646 299 and does the regression line predict a value higher or lower than the actual response from is 51, which indicates that the regression line prediction is lower than the actual is 60, which indicates that the regression line prediction is lower than the actual is -51, which indicates that the regression line prediction is lower than the actual

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data response value. d. The residual for response value.

ANSWER: a

is -60, which indicates that the regression line prediction is higher than the actual

90. A bivariate numerical data set is shown in the Table below along with the equation for the least squares regression line.

Predictor 21 56 34 44 78 15 49 63 What is the residual for the data set? a. The residual for response value. b. The residual for response value. c. The residual for response value. d. The residual for response value.

ANSWER: b

Response 280 595 330 408 653 193 449 299 and does the regression line predict a value higher or lower than the actual response from is -209, which indicates that the regression line prediction is lower than the actual is 129, which indicates that the regression line prediction is lower than the actual is 209, which indicates that the regression line prediction is higher than the actual is -129, which indicates that the regression line prediction is lower than the actual

91. A bivariate numerical data set is shown in the Table below along with the equation for the least squares regression line.

Predictor 20 57 33 45 76 17 48 67 What is the residual for

Response 1708 1040 1602 1550 778 1984 1292 1292 and does the regression line predict a value higher or lower than the actual response from

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data the data set? a. The residual for response value. b. The residual for response value. c. The residual for response value. d. The residual for response value.

ANSWER: a

is 138, which indicates that the regression line prediction is lower than the actual is -70, which indicates that the regression line prediction is higher than the actual is -138, which indicates that the regression line prediction is higher than the actual is 70, which indicates that the regression line prediction is lower than the actual

92. Which of the following steps should be used to construct a residual plot for use in a linear regression analysis?

I) Create a scatterplot of your data set with the predictor variable on the

and the response variable on the

II) Calculate the least squares regression line for the data set III) For each data point, calculate the residual, which is defined as the actual

minus the predicted

IV) Plot the square of the calculated residuals vs. the predictor values in a scatterplot. a. I and II only b. I, II, and III only c. I, II, III, and IV d. II, III, and IV only ANSWER: b 93. In which ways does construction of a residuals plot for use in a linear regression analysis differ from construction of a scatterplot for use in assessing the relationship between predictor and response variables?

I. II. III.

In the residuals plot the is the predictor variable In the residual plot, the difference between the response variable and the prediction of the regression line is plotted on the In the residuals plot, the square root of the prediction of the regression line is plotted on the

a. I only b. II only c. Neither I, nor II, nor III d. III only ANSWER: b 94. Which of the following will permit you to construct a residuals plot which will clearly show the appropriateness of the least squares regression line?

I) Always use the point (0,0) as the graph origin II) Scale the so that all points are clearly visible III) Include a distinctive color or another marking for the horizontal line

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data IV) Scale the

so that all points are clearly visible

a. I, II, and IV only b. I, II, and III only c. I, II, III, and IV d. II, III, and IV only ANSWER: d 95. The predictor and response variables and the least squares linear regression line equation are shown below:

Predictor 42 60 20 50 24 27 27

Response 1.42 4.75 0.67 2.66 0.52 2.35 1.4

Which of the following tables and plots show the correct residuals and residual plot for this data set?

Name:

Chapter 04 - Describing Bivariate Numerical Data

Class:

Date:

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data

a. Residuals plot (A) b. Residuals plot (B) c. Residuals plot (C) d. Residuals plot (D) ANSWER: a 96. On the residuals plot below, which of the four labeled points is an outlier or potential influential observation and why?

a. Points #2 and #4 are potential influential observations since they have range of for the data set.

at the far-right end of the

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data b. Point #3 is a potential influential observation since it has an or the data set.

at the far-left end of the range of

c. Point #1 is likely to be an outlier because it has a large residual. d. None of the labeled points is an outlier or potentially influential observation.

ANSWER: c 97. On the scatterplot below, three points were marked as being potential outliers or influential observations.

Which of the following best describes whether or not points #1, #2, and #3 are outliers or influential observations? a. Point #1 is an outlier because it has a y-value lower than those of most of the other data points b. Point #2 is an influential observation because it has an higher than those of most of the other data points c. Point #3 is an outlier because it has an lower than those of most of the other data points d. Without a plotted least squares regression line or a residuals plot, it is not possible to assess whether or not any of the three labeled points is an outlier or influential observation.

ANSWER: d 98. Given a tabulated data set, which of the following are essential steps to identifying outliers and potential influential observations?

I. II. III.

After ensuring reasonable linearity from a scatterplot of the response vs. predictor variable, calculate a least squares regression line.

Using the least squares regression line, calculate residuals and plot them vs. the predictor variable to create a residuals plot.

Using the residuals plot, look for unusual values such as those falling above or below the line and/or those with which differ greatly from others in the data set.

a. I and II b. II and III c. I and III d. I, II, and III ANSWER: d 99. The higher the value of the coefficient of determination, the greater the evidence for a causal relationship between

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data and . a. True b. False ANSWER: False 100. One application of a least squares regression line is substitution of a function of an easy-to-measure variable for another, difficult or impossible to measure variable. a. True b. False ANSWER: True 101. In order for a least squares regression line to serve as a useful predictor, there must be a strong relationship between (the predictor variable) and (the response variable). Choose the statement that best describes the values of and which indicate the fact that the relationship is very strong. a. The value of is very large and the value of is close to 1. b. The value of

is very large and the value of

is close to 0.

c. The value of

is small and the value of

is close to 0.

d. The value of

is small and the value of

is close to 1.

ANSWER: d 102. Assessing the goodness of fit of a regression line involves considering several things, and no single characteristic of data is sufficient for a good assessment. Consider the characteristics below: How does each contribute to an assessment of fit? That is, for each piece of information, what about it would indicate that a “good” best-fit line? a. b. c. d. e.

The shape of the residual plot The correlation coefficient The demonstration of seriously influential points The coefficient of determination The standard deviation about the least squares regression line

ANSWER:

a. A uniform point cloud with no apparent pattern b. Values of r that are close to -1 or 1 c. Points that are potentially influential would lie close to the regression line calculated with these points omitted (indicating that they have minimal effect on slope or y-intercept of the calculated least squares regression line) d. Value of close to 1 e. Value of

close to 0

103. You run a bakery which specializes in dessert pastries. You need to predict baking time for a popular pastry. Your colleague thinks that baking time correlates strongly with pastry weight. You and your colleague measure both weight and baking time for 15 pastries. The results of your measurement are displayed below in the scatterplot. The least squares regression line shown in red has the equation: where y is the pastry baking time in minutes and x is the pastry weight in grams. The correlation coefficient is 0.83, the coefficient of determination is 0.69, and the standard deviation about the least squares regression line is 1.67 minutes.

Name:

Class:

Date:

Chapter 04 - Describing Bivariate Numerical Data

Based on your results and analysis, which of the following can you conclude regarding the usefulness of the least squares regression line for predicting pastry baking time based on pastry weight? a. The least squares regression line is not a useful predictive tool since the residuals plot shows significant curvature, indicating a nonlinear relationship between pastry weight and baking time. b. The least squares regression line is not a useful predictive tool since the correlation coefficient indicates only a weak linear relationship between pastry weight and baking time. c. The least squares regression line is a moderately useful tool since it explains 69% of the variability in baking time. d. The least squares regression line is an excellent tool since it can reliably predict baking time to 1.67 minutes.

ANSWER: c

Name:

Class:

Date:

Chapter 05 - Probability 1. Which of the following best describes the relative frequency approach to probability?

I. II.

A personal measure of the strength of belief that an outcome will occur.

The proportion of time that an outcome will occur in the long run.

a. I only b. Both I and II c. Neither I nor II d. II only ANSWER: d 2. A probability is a number that reflects the likelihood of the occurrence of a particular outcome. The number which represents a probability will always lie within which of the following ranges? a. Greater than -1, but less than 1 b. Greater than or equal to -1, but less than or equal to 1 c. Greater than 0, but less than 1 d. Greater than or equal to 0, but less than or equal to 1 ANSWER: d 3. Assignment of a probability to an outcome is an attempt to do which of the following? a. Calculate a specific value for the outcome b. Determine a range of values for which the outcome is certain c. Determine whether or not an outcome is possible d. Quantify the likelihood of the occurrence of the outcome ANSWER: d 4. Which of the following is a characteristic of the relative frequency interpretation of probability? a. It can be estimated by observing the outcomes of a large number of observations b. It is based on the personal belief of individuals c. It can be determined with a small number of observations. d. Two different people can assign different probabilities to the same outcome ANSWER: a 5. Which of the following are essential components of the relative frequency interpretation of probability?

I. II.

The ratio of times that a particular outcome occurs to the number of times that any outcome could occur.

A sufficient number of potential occurrences

a. I only b. Neither I nor II c. Both I and II d. II only ANSWER: c 6. Which of the following best describes the Law of Large Numbers? a. The relative frequency of occurrence of a given outcome will fluctuate as the number of occurrences becomes

Name:

Class:

Date:

Chapter 05 - Probability large. b. The relative frequency of occurrence of a given outcome will approach 1 as the number of occurrences becomes large. c. The relative frequency of occurrence of a given outcome will approach a particular value as the number of occurrences becomes large. d. The relative frequency of occurrence of a given outcome will approach 0 as the number of occurrences become large.

ANSWER: c 7. An airline reports that for a particular flight operating daily between New York and London, the probability of an ontime arrival is 0.64. Give the relative frequency interpretation of this probability. a. In the long run, 0.64% of the time this particular flight that flies between New York and London will arrive on time. b. In the long run, 36% of the time this particular flight that flies between New York and London will arrive on time. c. In the long run, 64% of the time this particular flight that flies between New York and London will arrive on time. d. In the long run, 64% of the time this particular flight that flies between New York and London will arrive earlier than expected.

ANSWER: c 8. Historically, students graduating from a particular high school have pursued three different career paths: military service (33%), college (32%), and professional apprenticeships (35%). Suppose you have a friend ready to graduate from this high school. What is the probability that they will pursue military service after graduation? a. 35% b. 67% c. 33% d. 32% ANSWER: c 9. You’re enrolled in a professional training program that, over the past decade, has placed 55% of their graduates in government jobs, 20% of their graduates in jobs in large private firms, and 25% of their graduates in jobs in small private firms. When you graduate next year, what is the probability that you will get a job with a private firm? a. 55% b. 75% c. 45% d. 25% ANSWER: c 10. Your grocery delivery service boasts a 90% on-time delivery record. What is the probability that your next grocery delivery will not be on time? a. 10% b. 90% c. 50% d. None of these ANSWER: a

Name:

Class:

Date:

Chapter 05 - Probability 11. Suppose you’re gathering data to determine the relative frequency with which students complete an assignment in under one hour. You ask 15 students to attempt the assignment and record which ones did and did not complete it in under an hour. The results of your study are shown in the Table below:

Student #

Completed in < 1 hour?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

No No No Yes No No No No Yes No No Yes No Yes Yes

Relative Frequency of Student Who Complete in < 1 hour 0 0 0 0.25 0.20 0.17 0.14 0.13 0.22 0.20 0.18 0.25 0.23 0.29 0.33

Based on your study of 15 students, which of the following best represents the probability with which students complete the assignment in under an hour? a. 45% b. 20% c. 30% d. 67% ANSWER: c 12. If 5 cards are dealt from a well-mixed deck of 52 standard playing cards, there are 2,598,960 possible hands. Of these hands, only 4 hands are royal flushes. What is the probability that a hand will be a royal flush? a. b. c. d.

ANSWER: b 13. Suppose you want to estimate the probability that a randomly selected customer at a particular grocery store will pay by credit card. Over the past 3 months, 70,600 purchases were made, and 22,200 of them were paid for by credit card.

Name:

Class:

Date:

Chapter 05 - Probability What is the estimated probability that a randomly selected customer will pay by credit card? a. 0.6855 b. 0.3144 c. 0.4587 d. 0.5413 ANSWER: b 14. Suppose you want to estimate the probability that a patient will develop an infection while hospitalized at a particular hospital. In the past year, this hospital had 8,650 patients, and 812 of them developed an infection. What is the estimated probability that a patient at this hospital will develop an infection? a. b. c. d.

ANSWER: b 15. In the classical approach to calculating probabilities, the probability of an event occurring is equal to the number of outcomes in the event divided by the number of outcomes in the sample space. Under which of the following conditions can this definition of event probability be used? a. All conditions b. When the sample space is large c. When the number of outcomes is large d. When outcomes of the chance experiments are equally likely ANSWER: d 16. A chance experiment is the process of making an observation when there is uncertainty concerning which of two or more possible outcomes will result. a. True b. False ANSWER: True 17. Any collection of possible outcomes of a chance experiment is the sample space for the experiment. a. True b. False ANSWER: False 18. A simple event is an event consisting of exactly one of the outcomes in the sample space. a. True b. False ANSWER: True

Name:

Class:

Date:

Chapter 05 - Probability 19. In the relative frequency approach to calculating probabilities, the probability of an event occurring is equal to the number of times the event occurs divided by the number of observations. Under which of the following conditions can this definition of event probability be used? a. All conditions b. When the number of times the chance experiment is repeated is large c. When the number of outcomes is large d. When outcomes of the chance experiments are equally likely ANSWER: b 20. A junior chef and a senior chef each need an egg for the dishes they are cooking. The eggs are stored in a large container which includes both white and brown eggs. There is an equal probability of retrieving an egg of either color.

The egg container holds a large number of eggs, so retrieval of an egg of either color does not significantly change the probability of obtaining an egg of either color the next time an egg is retrieved. What is the probability of both the junior and senior chefs retrieving brown eggs? a. 75% b. 50% c. 25% d. None of these ANSWER: c 21. There is an instrument in your lab that occasionally gives an error signal upon start-up. You record the number of times the error signal occurs over one month. In that one month, the instrument was started up 2,000 times and the error signal appeared 58 times. What is the probability of the occurrence of the error? a. 5.8% b. 2.9% c. 6.2% d. 3.0% ANSWER: b 22. The faces of a twelve-sided die are numbered with numbers 1 through 12. If you roll this die 600 times, how many nines do you expect to roll? a. about 67 b. about 50 c. about 60 d. about 100 ANSWER: b 23. The U.S. Postal Service ran an internal audit to determine the number of letters mailed in the New York City metro area that arrived within two days of the mailing date. The study tracked 550 letters mailed in the New York City metro area, of which 405 arrived on time. What is the probability of on-time letter delivery in the New York metro area? a. b.

Name:

Class:

Date:

Chapter 05 - Probability c. d. None of these ANSWER: a 24. Suppose you’re playing a game that involves rolling a 6-sided die with sides labeled 1, 2, 3, 4, 5, and 6. Assume that the die is fair (equal probability of rolling any one of the six numbers). If an event is defined as rolling a 3 or a 5, what is the probability of the event? a. 1/6 b. 3/6 c. 5/6 d. 2/6 ANSWER: d 25. Four members of a student writing club submit work to a campus creative works publication. The publication will randomly select two of the four submitted works for publication in their upcoming issue. Two of the four writing club members submitting work are seniors and two are juniors. What is the probability that the two works selected for publication will include one work from a junior and one work from a senior? a. 1/6 b. 2/6 c. 3/6 d. 4/6 ANSWER: d 26. You’re estimating the probability that the beach at a nearby state park will be crowded (more than 100 visitors) on weekends. You request attendance data from the park service and receive the following information: Weekends queried = 183; Weekends with > 100 visitors = 35 What is the probability that the state park beach will be crowded this upcoming weekend? a. 81% b. 24% c. 19% d. 53% ANSWER: c 27. You’re evaluating the performance of an antique 4-sided die to determine whether or not it is fair. You perform a study in which you roll the antique die 100 times and get the results shown in the table below.

Die Side Times number is rolled

1 28

2 38

3 20

4 14

Is the antique die fair, and what is the probability of rolling an even number (2 or 4)? a. No, the die is not fair. The probability of rolling an even number is 52%. b. Yes, the die is fair. The probability of rolling an even number is 50%. c. No, the die is not fair. The probability of rolling an even number is 48%. d. Yes, the die is fair. The probability of rolling an even number is 25%.

ANSWER: a

Name:

Class:

Date:

Chapter 05 - Probability 28. You use a 12-sided die for a particular game of chance. The die sides are labeled 1 through 12. Assuming that the die is fair (equal chance of rolling any one of the twelve numbers), what is the probability of rolling a 1, 4, 5, 7, or 11? a. 6/12 b. 7/12 c. 5/12 d. None of these ANSWER: c 29. Two events are mutually exclusive if no outcome could result from both of these events occurring. a. True b. False ANSWER: True 30. If two events, E and F, are mutually exclusive, which of the following will also be true? a. b. c. Events E and F cannot occur at the same time d. All of these ANSWER: d 31. Which of the following pairs of events would be considered to be mutually exclusive?

I) Driving to work vs. taking the bus to work II) Staying in a luxury hotel vs. staying in a penthouse room III) Turning right when exiting a door vs. turning left when exiting a door IV) While traveling, stopping for the night in a given town vs. passing through the town a. I, III, and IV only b. I and II only c. II only d. II, III, and IV only ANSWER: a 32. Suppose you’re creating a 1000 table to help you calculate probabilities for unions and intersections of two events S and R. You can find and What else would you need to complete your 1000 table? a. b. c. The fact that

and

are mutually exclusive

d. Any of these would permit you to complete the 1000 table ANSWER: d 33. Which of the following pairs of events would be considered to be mutually exclusive?

I) Being a vegan vs. being a meat-eater II) Owning a cat vs. owning a dog III) Living in London vs. Living in Paris IV) Owning a bicycle vs. owning a car

Name:

Class:

Date:

Chapter 05 - Probability a. I and II only b. II and III only c. I and III only d. II and IV only ANSWER: c 34. Which of the following pairs of events would be considered to be mutually exclusive?

I) Being employed vs. being unemployed II) Being alive vs. being dead III) Living in France vs. Living in London IV) Being college educated vs. running your own business a. I and II only b. III and IV only c. I, II, and III only d. I, II, III, and IV ANSWER: c 35. You’re a public safety officer working on a project aimed at reducing traffic accidents during the holiday season.

You’re interested in the following two events: Event A = people remain at home and participate in virtual celebrations Event B = people travel and physically attend celebrations Which of the following is true of events A and B? I. II. III.

The probability of the intersection of events A and B is zero The probability of the union of events A and B is equal to the sum of the probabilities of events A and B Events A and B are mutually exclusive

a. I only b. II only c. II and III only d. I, II, and III ANSWER: d 36. Which of the following events are independent? a. You have a friend who is traveling to visit you using a commercial airline flight. Event A: your friend arrives to meet you on time. Event B: your friend boards their flight. b. You are a professional dancer attempting to secure a paid position with a well-respected performing arts company. Event A: you receive an offer for a paid position. Event B: you receive an invitation to audition (a pre-requisite to hiring). c. You are planning the menu for a family picnic. Event A: the weather is sunny on the day of the picnic. Event B: the salad you serve at the picnic is well-liked by the attending family members. d. You are concerned that you might have a serious autoimmune disease. Event A: you have the disease. Event B: you test negative for a sensitive screening test for the disease ANSWER: c 37. Given the following scenarios, each with associated Events A and B, for which are events A and B dependent?

Name:

Class:

Date:

Chapter 05 - Probability I. II. III. IV.

You’re trying to get hired by a particular company. Event A: you receive an offer of employment from the company. Event B: you are invited to interview for a position with the company.

You’re maintaining the test equipment in your school’s chemistry lab. Event A: the temperature recording instrument starts malfunctioning. Event B: the chemical supply company you work with initiates a sale of glassware.

You’re a nutritionist specializing in medically-recommended weight loss. Event A: your client loses weight, thereby achieving a health goal. Event B: your client adheres to the dietary regimen you recommended You need to travel from one side of your city to the other in a set period. Event A: you arrive at your destination on time. Event B: you encounter heavy traffic during your journey.

a. I, II, and IV only b. I, II, and III only c. II, III, and IV only d. I, III, and IV only ANSWER: d 38. Two events are independent if they cannot occur simultaneously. a. True b. False ANSWER: False 39. Two events are dependent if knowing that one of the events has occurred does not change your assessment of the probability that the other event has occurred. a. True b. False ANSWER: False 40. Two events are independent if knowing that one of the events has occurred does not change your assessment of the probability that the other event has occurred. a. True b. False ANSWER: True 41. You’re a building health inspector in a town with 800 homes. Some of the homes have copper piping and some have plastic piping. One of your duties is to select one house at random for a plumbing inspection. If 100 homes have copper piping and 700 homes have plastic piping, what is the probability that the home you will inspect will have copper piping? a. 87.5% b. 12.5% c. 14.3% d. 18.4% ANSWER: b 42. You’re a building health inspector in a town with 800 homes. The homes are distributed over three neighborhoods including a downtown neighborhood, a waterfront neighborhood, and a park side neighborhood. One of your duties is to select one house at random for a plumbing inspection.

The number of homes in each neighborhood is shown below:

Name:

Class:

Date:

Chapter 05 - Probability • • •

Downtown neighborhood: 250 homes Waterfront neighborhood: 300 homes Park side neighborhood: 250 homes

What is the probability that the home you will inspect will be in the waterfront neighborhood? a. 37.5% b. 62.5% c. 60.0% d. 42.5% ANSWER: a 43. You’re a building health inspector in a town with 800 homes. The homes are distributed over three neighborhoods including a downtown neighborhood, a waterfront neighborhood, and a park side neighborhood. One of your duties is to select one house at random for a plumbing inspection.

The number of homes in each neighborhood is shown below: • • •

Downtown neighborhood: 250 homes Waterfront neighborhood: 300 homes Park side neighborhood: 250 homes

If event D is defined as selecting a home from the downtown neighborhood for inspection, which of the following represents the probability for the compliment of D a. P(Dc) = 31.3% b. P(Dc) = 68.8% c. P(Dc) = 60.0% d. P(Dc) = 50.0% ANSWER: b 44. A town has 800 homes, one of which is randomly selected each week for a plumbing inspection. The homes are distributed over three neighborhoods including a downtown neighborhood, a waterfront neighborhood, and a park side neighborhood. The homes include those with copper piping and those with plastic piping.

The number of homes in each neighborhood and with each plumbing material is shown below: • • •

Downtown neighborhood: 250 homes Waterfront neighborhood: 300 homes Park side neighborhood: 250 homes

Homes with copper piping = 100, Homes with plastic piping = 700 Suppose you’re interested in the probabilities associated with two events: Event W = selected home is in the waterfront neighborhood; Event C = selected home has copper plumbing.

Which of the following two-way tables includes the correct total probabilities? a.

C Not C Total

W Not W Total

100

700

300 500 800

Name:

Class:

Date:

Chapter 05 - Probability b.

W Not W Total c.

W Not W Total d.

W Not W Total

C

Not C

100

700

C

Not C

700

100

C

Not C

700

100

Total 250 550 800 Total 300 500 800 Total 250 550 800

ANSWER: a 45. A town has 800 homes, one of which is randomly selected each week for a plumbing inspection. The homes are distributed over three neighborhoods including a downtown neighborhood, a waterfront neighborhood, and a park side neighborhood. The homes include those with copper piping and those with plastic piping.

The number of homes in each neighborhood and with each plumbing material is shown below: • • •

Downtown neighborhood: 250 homes Waterfront neighborhood: 300 homes Park side neighborhood: 250 homes

Homes with copper piping = 100, Homes with plastic piping = 700 Suppose you’re interested in the probabilities associated with two events: Event D = selected home is in the downtown neighborhood, Event C = selected home has copper plumbing.

Given the two-way table below, what is the probability that the home selected for next week’s inspection will be in the downtown neighborhood and have plastic piping?

D Not D Total

C 80 20 100

Not C 220 480 700

Total 300 500 800

a. 10% b. 60% c. 28% d. 13% ANSWER: c 46. A town has 800 homes, one of which is randomly selected each week for a plumbing inspection. The homes are distributed over three neighborhoods including a downtown neighborhood, a waterfront neighborhood, and a park side neighborhood. The homes include those with copper piping and those with plastic piping.

The number of homes in each neighborhood and with each plumbing material is shown below: • •

Downtown neighborhood: 250 homes Waterfront neighborhood: 300 homes

Name:

Class:

Date:

Chapter 05 - Probability •

Park side neighborhood: 250 homes

Homes with copper piping = 100, Homes with plastic piping = 700 Suppose you’re interested in the probabilities associated with two events: Event D = selected home is in the downtown neighborhood, Event C = selected home has copper plumbing.

Given the two-way table below, what is the probability that the home selected for next week’s inspection will be in the downtown neighborhood or have copper piping?

C 80 20 100

D Not D Total

Not C 220 480 700

Total 300 500 800

a. 10% b. 40% c. 90% d. 60% ANSWER: b 47.

Given two events A and B, probabilities of different scenarios are given by the two-way table below.

B 5 15 20

A Not A Total

Not B 45 135 180

Total 50 150 200

Given the information in the two-way table, which of the following describe the probabilities of the intersection and union, respectively of events A and B? a. b. c. d.

ANSWER: a 48. Farmer’s market organizers are interested in the fraction of shoppers who are looking for artichokes and the fraction of shoppers who travel to the market by bus.

Event A = shopper is looking for artichokes Event B = shopper arrived by bus Based on historical records, Which of the following represents an accurate 1000 table for this scenario? a.

A Not A Total b.

B 380 160 540

Not B 300 160 460

Total 680 320 1000

B

Not B

Total

Name:

Class:

Date:

Chapter 05 - Probability

A Not A Total

380 300 680

160 160 320

540 460 1000

A Not A Total

B 160 300 460

Not B 160 380 540

Total 320 680 1000

A Not A Total

B 80 240 320

Not B 380 300 680

Total 460 540 1000

c.

d.

ANSWER: a 49. The hypothetical 1000 table below relates probabilities for events A and B. Which of the following represents the probability of the union of events A and B?

B 80 240 320

A Not A Total

Not B 380 300 680

Total 460 540 1000

a. 70% b. 30% c. 78% d. 22% ANSWER: a 50. A large cable company reports that 70% of its customers subscribe to its cable TV service, 32% subscribe to its internet service, and 87% subscribe to at least one of these services. Use the given probability information to select a hypothetical 1000 table. a.

Internet service Not Internet service Total

Cable tv 150 550

Not Cable tv 170 130

Total 320 680

700

300

1,000

Cable tv 170

Not Cable tv 250

Total 420

b.

Internet service

Name:

Class:

Date:

Chapter 05 - Probability Not Internet service Total

30 200

550 800

580 1,000

Internet service Not Internet service Total

Cable tv 350 450 800

Not Cable tv 70 130 200

Total 520 580 1,000

Internet service Not Internet service Total

Cable tv 25 55 80

Not Cable tv 17 3 20

Total 42 58 100

c.

d.

ANSWER: a 51. A rental car company offers two options when a car is rented. A renter can choose to pre-purchase gas or not and can also choose to rent a GPS device or not. Suppose that the events can be described as: A = event that gas is pre-purchased B = event that a GPS is rented Based on historical records: Which of the following show the hypothetical 1000 table for this scenario? a.

B not B Total

A 175 325 500

not A 175 325 500

Total 350 650 1,000

B not B Total

A 170 30 200

not A 680 120 800

Total 850 150 1,000

B not B Total

A 680 120 800

not A 170 30 200

Total 850 150 1,000

B not B Total

A 175 175 330

not A 325 325 650

Total 350 650 1,000

b.

c.

d.

ANSWER: b

Name:

Class:

Date:

Chapter 05 - Probability 52. Suppose a survey was conducted among women aged 20 to 40 years. Consider the following events.

Event C = a randomly selected interviewed woman visits a cosmetologist Event A = a randomly selected survey participant has an age of 30 or over.

Data from the survey were used to estimate the following probabilities: Which of the following show the hypothetical 1000 table for this scenario? a.

C (Visit)

Total

120 350

Not C (Not Visit) 260 270

470

380

1,000

A (Age 30 to 40) Not A (Age 20 to 29 Total

C (Visit) 350 270 620

Not C (Not Visit) 120 260 380

Total 470 530 1,000

A (Age 30 to 40) Not A (Age 20 to 29 Total

C (Visit) 350 120 470

Not C (Not Visit) 270 260 580

Total 620 380 1,000

A (Age 30 to 40) Not A (Age 20 to 29 Total

C (Visit) 120 260 380

Not C (Not Visit) 350 270 620

Total 470 530 1,000

A (Age 30 to 40) Not A (Age 20 to 29 Total b.

c.

d.

380 620

ANSWER: c 53. Suppose there are two detectives in a small, private office that is engaged in the search for people. The probability that a person will be found for each of the two detectives is equal to 0.755 for Detective 1 and 0.832 for Detective 2. Further, suppose that Detective 1 works part-time and works 40% of cases of missing people, and Detective 2 works the remaining 60%. Use the given probability information to select a hypothetical 1000 table. a.

Detective 1 Detective 2 Total

Found 332 452 784

Not Found 68 148 216

Total 400 600 1,000

Detective 1 Detective 2 Total

Found 302 499 801

Not Found 98 101 199

Total 380 600 1,000

b.

Name:

Class:

Date:

Chapter 05 - Probability c.

Detective 1 Detective 2 Total d.

Detective 1 Detective 2 Total

Found 452 332 784 Found 299 502 801

Not Found 148 68 216 Not Found 101 98 199

Total 600 400 1,000 Total 400 600 1,000

ANSWER: b 54. A college sponsors a fitness program for freshmen and sophomores. The probability of freshmen succeeding in the program is 20%, while the probability of sophomores succeeding in the program is 65%. What is the probability that either a freshman or a sophomore will succeed in the fitness program? a. 20% b. 80% c. 85% d. 65% ANSWER: c 55. Suppose you’re planning a dinner party and inviting 100 guests. Some guests are meat-eaters while others are vegans.

If event A = guest will be a vegan and event B = guest will be a meat-eater, and the probabilities of events A and B are 33% and 59%, respectively. What is the value of a. 33% b. 26% c. 92% d. 59% ANSWER: c 56. Some ski enthusiasts enjoy sunny days, while others prefer snowy days. The probability that the majority of lift tickets at a particular resort will be purchased by skiers who prefer sunny days is 33%. The probability that the majority of lift tickets at the same resort will be purchased by skiers who prefer snowy days is 15%. What is the probability that the majority of lift tickets at the resort will be purchased by skiers who prefer either sunny or snowy days? a. 24% b. 48% c. 52% d. 76% ANSWER: b 57. You’re an instructor planning a curriculum for a new program. Some of your prospective students have never attended college, while others are transferring from other colleges. If event A = student has never attended college and event B = student is transferring from another college and the probabilities of events A and B are 13% and 20%, respectively. What is the value of a. 33%

Name:

Class:

Date:

Chapter 05 - Probability b. 17% c. 87% d. 80% ANSWER: a 58. You’re scheduling workers for a factory that operates 24 hours per day. Some workers work night-shift only while others work day-shift only. If event A = night-shift-only workers and event B = day-shift-only workers, and the probabilities of events A and B are 73% and 5%, respectively. What is the value of a. 61% b. 39% c. 22% d. 78% ANSWER: d 59. Event A represents people who travel to work on foot while event B represents people who travel to work by bike. If the probabilities of events A and B are 4% and 20%, respectively, what is the value of a. 24% b. 76% c. 80% d. 96% ANSWER: a 60. Event A represents the number of students in your class who have brown hair, while event B represents the number of students in your class who are left-handed. If the probabilities of events A and B are 40% and 20%, respectively, what is the value of a. 4% b. 8% c. 0.8% d. 2% ANSWER: b 61. Event A represents the number of residents in your town that live in apartments while event B represents the number of residents in your town who are overweight. If the probabilities of events A and B are 40% and 80%, respectively, what is the value of a. 68% b. 60% c. 32% d. 20% ANSWER: c 62. Event A represents the number of shops in a downtown area that sell food, while event B represents the typical daily high temperature recorded for the downtown area. If the probabilities of events A and B are 65% and 25%, respectively, what is the value of a. 84%

Name:

Class:

Date:

Chapter 05 - Probability b. 90% c. 16% d. 45% ANSWER: c 63. Event A represents the average snowfall in a particular area, while event B represents the number of area residents who prefer chocolate cake for dessert. If the probabilities of events A and B are 95% and 90%, respectively, what is the value of a. 95.5% b. 90.5% c. 85.5% d. 87.5% ANSWER: c 64. Which of the following probabilities are conditional?

I. II. III. a. I and II only b. II and III only c. I and III only d. I, II, and III ANSWER: d 65. In a few sentences, explain the difference between conditional probability and unconditional probability.

ANSWER: When we calculate a conditional probability, we use information about events that have already occurred. This is not true with unconditional probability.

66. Which of the following probabilities are conditional? a. b. c. d.

ANSWER: b 67. Which of the following probabilities are unconditional? a. b. c. d.

ANSWER: c

Name:

Class:

Date:

Chapter 05 - Probability 68. Experimental medical studies routinely utilize blinding to prevent researchers from inadvertently biasing their measurements of patient outcomes. Unfortunately, depending on the nature of the treatment, researchers can often guess what treatment patients received. The table below summarizes the number of times researchers correctly and incorrectly guessed whether a patient received a therapeutic treatment or a placebo treatment.

Therapeutic Treatment Placebo Treatment

Correct Guess 30 24

Incorrect Guess 8 12

a) What is the probability that researchers will correctly guess the treatment for a randomly chosen subject? b) If a randomly chosen subject received the placebo, what is the probability that the researcher correctly guesses the treatment?

ANSWER: a) b) 69. Investigators recently reported the results of a study designed to assess whether or not the herb St. John’s Wort is an effective treatment for moderately severe cases of depression. The study involved 338 subjects, randomly assigned to receive one of three treatments: St. John’s Wort, Zoloft, or a placebo. The authors were primarily interested in whether St. John’s Wort performed better than the placebo. Zoloft was included as a “way to measure the trial’s sensitivity to antidepressant effects on patients”. The results are shown in the Table below:

a) What is the probability that a randomly selected subject had no response? b) What is the probability that a randomly selected subject was treated with Zoloft and had a full response? c) What is the probability that a randomly selected subject had a full or partial response given that they were treated with St. John’s Wort? d) What is the probability that a randomly selected subject was treated with the Placebo, given that they didn’t have a full response?

ANSWER: a) 0.568, b) 0.080, c) 0.381, d) 0.320 70. In a survey of airline travelers, subjects were observed in the coach section of airplanes to determine if men or women are bothered by a seatmate of the opposite gender using the common armrest. Study results are summarized in the table below. The “Bothered” Event = discontentment felt when the seatmate used the common armrest.

Suppose one of these passengers was randomly selected. Use the information in the table above to answer the following questions. a) What is the probability that the passenger is female? b) What is the probability that the passenger is either female or bothered?

Name:

Class:

Date:

Chapter 05 - Probability c) What is the probability that, if a passenger is male, they will also be bothered?

ANSWER: a) 44.6%, b) 82.2%, c) 67.9% 71. In a survey of airline travelers, subjects were observed in the coach section of airplanes to determine if men or women are bothered by a seatmate of the opposite gender using the common armrest. Passengers were also classified by age (under 40 years vs. 40 years or older). Study results are summarized in the table below. The “Bothered” Event = discontentment felt when the seatmate used the common armrest.

Bothered Not Bothered Totals Females under 40 years 14 10 24 Males under 40 years 23 2 25 Females 40 years or older 5 16 21 Males 40 years or older 15 16 31 Totals 57 44 101 Suppose one of these passengers was randomly selected. Use the information in the table above to give the probability that: a) The passenger is under 40, given that they are female. b) The passenger was bothered, given that they were over 40. c) The passenger was bothered, given that they were female.

ANSWER: a) 53.3%, b) 38.5%, c) 42.2% 72. You own a restaurant with both a lunch and dinner service. You are considering adding a new tomato-basil soup to your lunch menu in hopes of increasing the number of customers who dine at your restaurant. In order to assess the potential impact of adding the soup, you conduct a survey of 100 of your existing customers to determine which of them like tomato-basil soup and whether they come to the restaurant for lunch or dinner.

Event T = customer likes tomato-basil soup Event L = customer comes to the restaurant for lunch L Not L Total T 40 45 85 Not T 5 10 15 Total 45 55 100 Which of the following best describes the probability which would help you answer the question of whether or not you should add tomato-basil soup to your restaurant’s lunch menu? a. You need the conditional probability of T given L, which would be 40/45. b. You need the unconditional probability of T, which would be 85/100 c. You need the unconditional probability of T intersection with the unconditional probability of L, which would be 40/100 d. You would need the conditional probability of T given not-L, which would be 45/55.

ANSWER: a 73. You own a restaurant with both a lunch and dinner service. You are considering adding a new vegetarian dish to your lunch menu in hopes of increasing the number of customers who dine at your restaurant. In order to assess the potential impact of adding the dish, you conduct a survey of 100 of your existing customers to determine which of them enjoy vegetarian dishes and whether they come to the restaurant for lunch or dinner.

Event V = customer enjoys vegetarian dishes Event L = customer comes to the restaurant for lunch L Not L Total V 40 45 85 Not V 5 10 15

Name:

Class:

Date:

Chapter 05 - Probability Total 45 55 100 Which of the following best describes the probability which would help you answer the question of whether or not you should add the vegetarian dish to your restaurant’s dinner menu? a. You need the conditional probability of V given not-L, which would be 45/55. b. You need the unconditional probability of V, which would be 85/100 c. You need the unconditional probability of V intersection with the unconditional probability of not-L, which would be 45/100 d. You would need the conditional probability of V given L, which would be 40/45.

ANSWER: d 74. You own a restaurant with both a lunch and dinner service. You are considering expanding both your lunch and dinner menus to include appetizers in hopes of increasing the number of customers who dine at your restaurant. In order to assess the potential impact of adding the appetizer, you conduct a survey of 100 of your existing customers to determine which of them enjoy appetizers and whether they come to the restaurant for lunch or dinner.

Event A = customer enjoys appetizers dishes Event L = customer comes to the restaurant for lunch L Not L Total A 40 45 85 Not A 5 10 15 Total 45 55 100 Which of the following best describes the probability which would help you answer the question of whether or not you should add appetizers to both your lunch and dinner menus? a. You need the conditional probability of A given not-L, which would be 45/55. b. You need the unconditional probability of A, which would be 85/100 c. You would need the conditional probability of not-L given A, which would be 45/85 d. You would need the conditional probability of L given not-A, which would be 5/15.

ANSWER: b 75. Travelers at certain airports are subject to random searches of their carry-on luggage to see if they contain disallowed items. The table below summarizes the results of 1000 random searches of passengers based on the passenger’s race.

Disallowed Items Found Disallowed Items Not Found Total Black 50 428 478 Latinx 80 252 332 White 120 70 190 Total 250 750 1000 How does the probability that a passenger was carrying a disallowed item given that the passenger was Latinx compare to the unconditional probability of a passenger carrying a disallowed item? a. The conditional probability of a passenger carrying a disallowed item given that they were Latinx is 32% compared to the unconditional probability of a passenger carrying a disallowed time, which is 25%. b. The conditional probability of a passenger carrying a disallowed item given that they were Latinx is 34% compared to the unconditional probability of a passenger carrying a disallowed time, which is 25%. c. The conditional probability of a passenger carrying a disallowed item given that they were Latinx is 24% compared to the unconditional probability of a passenger carrying a disallowed time, which is 25%. d. The conditional probability of a passenger carrying a disallowed item given that they were Latinx is 11% compared to the unconditional probability of a passenger carrying a disallowed time, which is 25%.

ANSWER: c

Name:

Class:

Date:

Chapter 05 - Probability 76. Suppose you’re running a business and tracking your monthly sales. You’re interested in the relationship between the percent of the total items that are discounted and the percent of the total items for which customers paid full price. Out of 1000 total items for sale, 300 were discounted. Customers paid full price for 250 items. Which of the following represents the probability that a customer would pay full price for an item or that an item was discounted? a. 15% b. 55% c. 30% d. 25% ANSWER: b 77. The tourism board for a particular city keeps records of the types of hotels the average holiday traveler chooses. Based on their records, 10% of travelers chose economy hotels and 36% chose luxury hotels. What is the probability that a holiday traveler chose a hotel that was neither a luxury hotel nor an economy hotel? a. 23% b. 77% c. 54% d. 46% ANSWER: c 78. Suppose you’re considering two events, A and B which have probabilities P(A) = 0.30 and P(B) = 0.65. If the probability of the intersection of events A and B is 0.15, which of the following represents the probability of the union of events A and B? a. 0.95 b. 0.05 c. 0.35 d. 0.80 ANSWER: d 79. Suppose you’re considering two events, A and B which have probabilities and If the conditional probability of B given A is 0.85, which of the following represents the probability of the intersection of events A and B? a. 0.26 b. 0.70 c. 0.45 d. 0.80 ANSWER: a 80. The following table summarizes complaints received by the United States Department of Transportation for five major U.S.-based airlines. The data in the table show the proportions of the total complaints received by airline and complaint type.

Name:

Class:

Date:

Chapter 05 - Probability

Based on the data in the table, which airline(s) would you avoid if you wanted to avoid having flight problems? a. American and Jetblue b. United c. Delta d. Southwest ANSWER: a 81. The following table summarizes complaints received by the United States Department of Transportation for five major U.S.-based airlines. The data in the table show the proportions of the total complaints received by airline and complaint type.

Based on the data in the table, which airline(s) would you avoid flying if you wanted to avoid problems with your baggage? a. Southwest b. JetBlue c. Delta or Southwest d. American ANSWER: d 82. The following table summarizes complaints received by the United States Department of Transportation for five major U.S.-based airlines. The data in the table show the proportions of the total complaints received by airline and complaint type.

Based on the data in the table, which airline(s) would you avoid if you thought that you might need to seek a refund for your fare?

Name:

Class:

Date:

Chapter 05 - Probability a. JetBlue or Southwest b. Delta c. American d. United ANSWER: d 83. Under which of the following conditions would you use an empirical approach to estimate probabilities?

I. II. III.

You know the actual long-run proportion of times events will occur.

You can calculate probabilities from basic formulas You can determine probabilities from hypothetical 1000 tables

a. I and II only b. I, II, and III c. Neither I nor II nor III d. II and III only ANSWER: c 84. Which of the following steps are essential for estimating probabilities empirically?

I. II. III.

Observe a large number of chance outcomes under controlled circumstances.

Interpret probabilities and long-run relative frequencies.

Estimate the probability of any given event by using the observed proportion of its occurrence.

a. I and II only b. I, II, and III c. Neither I nor II nor III d. II and III only ANSWER: b 85. Suppose you need to know the probability of event A to make an important decision. You do not know the actual long-run proportion of the time event A will occur, nor can you calculate it from the probabilities for related events.

Which of the following would be appropriate to use in order to estimate the probability of event A? I. II.

A published study carried out under controlled circumstances and involving a large number of observations.

A published observational study involving a limited number of subjects.

a. I only b. Neither I nor II c. Both I and II d. II only ANSWER: a 86. Under which of the following conditions would you use simulation to estimate the probability of an event?

I. II.

You do not have the time or resources to determine probabilities analytically.

It is impractical or overly time-consuming to estimate empirically by observation

Name:

Class:

Date:

Chapter 05 - Probability a. I only b. Neither I nor II c. II only d. Both I and II ANSWER: d 87. Suppose you’re estimating the probability of a student correctly guessing the answer to a multiple-choice question with five answer selections. You’re using random digits as a substitute for a physical random mechanism. Which of the following would preserve the important characteristics of the process being considered? a. Use 0,1, to represent correct responses and 2,3,4,5,6,7,8, and 9 to represent incorrect responses b. Use 0, 1, 2, and 3 to represent correct responses and 4,5,6,7,8,9 to represent incorrect responses c. Use even numbers 0,2,4,6,8 to represent correct responses and odd numbers 1,3,5,7,9 to represent incorrect responses d. Use 0, 1, and 2 to represent correct responses and 3, 4, 5, 6, 7, 8, 9 to represent incorrect responses ANSWER: a 88. Which of the following are essential steps for using simulation to approximate the probability of an event?

I. II. III.

Use a random mechanism that represents the important characteristics of the processes being observed to represent a single observation.

Repeat the use of the random mechanism a large number of times Calculate the estimated probability of the event by dividing the number of observations for the event by the total number of observations.

a. I only b. I and II only c. II and III only d. I, II, and III ANSWER: d

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions 1. Which of the following accurately describes discrete random variables?

I. II.

Numerical variables whose value depends on the outcome of a chance experiment and which can assume all possible values in some interval.

Numerical variables whose value depends on the outcome of a chance experiment and which can only assume values corresponding to isolated points along a number line.

a. I only b. Neither I nor II c. II only d. Both I and II ANSWER: c 2. Which of the following accurately describes a continuous random variable?

I. II.

Numerical variable whose value depends on the outcome of a chance experiment and which can assume all possible values in some interval.

Numerical variable whose value depends on the outcome of a chance experiment and which can only assume values corresponding to isolated points along a number line.

a. I only b. Both I and II c. Neither I nor II d. II only ANSWER: a 3. A random variable is discrete if the value of the random variable depends upon the outcome of a chance experiment. a. True b. False ANSWER: False 4. A random variable is continuous if the set of possible values it can assume includes an entire interval on the number line. a. True b. False ANSWER: True 5. Which of the following random variables is discrete? a. The number of broken eggs in a carton b. The temperature inside a room c. The weight of an apple d. The speed a vehicle is traveling ANSWER: a 6. Which of the following random variables is continuous? a. The number of chocolate candies in a box

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions b. The number of books purchased by a customer c. The weight of a jar of peanut butter d. The number of cars in a parking lot ANSWER: c 7. Which of the following accurately describes the probability distribution of a discrete random variable? a. The exact behavior of a dependent variable P on a random variable x for each possible value of x. b. The probability associated with a particular value of a random variable x. c. The probability associated with each possible value of x where each probability is the proportion of time, for a discrete period, that the corresponding x value will occur. d. The probability associated with each possible value of x where each probability is the long-run proportion of time that the corresponding x value will occur.

ANSWER: d 8. Due to space limitations, residents of a given neighborhood are restricted to parking no more than three vehicles per dwelling. If you had the probability distribution for the number of cars parked per dwelling, which of the following questions could you answer?

I. II.

The number of cars parked for a particular dwelling The proportion of the dwellings with two cars parked

a. I only b. II only c. Neither I nor II d. Both I and II ANSWER: b 9. As an energy conservation professional, you’re interested in the amount of electricity (kWh) used by businesses in a downtown area during a busy shopping week. If you had the probability distribution for the electricity used per business, which of the following could you determine?

I. II.

The most common value for the per-business electricity use The range of values for the per-business electricity use

a. I only b. Neither I nor II c. Both I and II d. II only ANSWER: c 10. You’re conducting a survey of students at your college to assess the number of pairs of shoes owned by students living on campus. Due to space limitations in on-campus housing, you can assume with some accuracy that no student owns more than 8 pairs of shoes. Due to health regulations requiring shoe-wearing in public spaces, you can also assume that no student owns fewer than one pair of shoes. Using x as the random variable representing the pairs of shoes per student, which of the following could you determine from the probability distribution of x?

I. II.

The typical number of pairs of shoes owned by on-campus students The proportion of on-campus students who own two pairs of shoes

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions III.

The proportion of on-campus students who own five pairs of shoes

a. I and II only b. II and III only c. I and III only d. I, II, and III ANSWER: d 11. You’re interested in the fraction of symptomatic knee arthritis patients whose knees include multiple damaged structures. There are typically four damaged knee structures in most symptomatic knee arthritis patients: ligaments, tendons, menisci, and bone. If the random variable x represents the number of damaged knee structures, which of the following could you determine from a probability distribution of x?

I. II. III.

The proportion of symptomatic knee arthritis patients with a single damaged structure.

The proportion of symptomatic knee arthritis patients with four damaged structures.

The typical number of damaged structures for symptomatic knee arthritis patients.

a. I and II only b. II and III only c. I and III only d. I, II, and III ANSWER: d 12. The table below gives the percentage of new bicycle frames that have a certain number of paint defects. The data in the table is based on testing a large number of newly painted bicycle frames. The random variable x corresponds to the number of paint defects per frame and p(x) is the proportion of painted frames with x paint defects. x 0 1 2 3 4 5 6 7 8 9 10 p(x) 0.041 0.130 0.209 0.223 0.178 0.114 0.061 0.028 0.011 0.004 0.001 What is the probability that bicycle frames will have 8, 9, or 10 paint defects? a. 0.016 b. 0.011 c. 0.005 d. 0.015 ANSWER: a 13. A large number of travel groups visiting a particular island resort were surveyed to determine the number of people in their groups. The table below gives the fraction of the surveyed groups that have a certain number of people per group.

x p(x)

1 0.041

2 0.130

3 0.209

4 0.223

5 0.178

6 0.114

7 0.061

What is the probability that a travel group will have three to five persons, inclusive? a. 61% b. 39% c. 22% d. 39% ANSWER: a

8 0.028

9 0.011

10 0.005

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions 14. Suppose that fund-raisers at a university call recent graduates to request donations for campus outreach programs. The following report summarizes information for last year’s graduates:

Donation Size Proportion of Calls

$0 0.35

$10 0.15

$25 0.40

$50 0.10

If the random variable x = donation size for a person selected at random from the population of last year’s graduates, what is P (x $10)? a. 0.50 b. 0.35 c. 0.15 d. 0.90 ANSWER: a 15. The sales of a newspaper vary from week to week, depending on the importance of the news the previous week. From empirical data over many years, the proportion of weekly sales (rounded to the nearest million) has been carefully constructed.

X p(x)

0 0.15

1 0.25

2 0.40

3 0.20

What is the probability that weekly sales will be more than $2 million? a. 20% b. 80% c. 60% d. 40% ANSWER: a 16. A large number of residents of one municipal area were surveyed to determine the number of pets each resident owned. Results of the survey are shown in the table below where x = the number of pets and p (x) is the fraction of surveyed residents with x pets.

x p(x)

0 0.05

1 0.10

2 0.45

3 0.29

4 0.06

5 0.05

What is the probability that a resident of the municipality will have three or more pets? a. 0.60 b. 0.40 c. 0.55 d. 0.11 ANSWER: b 17. Thirty-seven percent of the customers of a grocery store use an express checkout. Consider four randomly selected customers, and let x denote the number among the four who use the express checkout. Calculate P (x 2). a. 0.47 b. 0.33 c. 0.85 d. 0.82 ANSWER: c 18. Twenty-two percent of customers at a gardening supply store opt for in-store pick-up while the remainder opts for on-

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions site delivery. Consider four randomly selected customers, let y represent the number among the four who opt for in-store pick-up. Calculate P (x 2). a. 0.21 b. 0.18 c. 0.96 d. 0.63 ANSWER: a 19. A particular college has a reputation for awarding too many good grades in math courses. The grade distribution for the college’s math courses is given in the table below: Grade A B C D F Proportion 0.30 0.35 0.25 0.09 0.01 Suppose three students are to be selected at random. As each is selected, their math grades are written down and they are replaced into the population of students. Three possible outcomes of this experiment are listed below. Calculate the probabilities of these three sequences appearances. a) BAC b) CFF c) ABA ANSWER: a) P (BAC) = P ( B ) P ( A ) P ( C ) = (0.35) (0.30) (0.25) = 0.02625 b) P (CFF) = P ( C ) P ( F ) P ( F ) = (0.25) (0.01) (0.01) = 0.00002 c) P (ABA) = P (A) P ( B ) P ( A ) = (0.30) (0.35) (0.30) = 0.03150 20. A particular college has the reputation of awarding very few high grades in their math courses. The grade distribution for the college’s math courses is given in the table below: Grade A B C D F Proportion 0.10 0.15 0.35 0.35 0.05 Suppose three students are to be selected at random. As each is selected, their math grades are written down and they are replaced into the population of students. Three possible outcomes of this experiment are listed below. Calculate the probabilities of these three sequenced appearances. a) ABC b) CCF c) BBA ANSWER: a) P (ABC) = P ( A ) P ( B ) P ( C ) = (0.10) (0.15) (0.35) = 0.00525 b) P (CCF) = P ( C ) P ( C ) P ( F ) = (0.35) (0.35) (0.05) = 0.00613 c) P (BBA) = P (B) P ( B ) P ( A ) = (0.15) (0.15) (0.10) = 0.00225 21. One common method used to forecast the results of elections is to take an “exit poll”, asking people whom they supported as they come out of the voting place. Suppose candidate A and candidate B are running for a particular public office. In point of fact, 60% of the voting public in the neighborhood of the polling place support candidate A. Assuming that the candidate of choice for a voter leaving the polling place is independent of the candidate of choice for the next person to leave, what is the probability that the first 5 voters to leave the polling place would have this sequence of candidate of choice? AAABA ANSWER: P (BBA) = P(A) P(A) P(A) P(B) P(A) = (0.60) (0.60) (0.60)(0.40) (0.6) = 0.05184 22. The probability distribution of a continuous random variable will describe which of the following?

I. II.

The probability associated with a particular value of the random variable.

The probability associated with a particular interval of possible values.

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions a. I only b. II only c. Both I and II d. Neither I nor II ANSWER: b 23. If a random variable is continuous, which of the following describes its probability distribution?

I. II.

For a single value of the variable, the proportion of time, in the long run, that the variable will take on that value.

For a particular interval of possible values of the variable, the proportion of time, in the long run, that the variable will take on a value in that interval.

a. I only b. II only c. Both I and II d. Neither I nor II ANSWER: b 24. Which of the following are properties of functions representing probability distributions for continuous random variable x? a. b. c. d.

ANSWER: c 25. The curve defined by the probability distribution of a continuous random variable is called the density function f (x). Which of the following is a property of f (x)? a. The total area under b. The total area under c. The total area under d. The total area under ANSWER: c 26. The probability distribution for a continuous random variable x can be described by the function f (x). The area under f (x) between x = 6 and x = 6 is equal to 0.33. Which of the following can be said of the proportion of time, in the long run, that x will be between 2 and 6? a. 0.66 b. 0.33 c. 0.58 d. 0.45 ANSWER: b 27. What is the probability of observing continuous random variable x in an interval from x = 1 to x = 10 if the area under

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions the density curve above the interval 1

x

10 is 0.78?

a. 22% b. 11% c. 78% d. 39% ANSWER: c 28. The probability distribution P (x) for continuous random variable x is shown in the figure below. If the shaded portion, which represents the area under P(x) between x = a and x = b is equal to 0.68, then what is the probability that x will lie between a and b?

a. 32% b. 68% c. 16% d. 84% ANSWER: b 29. The probability distribution P (x) for continuous random variable x is shown in the figure below. If the shaded portion, which represents the area under P(x) for values of x a is equal to 0.25, then what is the probability that x will be less than a?

a. 25% b. 50% c. 75% d. 100% ANSWER: a

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions 30. The probability distribution P (x) for continuous random variable x is shown in the figure below. If the shaded portion, which represents the area under P(x) for values of x a is equal to 0.25, then what is the probability that x will be less than a?

a. 25% b. 50% c. 75% d. 100% ANSWER: c 31. The probability distribution P (x) for continuous random variable x is shown in the figure below. If the shaded portion, which represents the area under P(x) between x = a and x = b is equal to 0.68, then what is the probability that x will be less than a or greater than b?

a. 32% b. 68% c. 16% d. 84% ANSWER: a 32. Suppose that a call center receives on average 1.7 calls per minute. The graphs below show the probability of receiving calls.

Which distribution curve has a shaded region that corresponds to the probability of a call happening between two and six minutes?

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions a.

b.

c.

d.

ANSWER: b 33. Suppose that the random variable is the percentage of the total number of diet sodas consumed over several years by U.S. residents for a given age has the probability distribution described by the following density curve.

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions

What probability is represented by the shaded portion assuming that the shaded portion has an area of 0.65? How can this probability be interpreted in the context of this problem? a. P(x ≤ 20), about 65% of the U.S. population consuming diet sodas are people aged less than 20 years. b. P(x > 50), about 65% of the U.S. population consuming diet sodas are people aged 50 years and older. c. P(20 ≤ x ≤ 50), about 65% of the U.S. population consuming diet sodas are people aged between 20 and 50 years. d. P(20 ≤ x ≤ 50), about 35% of the U.S. population consuming diet sodas are people aged between 20 and 50 years.

ANSWER: c 34. Suppose x is a continuous random variable with the probability distribution shown below.

What probability is represented by the shaded area? a. P (0 < x < 20) b. P (20 < x < 50) c. 1 - P (20 < x < 50) d. P (x > 50) ANSWER: b 35. Suppose that a continuous random variable x has a probability distribution with density function f(x). The area under f(x) between x = 5 and x = 8 is 0.34. What is the probability that x is less than five or greater than 8? a. 0.34

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions b. 0.17 c. 0.66 d. 0.94 ANSWER: c 36. Suppose that a continuous random variable x has a probability distribution with density function f(x). The area under f(x) for x < 500 is 0.45. What is the probability that x > 500? a. 0.25 b. 0.45 c. 0.55 d. 0.75 ANSWER: c 37. Let x represent a continuous random variable defined as the time in minutes required to cook eggs at a particular elevation. Supposed that x has a probability distribution with a density function defined as:

What is the probability that an egg will cook is less than 8 minutes? a. 25% b. 75% c. 50% d. 100% ANSWER: c 38. Let x represent a continuous random variable defined as the time in hours required to drive between two small towns.

Supposed that x has a probability distribution with a density function defined as:

What is the probability that a driver will require between 2 and 2.5 hours to drive between the two towns? a. 40% b. 60% c. 50% d. 20% ANSWER: a 39. The density curve for a continuous random variable is shown below. Use this curve to find the following probabilities: a) P(x < 1) b) P (2 < x <3) c) P( x ≥ 3)

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions

You may use the following area formulas in your calculations: area of a rectangle = (length)(width) area of a trapezoid = area of a right traingle =

(height) (base1 + base2) (base) (height)

ANSWER: a) Area of a trapezoid defined by the area under P(x) for 0 < x < 1

b) Area of a trapezoid defined by the area under P(x) for 2 < x < 3

c) Area of a triangle defined by the area under P(x) for x greater than or equal to 3

40. The density curve for a continuous random variable is shown below. Use this curve to find the following probabilities: a) P(x < 1) b) P (2 < x <3) c) P( x ≥ 3)

You may use the following area formulas in your calculations: area of a rectangle = (length)(width)

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions area of a trapezoid = area of a right traingle =

(height) (base1 + base2) (base) (height)

ANSWER: a) Area of a trapezoid defined by the area under P(x) for 0 < x < 1

b) Area of a trapezoid defined by the area under P(x) for 2 < x < 3

c) Area of a triangle defined by the area under P(x) for x greater than or equal to 3

41. In a certain very large city, the Department of Transportation (D.O.T.) has organized a complex system of bus routes.

In an advertising campaign, citizens are encouraged to head for the nearest bus stop to be transported to and from the central city. Suppose that at one of the bus stops, the amount of time (in minutes) that a commuter must wait for a bus is a continuous random variable, T . The density function for P(T) is a nonzero constant value for 0 < T < 30 minutes and zero for all values of T > 30 minutes. a) Sketch the probability distribution of T. b) What is the probability that a random commuter will spend more than 12 minutes waiting for a bus?

ANSWER: The probability density function is a straight, horizontal line with an area under the curve with a height of (1/30) and a length of 30 (see figure to the left). The probability of a commuter waiting more than 12 minutes for a bus is the shaded area under the curve on the right and has a value of (18/30) = 0.60.

42. Which of the following accurately describes the mean of a random variable? a. The average value of a sample of a few chance experiment outcomes b. The sample mean c. The value of the random variable for which its probability distribution is centered d. The sample median ANSWER: c 43. Which of the following plots shows a probability distribution whose random variable has a mean of 10?

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions

a. A and B only b. A and C only c. B, C, and D only d. A, B, and D only ANSWER: d 44. Which of the following accurately describes the standard deviation of a random variable? a. The standard deviation of a sample of a few chance experiment outcomes b. The sample standard deviation c. The variability in the random variable’s probability distribution d. The sample variance ANSWER: c 45. For which of the following probability distributions would you expect the standard deviation of its random variable to be highest?

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions

a. Probability distribution A b. Probability distribution B c. Probability distribution C d. Probability distribution D ANSWER: d 46. Under which of the following conditions will sample relative frequencies approach probabilities for given values of a random variable? a. Small sample sizes b. Large sample sizes c. Sample size is unrelated to the extent to which relative frequencies approach probabilities d. Relative frequencies never approach probabilities ANSWER: b 47. Which of the following are characteristics of the mean of a random variable?

I. II.

Identifies where the variable’s probability distribution is centered Can be interpreted as the average value in a large number of observations of the variable.

a. I only b. II only c. Both I and II d. Neither I nor II ANSWER: c

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions 48. A college has a long-standing tradition of putting on a mid-summer play for the local community. Performing arts students from the college and amateur actors from the region audition for roles in the play. Historically, the proportion of college students (as opposed to amateur actors) who are chosen for the six lead roles is shown in the table below where x = the number of college students chosen.

x = #students chosen 0 1 2 3 4 5 6

p(x) 0 0.35 0.25 0.15 0.1 0.1 0.05

Which of the following represents the mean ( x) and standard deviation ( x) of the number of students chosen? a. b. c. d.

ANSWER: b 49. A college has a long-standing tradition of putting on a mid-summer play for the local community. Performing arts students from the college and amateur actors from the region audition for roles in the play. Historically, the proportion of amateur actors (as opposed to performing arts students) who are chosen for the six lead roles is shown in the table below where x = the number of college students chosen.

x = #students chosen 0 1 2 3 4 5 6

p(x) 0 0 0.05 0.05 0.25 0.35 0.3

Which of the following represents the mean ( x) and standard deviation ( x) of the number of students chosen? a. b. c. d.

ANSWER: c 50. While playing Monopoly, one player estimated the probabilities of the non-zero rents according to the following probability distribution.

x

p(x)

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions

$10 $20 $50 $130

0.20 0.20 0.40 0.20

Consider the random variable x = dollar amount in rent in a Monopoly roll. a) If the table above specifies the probability distribution p(x), what is the mean of the random variable x? b) If the probabilities are associated with the outcomes as in the table above, what is the standard deviation of the random variable x?

ANSWER:

51. While playing a card game, one player estimated the probabilities of having a winning hand a certain number of times in an afternoon of card play. Their results are summarized in the table below where random variable x = number of winning hands.

x 1 4 9 12

p(x) 0.40 0.20 0.20 0.20

a) If the table above specifies the probability distribution p(x), what is the mean of the random variable x? b) If the probabilities are associated with the outcomes as in the table above, what is the standard deviation of the random variable x?

ANSWER:

52. At a large university, students have either a final exam or a final paper at the end of a course. The table below lists the distribution of the number of final exams that students at the university will take, and their associated probabilities. What are the mean and standard deviation of this distribution?

x 0 1 2 3

p(x) 0.05 0.25 0.40 0.30

ANSWER:

53. The sales of a news magazine vary from week to week, depending on the importance of the news of the previous week. From empirical data over many years, the following distribution of sales (rounded to the nearest million) has been carefully constructed and are displayed in the table below. What are the mean and standard deviation of this distribution?

x 0 1 2 3

p(x) 0.15 0.25 0.40 0.20

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions ANSWER:

54. For a continuous random variable x, the height of the density curve over an interval a to b represents the probability that x is between a and b. a. True b. False ANSWER: False 55. Suppose the shaded area under the portion of the normal distribution for x > 8 is 0.23. What is the probability that x is less than 8?

a. 0.23 b. 0.77 c. 0.46 d. 0.39 ANSWER: b 56. Suppose the shaded area under the portion of the normal distribution for 6.5 < x < 8 is 0.68. What is the probability that x will be between 6.5 and 8?

a. 0.32 b. 0.16 c. 0.68 d. 0.84 ANSWER: c 57. Suppose the shaded area under the portion of the normal distribution for x > 8 is 0.23. What is the probability that x is greater than 8?

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions

a. 0.23 b. 0.77 c. 0.46 d. 0.39 ANSWER: a 58. Suppose the shaded area under the portion of the normal distribution for 6.5 < x < 8 is 0.68. What is the probability that x will be less than 6.5 or greater than 8?

a. 0.32 b. 0.16 c. 0.68 d. 0.84 ANSWER: a 59. The standard normal distribution has a mean of 0 and a standard deviation of 1. a. True b. False ANSWER: True 60. Determine the area under the curve to the right of -1.82. a. P(z ≥ -1.82) = 0.0015 b. P(z ≥ -1.82) = 0.0344 c. P(z ≥ -1.82) = 0.9656 d. P(z ≥ -1.82) = 0.9641 ANSWER: c 61. Determine the following areas under the standard normal (z) curve. a. The area under the z curve to the left of 2.53

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions b. c. d. e. f.

The area under the z curve to the left of -1.53 The area under the z curve to the right of 0.76 The area under the z curve to the right of -1.47 The area under the z curve between -1 and 3 The area under the z curve between -2.6 and -1.2

ANSWER: (a) 0.9943, (b) 0.0918, (c) 0.2236, (d) 0.9292, (e) 0.8400, (f) 0.1104 62. For a normal probability distribution of random variable x with a mean of 10 and a standard deviation of 1.5, what is the probability that x will be less than 8? a. 0.091 b. 0.909 c. 0.2525 d. 0.7475 ANSWER: a 63. For a normal probability distribution of random variable x with a mean of 20 and a standard deviation of 6, what is the probability that x will be between 9 and 25? a. 0.7643 b. 0.0333 c. 0.7977 d. 0.2357 ANSWER: a 64. When mature deciduous trees in certain temperate areas are lost to fire or logging, they are often naturally replaced by opportunistic tree species such as alders. At five years following the loss of the mature deciduous trees, the relationship between the height of alders in the regrowth area will follow a normal distribution with a mean of 12.05 feet and a standard deviation of 4.75 feet. What is the probability of finding an alder with a height greater than 13.00 feet? a. 0.42 b. 0.58 c. 0.79 d. 0.37 ANSWER: a 65. When mature deciduous trees in certain temperate areas are lost to fire or logging, they are often naturally replaced by opportunistic tree species such as alders. At five years following the loss of the mature deciduous trees, the relationship between the height of alders in the regrowth area will follow a normal distribution with a mean of 12.05 feet and a standard deviation of 4.75 feet. What is the probability of finding an alder with a height between 13.00 feet and 15.00 feet? a. 0.58 b. 0.73 c. 0.27 d. 0.15 ANSWER: d 66. Certain marine species require shoreline gravel of a particular size for reproduction and successful maturation of juvenile species. Samples taken from a particular gravel bar over a long period have diameters that follow a normal

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions distribution with a mean of 1.350 inches and a standard deviation of 0.220 inches. The marine species require gravel with diameter in a range of 0.920 to 0.980. What proportion of the gravel bar gravel is suitable for marine species? a. 0.025 b. 0.046 c. 0.021 d. 0.036 ANSWER: c 67. Certain marine species requires shoreline gravel of a particular size for reproduction and successful maturation of juvenile species. Samples taken from a particular gravel bar over a long period have diameters that follow a normal distribution with a mean of 1.350 inches and a standard deviation of 0.220 inches. The marine species require gravel with a diameter of at least 1.550 inches. What proportion of the gravel bar gravel is suitable for marine species? a. 0.818 b. 0.409 c. 0.182 d. 0.296 ANSWER: c 68. A gasoline tank for a certain model car is designed to hold 12 gallons of gas. Suppose that the actual capacity of the gas tank in cars of this type is well approximated by a normal distribution with a mean of 12.0 gallons and a standard deviation of 0.2 gallons. What is the probability that a randomly selected car of this model will have a gas tank that holds at most 11.7 gallons? a. 0.0668 b. 0.0334 c. 0.1336 d. 0.936 ANSWER: a 69. Which of the following are the essential steps for constructing a normal probability plot?

I. II. III. IV.

Select normal scores from a table or software package with an n-value corresponding to the number of observations in your data set.

Arrange your observations in order from smallest to largest.

Create (x, y) data pairs with the smallest normal scores as the x-value paired with the smallest value observation as the y-value and continuing for all n observations.

Create a scatterplot of your data pairs and check for linearity.

a. I and IV only b. I, II, and IV only c. I, III, and IV only d. I, II, III, and IV ANSWER: d 70. The data set below represents weights in grams of raspberries that customers picked at a local farm where customers are welcome to pick their own produce.

53.04,53.50,52.53,53.00,53.07,52.86,52.66,53.23,53.26,53.16 Which of the following best represents a normal probability plot constructed from the data above?

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions

a. Plot A b. Plot B c. Plot C d. Plot D ANSWER: d 71. For the normal probability plot below, how many normal scores were required in order to construct the plot?

a. Twenty b. Ten c. Thirty-five d. Fifteen ANSWER: b

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions 72. Which of the following would you expect for a normal probability plot constructed from a sample selected from a standard normal distribution? a. For each (x,y) data pair, the value for the x-term and the y-term are reasonably close. b. The plotted points will fall near a line with a 2:1 slope (63 line). c. The plotted points will fall near a line that passes through the point (0,1). d. The plotted points will fall near a line that passes through the point (0,0).

ANSWER: a 73. A normal probability plot suggests that a normal probability model is plausible if there is no obvious pattern in the scatterplot of points. a. True b. False ANSWER: False 74. The graphs below are normal probability plots of the vocabulary and math concepts scores on a standardized exam for a large sample of students. One of the score distributions is approximately normal. Identify the score distribution that is approximately normal and explain the reason for your choice.

ANSWER: The Math Concepts Score appears to be normally distributed since the normal probability plot shows a straight line. The plot of the Vocabulary Score shows a distinct “S” shape, indicating that the distribution is not normal.

75. Briefly describe how the correlation coefficient can be used to check for normality.

ANSWER: If the normal probability plot shows a strong linear pattern, it is reasonable to think that the population distribution may be approximately normal. The correlation coefficient is an indication of linearity, so, if the correlation coefficient of a normal probability plot is close to one (indicating linearity), then population distribution may be approximately normal.

76. The normal probability plots below do not show a strong linear pattern.

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions

Which of the following characteristics of the population distribution could have contributed to the nonlinearity of the normal probability plots: I. II. III.

There are outliers in the population distribution The population distribution is skewed (asymmetric) The population distribution is symmetric, but has heavier tails than a normal distribution

a. I and II only b. II and III only c. I and III only d. I, II, and III ANSWER: d 77. You have three different data sets, all of which you hope to model using a normal distribution. All data sets have ten observations (n = 10). To ensure that the populations from which the data sets are drawn are approximately normal, you create normal probability plots for all three data sets. You calculate the correlation coefficient for the data value vs. zscore for the least squares line for each plot and get the following: Data Set A, r value for normal probability plot = 0.32 Data Set B, r value for normal probability plot = 0.62 Data Set C, r value for normal probability plot = 0.91 Which of the three data sets was drawn from an approximately normal population? a. Data Sets A only b. Data Set C only c. Data Sets B and C d. Data Sets A and B ANSWER: b 78. Suppose you’re assessing the normality of the population from which a sampled data set is drawn. A colleague constructed a normal probability plot and calculated the correlation coefficient. Your colleague only reported their calculated r value of 0.915 to you. For which of the following sample sizes would it be reasonable to think that the population distribution is normal?

I) 10 II) 15 III) 25 IV) 40 a. I only b. I and II only c. III and IV only d. I, II, and III only

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions ANSWER: b 79. Which of the following are the same for binomial and geometric random variables?

I. II. III.

Both involve trials with only two outcomes (success or failure) Both require that trial outcomes be independent Both require that the probability of success of individual trials be the same

a. I and II only b. II and III only c. I and III only d. I, II, and III ANSWER: d 80. Which of the following is true for geometric random variables?

I) Represents the number of successes observed for a given number of independent trials II) Trials must be independent III) Trials must have only one of two outcomes (success or failure) IV) Include a fixed number of trials a. II and III only b. I, II, and IV c. I, II, and III d. II, III, and IV ANSWER: a 81. Which of the following is true for binomial random variables?

I) Represents the number of trials that must be run until a success is observed II) The probability of success for each individual trial must be the same III) Includes a fixed number of trials IV) Trials must have only one of two outcomes (success or failure) a. I, II, and IV only b. II, III, and IV only c. I, II, and IV only d. III and IV only ANSWER: b 82. Suppose you were interested in the number of times you needed to roll a twelve-sided die before getting a 3, 5, or 6.

Which of the following random variables and associated probability distributions would you use?

I. II.

Binomial Distribution Geometric Distribution a. I only b. II only c. Neither I nor II

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions d. Both I and II ANSWER: b 83. Suppose you have a bowl with six pears and six apples. Without looking, you select a fruit and place it in another container. Which of the following random variables and associated probability distributions would you use to determine the number of fruits you needed to select before you selected a pear?

I. II.

Binomial Distribution Geometric Distribution

a. I only b. Both I and II c. II only d. Neither I nor II ANSWER: d 84. You’re an environmental engineering technician sampling water from a creek for E. Coli testing. Presence of E. Coli in the surface water is usually an indication of improperly functioning septic systems and can pose a public health hazard.

A quick review of the history of E. Coli testing of water from this creek shows that 20% of the samples have E. Coli concentrations in excess of the legal limit. Your sampling protocol requires that you gather 20 water samples for testing.

What is the probability that no more than 3 of your samples will have E. Coli concentrations in excess of the legal limit? a. 0.41 b. 0.60 c. 0.21 d. 0.79 ANSWER: a 85. You’re a community energy safety technician reviewing the power outages across several neighborhoods following a severe ice storm. Based on the outage history for storms of this type, the probability that a neighborhood will have a power outage is 25%. Your job is to assess power availability to 5 neighborhoods. What is the probability that 3 or more of the 5 neighborhoods will have power outages? a. 8.8% b. 1.5% c. 10.3% d. 3.5% ANSWER: c 86. You’re the representative for a local farm cooperative that promotes the use of locally grown produce in upscale restaurants. Historical data has shown that 88% of local restaurants use locally-grown produce. You’re skeptical of this number, so you query 20 restaurants regarding their use of locally-grown produce. Assuming that the historical data is correct, what is the probability that 18 or more restaurants will say that they use local produce? a. 27.4% b. 7.8% c. 21.1% d. 56.3% ANSWER: d

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions 87. You’re a landscape designer assessing the success of a new variety of evergreen tree you planted in 6 yards. Based on the published ecological literature about this tree, the expected success rate is 90%. What is the probability that you will find success for the trees in all 6 of the yards? a. 0.354 b. 0.531 c. 0.885 d. 0.469 ANSWER: b 88. Suppose that in a certain metropolitan area, 18% of all automobiles are equipped with an electric engine. If you were to conduct a random check of 9 motorists, what is the probability that 4 of the 9 would be vehicles with electric engines?

ANSWER: 0.0490 89. A gambler rolls a six-sided die until the number six is shown. What is the probability that the gambler rolls the die more than twice? What is the probability that the gambler rolls the die at least four times? a. 0.3056; 0.5177 b. 0.3056; 0.4823 c. 0.6944; 0.5787 d. 0.6944; 0.4823 ANSWER: c 90. The results of several years of data gathering show that approximately 40% of the students at your school carry paper textbooks to class in addition to their calculator and laptop computers. As the student safety officer, you’re concerned that the weight of textbooks and computers could result in poor ergonomics and repetitive lifting injuries among students. You conduct a survey to see how many students on a given day are carrying a paper textbook and a laptop to class. If you queried one student at a time, what is the probability that you would need to query no more than three students before finding one carrying both a textbook and a laptop? a. 0.144 b. 0.784 c. 0.240 d. 0.216 ANSWER: b 91. You’re at a second-hand clothing store looking for a wool sweater. The shop has sweaters made from many different materials for sale, but only 38% of them are made from wool. The sweater material is listed on tags attached to each sweater. What is the probability that you would find a wool sweater after examining no more than five sweaters? a. 0.380 b. 0.620 c. 0.908 d. 0.056 ANSWER: c 92. You’re a quality inspector in a manufacturing facility. You’re inspecting parts at a particular point in the manufacturing process to ensure that defective parts do not proceed to downstream manufacturing steps. The historical defect rate for the parts you’re inspecting is high and equal to 66%. What is the probability that you will discover a defective part in the first 3 parts you inspect.? Assume that your inspection method is 100% effective for detecting the part

Name:

Class:

Date:

Chapter 06 - Random Variables and Probability Distributions defect you’re looking for. a. 96% b. 99% c. 88% d. 93% ANSWER: a 93. Suppose that, based on long-term records, 73% of visitors to a certain barbershop have a beard. On any given day that the barbershop is open, what is the probability that your first non-bearded customer will be the fourth customer to enter the store?

ANSWER: Geometric distribution with x = number of customers entering the store, including the customer which represents a success: P(x ≤ 4) = 0.995 94. If x is a binomial random variable based on n trials with per-trial success probability p, under which of the following conditions will the probability distribution of x be approximately normal? a. np ≤ 10 and n (1 - p) ≥ 10 b. np < 10 and n (1 - p) < 10 c. np ≥ 10 and n (1 - p) ≥ 10 d. np < 10 and n (1 - p) >10 ANSWER: c 95. If x is a binomial random variable based on 500 trials with a per-trial success probability of 0.12, what is the mean and standard deviation of the distribution, and is it approximately normal? a. ; yes it is approximately normal b.

; no it is not approximately normal

c.

; yes it is approximately normal

d.

; no it is not approximately normal

ANSWER: a 96. If x is a binomial random variable based on 50 trials with a per-trial success probability of 0.17, could you approximate the probability distribution for x with a normal distribution? a. Yes, because np < 10 b. No, because np is not ≥ 10 c. Yes, because n (1-p) < 10 d. Yes, because n (1-p) is ≥ 10 ANSWER: b 97. Historically, only 10.1% of U.S. holiday shoppers limit their holiday purchases to those they can make without incurring debt. Suppose 1000 shoppers are randomly selected at the end of the holiday season and asked if they incurred holiday-related debt. What is the probability that your sample of 1000 shoppers will include at least 90 who did not incur debt? a. 86.4% b. 88.8% c. 12.1%

Name:

Class:

Chapter 06 - Random Variables and Probability Distributions d. 87.6% ANSWER: b

Date:

Name:

Class:

Date:

Chapter 07 - Overview of Statistical Inference 1. Suppose you want to assess the number of students of voting age enrolled in your college who are registered to vote.

You mail surveys to the address on file with the registrar’s office for all students registered for a class that academic term.

Which of the following are risks that your sample (students who respond to the survey) will not represent the population (all students of voting age enrolled at your college)?

I. II. III.

Students in their final term of graduation may not have their current address listed with the registrar.

Students in their first term may have their parents’ address listed with the registrar rather than the one they use at college.

Students who are politically active would be more likely to be registered to vote and would be more likely to respond to the survey.

a. I and II only b. II and III only c. I and III only d. I, II, and III ANSWER: d 2. Suppose a researcher is collecting data about the amount of soda Americans consume in one day. If the researcher was to gather two separate representative samples from the population, differences may exist between the samples. These differences may be attributed to what?

ANSWER: Sampling variability 3. Data from a poll of adults aged 30 to 40 in a small town led to the following estimates: Approximately 54% of adults aged 30 to 40 want to improve housing conditions and 72% of adults aged 30 to 40 consider the presence of a garage for a car as a very important attribute in a new house. What additional information about the survey would you need to decide if it is reasonable to generalize these estimates to the population of adults aged 30 to 40 in this small town? a. In addition to the information provided, we would need to know if the subjects were randomly selected or not. b. In addition to the information provided, we would need to know the total population of the city. c. In addition to the information provided, we would need to know the number of adults aged 30 to 40. d. In addition to the information provided, we would need to know the number of adults aged 30 to 40 who have a garage.

ANSWER: a 4. When you are conducting a survey, which of the following sources of variability present risk in making an accurate estimation of population parameters?

I. II.

Sample-to-sample variability Variability in the population which makes representative sampling impractical

a. I only b. Neither I nor II c. Both I and II d. II only ANSWER: c 5. A technician wants to determine the typical strength of a particular brand of nylon rope. They assemble several samples of rope and subject each one to a tensile test under controlled conditions. They report the strength of each rope in pounds.

Which of the following presents a risk in using the average strength of the sampled ropes to estimate the population

Name:

Class:

Date:

Chapter 07 - Overview of Statistical Inference mean?

I. II.

Variation in sample-to-sample break strengths Variation in testing conditions from one sample to another

a. I only b. Neither I nor II c. Both I and II d. II only ANSWER: c 6. Suppose you’re running an experiment in the lab to determine the effect of a particular paint on the corrosion rate of steel in seawater. According to the paint manufacturer, the paint must be applied to a clean, sanded metal surface and cured for at least 72 hours. You prepare 20 steel test coupons, apply and cure the paint, then subject all samples to simulated seawater at a controlled temperature for one month. At the end of one month, you give each steel coupon a corrosion rating based on the number and size of visible rust spots. Based on the value of the corrosion rating, you determine whether or not the paint primer was effective for the prevention of corrosion on steel in seawater. Which of the following might be reasons your observed response (corrosion rating) might be the result of treatment effects rather than paint performance?

I. II. III.

Not cleaning the steel coupon surface before applying the paint Not sanding the coupon surface before applying the paint Curing the paint for less than 72 hours

a. I and II only b. II and III only c. I and III only d. I, II, and III ANSWER: d 7. Suppose a researcher is conducting an experiment to evaluate the effect of soda consumption on blood sugar fluctuations in people aged 50 to 70. The researcher randomly selected subjects and randomly assigned them to treatment groups. In one treatment group subjects were prohibited from drinking soda for the study duration. In the second treatment group subjects were asked to drink exactly one 12-ounce soda every eight hours for the study duration. Blood sugar levels were continuously monitored for all subjects and average fluctuations were reported. Which of the following would pose a risk to determining the effect of the treatment (soda consumption vs. no soda consumption) on blood sugar variability?

I. II.

Person-to-person variability in each treatment group Variability in the random assignment of persons to treatment groups

a. I only b. II only c. Neither I nor II d. Both I and II ANSWER: d 8. When you are conducting an experiment, which of the following sources of variability permit you to draw conclusions?

I.

Variability due to the effect of the experimental conditions (treatments)

Name:

Class:

Date:

Chapter 07 - Overview of Statistical Inference II. III.

Subject-to-subject variability within treatment groups Variability in random subject assignment to treatment groups

a. I only b. I and II only c. I and III only d. I, II, and III ANSWER: a 9. When you are conducting an experiment, which of the following sources of variability contribute to risk in your statistical inference?

I. II. III.

Variability due to the effect of the experimental conditions (treatments) Subject-to-subject variability within treatment groups Variability in random subject assignment to treatment groups

a. II only b. III only c. II and III only d. I, II, and III ANSWER: c 10. In many areas of the U.S., honey bee populations have been devastated in recent years, and the cause is not yet wellunderstood. The general opinion amongst the beekeepers in a particular region is that the problem is intensifying, and a researcher sets out to settle this question by surveying the health of a large number of randomly-selected hives.

Which of the following best describes this study? a. Hypothesis test with sample data b. Estimation study with sample data c. Hypothesis test with experimental data d. Estimation study with experimental data ANSWER: a 11. Suppose researchers would like to determine the proportion of Americans who own dogs. This would be a hypothesistesting problem. a. True b. False ANSWER: False 12. Consider the following two statistical inference situations: I. II.

A technician at a water-bottling facility wishes to test whether one of the filling machines is delivering less fluid per bottle than it is intended to deliver.

Another technician at this same facility wishes to determine the number of milliliters of water being delivered per bottle for the filling machine in question.

Which of these inference situations are hypothesis testing problems? a. I only

Name:

Class:

Date:

Chapter 07 - Overview of Statistical Inference b. II only c. Both I and II d. Neither I nor II ANSWER: a 13. Describe the difference between an estimation problem and a hypothesis testing problem.

ANSWER: An estimation problem is one in which we would like to learn something about the characteristics of a population. A hypothesis testing problem is one in which we would like to decide if there is evidence to support a particular claim.

14. Suppose a researcher is collecting data about the amount of soda Americans consume in one day. The researcher would like to determine if Americans consume over 12 ounces of soda per day on average. Is the problem being posed an estimation problem or a hypothesis test?

ANSWER: Hypothesis test 15. Consider the following two statistical inference situations: I. II.

An engineer at a civil engineering firm wants to assess clay content in the soils at several prospective building sites to determine which ones are suitable for building Another engineer at the same firm suspects that no more than half of these same building sites are suitable for building and wants to assess clay content at each site to confirm their suspicion.

Which of these inference situations is a hypothesis-testing problem? a. I only b. II only c. Both I and II d. Neither I nor II ANSWER: b 16. For which of the following questions would you be most interested in the population proportion instead of the population mean? a. Of the students at your university, how many minutes per day do they exercise? b. Do students at your university intend to seek work immediately after graduation? c. Is the grade point average of statistics students at this university higher than the national average? d. Of the students at your university, how many kilometers must they travel to and from campus each day?

ANSWER: b 17. In many areas of the U.S., honey bee populations have been devastated in recent years, and the cause is not yet wellunderstood. Researcher A surveys a large sample of honeybee colonies and rates each hive as “healthy” or “unhealthy”.

Researcher B surveys a large sample of honeybee colonies and assigns them a value from 0 to 100 based on the observed vigor of workers and drones. Which of the two studies attempts to make an inference regarding population proportions?

Which one attempts to make an inference regarding population means? a. Researcher A will make an inference regarding population proportions; researcher B will make an inference regarding population means b. Researcher B will make an inference regarding population proportions; researcher A will make an inference regarding population means. c. Both researcher A and researcher B will make inferences regarding population proportions.

Name:

Class:

Date:

Chapter 07 - Overview of Statistical Inference d. Both researcher A and researcher B will make inferences regarding population means ANSWER: a 18. Suppose two researchers are collecting data to compare the average amount of soda consumed daily by men and women. Researcher A asks participants to state the amount of soda (liters) they consumed the previous day. Researcher B asks the participants who report their soda consumption as one liter or more to report their gender. Which of the two studies attempts to make an inference regarding population proportions? Which one attempts to make an inference regarding population means? a. Researcher A will make an inference regarding population proportions; researcher B will make an inference regarding population means b. Researcher B will make an inference regarding population proportions; researcher A will make an inference regarding population means. c. Both researcher A and researcher B will make inferences regarding population proportions. d. Both researcher A and researcher B will make inferences regarding population means ANSWER: b 19. For which of the following questions would you be most interested in the population mean instead of the population proportion? a. Of the diners at a restaurant, what is the average volume (ounces) of wine consumed per customer per evening? b. Of the diners at a particular restaurant, which prefer vanilla ice cream over chocolate fudge cake for dessert? c. Do pet-owning apartment dwellers in a particular city prefer cats or dogs? d. Do passengers on winter-season transatlantic ocean liner crossings prefer balconies or inside cabins?

ANSWER: a 20. For which of the following questions would you be most interested in population proportion instead of the population mean? a. How many gallons of gas does the average resident of a particular town use each month? b. How many alcoholic beverages does the average cruise passenger consume over the course of a seven-day cruise? c. How many times per week do graduate students at your university visit the campus fitness center? d. Are students in your department at college registered to vote?

ANSWER: d 21. For which of the following studies would you obtain information about the population proportion instead of the population mean? a. A study evaluating the effect of workplace stress on body mass index b. A study evaluating the effect of latitude on weekly hours spent exercising in a gym c. A study evaluating the effect of a particular nutrient deficiency on hair color d. A study evaluating the effect of average daily temperature on the daily number of steps taken per person ANSWER: c 22. When selecting an appropriate method for data analysis, one important consideration is the number of variables and type of variables involved in the situation. a. True b. False

Name:

Class:

Date:

Chapter 07 - Overview of Statistical Inference ANSWER: True 23. When selecting an appropriate method for data analysis, the only important consideration is the number and type of variables involved in the situation. a. True b. False ANSWER: False 24. For the described study below, select the answers for the key questions listed in the table below:

A study was conducted to test an old adage that cats sleep more when the ambient temperature is higher. In the study, cats were isolated from distractions in areas of fixed temperature and were videotaped. The videotape footage was then reviewed to determine the percent of each 24-hour day spent asleep. Three large groups of randomly selected casts were randomly assigned to one of three environmental temperatures. a. Hypothesis testing; experimental data; univariate numerical data; one treatment b. Estimation; sample data; univariate numerical data; one treatment c. Hypothesis testing; experimental data; bivariate numerical data; three treatments d. Estimation; sample data; bivariate categorical data; three treatments ANSWER: c 25. A group of researchers surveyed 350 adults that were selected in a way that would produce a representative sample of adult residents of a particular city. One question in the survey asked, “Do you plan to go abroad for vacation this year?”

The researchers hoped to learn about the proportion of adult residents of the city that planned to go abroad for vacation that year.

For this study, answer the key questions listed in the table below:

Name:

Class:

Date:

Chapter 07 - Overview of Statistical Inference

a. Q = estimation; S = sample data; T = one variable, numerical; N = one sample b. Q = hypothesis testing; S = sample data; T = one variable, categorical; N = one sample c. Q = hypothesis testing; S = experimental data; T = one variable, numerical; N = one sample d. Q = estimation; S = sample data; T = one variable, categorical; N = one sample ANSWER: d 26. A company conducted a survey that investigated whether or not the classical music playing while waiting for the operator’s response affected the irritability of customers. In this one-week study, customers were randomly assigned to either a control group (who listened to periodic beeps while waiting for the operator’s response) or to an experimental group (who listened to classical music while waiting for the operator’s response). The operators during the conversation evaluated the level of irritability of the client as low, medium, and high. The company used these data to determine if there was evidence to support the claim that the mean level of irritability is higher for customers who listened to classical music while waiting for the operator’s response.

For this study, answer the key questions listed in the table below:

a. Q = estimation; S = experimental data; T = one variable, categorical; N = two treatments b. Q = hypothesis testing; S = sample data; T = one variable, numerical; N = one sample c. Q = hypothesis testing; S = experimental data; T = one variable, categorical; N = two treatments d. Q = estimation; S = sample data; T = one variable, categorical; N = two samples ANSWER: c 27. A materials engineer wants to characterize the adhesion strength, in pounds per square inch, of three different brands of adhesives. The engineer conducts a study in which they test the adhesion strength of two samples each of each brand of

Name:

Class:

Date:

Chapter 07 - Overview of Statistical Inference adhesive using a standard test and recording the adhesion strength in pounds per square inch.

For this study, answer the key questions listed in the table below:

a. Q = estimation; S = experimental data; T = one variable, categorical; N = two treatments b. Q = hypothesis testing; S = sample data; T = one variable, numerical; N = two samples c. Q = hypothesis testing; S = experimental data; T = one variable, categorical; N = two treatments d. Q = estimation; S = sample data; T = one variable, numerical; N = two samples ANSWER: d 28. List the five-step process that should be used in an estimation problem.

ANSWER: The first step is to explain what population characteristic you are estimating. The second step is to select a potential method using the four key questions (QSTN). The third step is to check that the method selected is appropriate. The fourth step is to use your sample data to perform any necessary calculations. The fifth step is to communicate the results of your results, thereby answering your question of interest.

29. Which of the following are reasons why communication of results is a critical step in the EMC3 process?

I. II. III.

Describe how the results of calculations answer the question of interest.

Explain what you’ve learned from the data.

Acknowledge potential risks to statistical inference.

a. I and II b. II and III c. I and III d. I, II, and III ANSWER: d 30. You and a colleague are both researchers evaluating the health of office workers in your regional area. You and your colleague collaborate in applying the five-step EMC3 process to estimate the typical fitness level of office workers in your area. Your colleague proposes to issue a single survey to 1000 randomly selected office workers in your region asking them to report their weekly exercise time in hours and whether or not they engage in any regular strength-building exercises. Your colleague proposes a method based on the study being an estimation involving a survey with numerical data and a single sample and asks you to perform the Check (step three of the five-step method). Which of the following might you recommend as part of your check?

I.

Your colleague can use their proposed method for the weekly exercise time data, but not the yes-no question

Name:

Class:

Date:

Chapter 07 - Overview of Statistical Inference II. III.

regarding strength-building exercise.

Your colleague could use a second method appropriate for categorical data used for estimation based on singlesample surveys to analyze the strength-building exercise responses.

Your colleague must select a method appropriate for two samples rather than one.

a. I and II only b. III only c. I and III only d. I only ANSWER: a 31. You and a colleague are collaborating to evaluate the prevalence of toxic metals in rural drinking water wells in your local area. You follow the five-step EMC3 method and select a method based on lab analysis of a single round of water sampling. You receive your lab results and decide that you will include a second round of water sampling. How should you apply the EMC3 process at this point?

I. II. III.

Proceed with the second round of water sampling, combine the results of both sampling rounds and perform calculations on the data using your initially selected method.

Discard the study since the addition of a second round of sampling would change the population characteristic your study is estimating.

Check to make sure that your initially selected method is appropriate and consider changing to one intended for two-sample studies.

a. I only b. II only c. III only d. Neither I nor II nor III ANSWER: c 32. List the five-step process that should be used in hypothesis testing.

ANSWER: The first step is to define the hypothesis that will be tested. The second step is to select a potential method using the four key questions (QSTN). The third step is the check to make sure that your selected method is appropriate. The fourth step is to use your sample data to perform any necessary calculations. The fifth step is the communicate the results of your results, thereby answering your question of interest.

33. You and a friend would like to answer the question of whether residential prices are higher in the downtown district or the waterfront district of a particular metropolitan area. You offer to apply the HMC3 method with the defined hypothesis that the downtown district has higher residential prices to answer the question. There are four published housing price surveys available for your metropolitan area, which you plan to use in your own study. You assemble the data from all four surveys into a single document which you use as input for your calculations. You propose a method appropriate for hypothesis testing using numerical survey data from a single sample. Which of the following must you do to complete the HMC3 process?

I. II. III.

Check your method, notice that a multi-sample method would be more appropriate given that your data came from four surveys, and use your data to perform calculations for the multi-sample method Use the data from the four published surveys to calculate results using your initially selected single-sample method Share the results of your calculations with your friend

Name:

Class:

Date:

Chapter 07 - Overview of Statistical Inference IV.

Let your friend know which district is more expensive and why

a. II and III only b. I and III only c. II, III, and IV only d. I, III, and IV only ANSWER: d 34. You are a veterinary researcher applying the HMC3 method to test the hypothesis that long-haired domestic cats shed more fur when exposed to more natural daylight. You conduct an experiment on two groups of randomly selected longhair cats in which one group is exposed to solar-matched lighting simulating summer solstice conditions (plentiful daylight) and another group is exposed to solar-matched lighting simulating winter solstice conditions (minimal daylight).

Cats exposed to both lighting conditions are groomed daily and the weight of removed hair is measured and recorded.

Which of the following additional steps must you take?

I. II. III. IV.

Select a method appropriate for hypothesis testing via experiment producing numerical data for two treatment groups Use the data from your experiment to perform calculations appropriate for your initially selected method and share your calculation results with your colleagues and supervisor.

Check to make sure that you selected the correct method for your experimental approach and data type, then use your data to perform calculations appropriate for the method.

Communicate the impact of daylight on long-haired cat shedding based on the results of your study and analysis.

a. I and II only b. I, II, and III only c. I, III, and IV d. I, II, and IV ANSWER: c 35. When applying the HMC3 process for hypothesis testing, the first step involves defining the actual hypothesis that will be tested. Without a defined hypothesis, it is difficult (if not impossible) to determine an appropriate statistical method.

Suppose you’re interested in the impact of grooming tools on the effectiveness of de-shedding (shed fur removal) from long-haired dogs. Which of the following would properly accomplish the first step of the HMC3 process related to this topic?

I. II.

How much shed fur does grooming tool A remove from the average long-haired dog during a typical professional grooming session?

Grooming tool A will remove 50% more shed fur from the average long-haired dog than grooming tool B during a typical professional grooming session.

a. I only b. II only c. Both I and II d. Neither I nor II ANSWER: b

Name:

Class:

Date:

Chapter 08 - Sampling Variability and Sampling Distributions 1. Suppose you’re studying water pollution in a lake. Which of the following best describes why you might want to take water samples from the lake for lab analysis?

I) To learn something about the pollutant type and concentration in the sampled water.

II) To infer something about the typical pollutant type and concentration in the lake water.

III) To infer something about the differences in pollutant type and concentration at different points in the lake. a. I only b. II only c. III only d. II and III only ANSWER: d 2. Under what conditions will the sample proportion I. II. III.

equal the population proportion p?

When populations are very small When sample sizes are very large When many samples are taken

a. I only b. Neither I, nor II, nor III c. II only d. III only ANSWER: b 3. Suppose you’re a soil scientist. You and two colleagues are taking soil samples to determine clay content. You each take a soil sample and analyze it to determine the proportion of sample weight attributable to clay. Clay proportions for your five-sample sets are shown below: For which of the two pairs of scientists is the sampling variability highest? a. Scientist #1 vs. Scientist #2 b. Scientist #2 vs. Scientist #3 c. Scientist #1 vs. Scientist #3 d. Cannot tell from the information given ANSWER: c 4. Suppose you’re interested in the mean of a particular population of 100 total items. You take samples of 4 items per sample and calculate sample means in the hopes of learning something about the population mean. After taking five samples of four items per sample, you notice that your value for distribution help you in this case?

I. II.

varies from sample to sample. How could the sampling

The sampling distribution would help you determine the typical value you should expect for calculated for any sample of four taken from the population.

The sampling distribution would show the variability of values calculated from samples of four taken from the population. a. I only b. Both I and II

Name:

Class:

Date:

Chapter 08 - Sampling Variability and Sampling Distributions c. Neither I nor II d. II only ANSWER: b 5. Suppose you’re interested in the proportion of students in your university who prefer green tea vs. black or white tea.

There are 880 students at your university. You take ten samples of five students per sample and ask them to complete a survey regarding their tea preference. For each of the ten samples, you calculate , the proportion of students who prefer green tea. You notice that the value of varies more from sample to sample than you thought that it would. A friend suggests that you calculate the sampling distribution to give you a better idea of the range of variability of Which of the following is true regarding the usefulness of the sampling distribution for determining the range of and the practicality of calculating it.?

I) The sampling distribution would not help you to assess the range of variability of , but it would be simple to calculate as it only involves creating a histogram of the of your ten samples.

II) The sampling distribution would help you to assess the range of variability of , but it would not be practical to calculate since it would require that you calculate for every possible different sample of 4 items from your 880item population.

III) Although the sampling distribution would help you to assess the range of variability of , it is not practical to calculate. You could estimate the sampling distribution from a histogram of relative frequencies for several samples. a. I only b. II only c. I and II d. II and III ANSWER: d 6. A statistic is a characteristic of the population. a. True b. False ANSWER: False 7. The quantities

and

are statistics.

a. True b. False ANSWER: True 8. Which of the following is a statistic?

I) Sample mean II) Population mean III) Sample variance IV) Sample proportion a. I and II only b. I, II, and III only

Name:

Class:

Date:

Chapter 08 - Sampling Variability and Sampling Distributions c. II, III, and IV only d. I, II, and IV only ANSWER: c 9. Which of the following are characteristics of sampling variability? a. Does not vary with sample size b. Is constant from sample to sample c. Describes the difference between the observed value of a statistic and the corresponding population parameter d. Describes the sample-to-sample variability of a statistic ANSWER: d 10. Which of the following is a statistic?

I) Sample mean II) Population mean III) Sample standard deviation IV) Population proportion a. I and III only b. III only c. IV only d. II and IV ANSWER: a 11. Which of the following is true for sample vs. population proportions?

I) Both express fractions of interest II) Both change from sample to sample III) Both are statistics a. I only b. II only c. III only d. II and III only ANSWER: a 12. Suppose you want to know the proportion of students at your university

who prefer milk chocolate over dark

chocolate. You conduct five surveys of twenty students each and get the following sample proportions: .

Using the five sample proportions above, what can we infer regarding the proportion of students at your university who prefer milk chocolate?

I. II.

The population proportion is equal to the average of the five sample proportions The population proportion lies somewhere between and a. I only b. Both I and II

Name:

Class:

Date:

Chapter 08 - Sampling Variability and Sampling Distributions c. Neither I nor II d. II only ANSWER: c 13. Based on extensive historical records, the proportion of guests at a particular hotel who request ground-floor rooms is 33%. What proportion of guests will request a ground-floor room on any given weekend night? a. 33% b. At least 33% c. No more than 33% d. Cannot tell from the information given ANSWER: d 14. Based on historical records, the proportion of passengers on transatlantic cruises who request an inside cabin near the center of the ship is 28%. What can we say about the proportion of passengers taken from a sample of transatlantic cruises held during the months of January and February who request an inside cabin? a. Proportion for January-February cruises will be < 28% b. Proportion for January-February cruises will be = 28% c. Proportion for January-February cruises will be > 28% d. Cannot tell from the information given ANSWER: d 15. Suppose you want to know the proportion of the residents of a metropolitan area

who use public transportation

exclusively. You conduct four surveys of 1,500 people each and get the following sample proportions: .

Using the four sample proportions above, what can we infer regarding the proportion of the metropolitan area residents who use public transportation exclusively?

I. II.

The population proportion is equal to the average of the four sample proportions The population proportion lies somewhere between and

a. I only b. Both I and II c. II only d. Neither I nor II ANSWER: d 16. You’re a market researcher for a company that manufactures winter outerwear. You would like to learn the proportion of mass transit riders in a particular region who need winter coats that are both waterproof and insulating. You plan to conduct 15 surveys of year-round transit riders in your area and use the surveys to construct a sampling distribution. You will be basing the upcoming year’s manufacturing plans on the survey data, so you would like to minimize the standard deviation of the sampling distribution. Which of the following survey sizes (n = number of persons per survey) should you choose? a. n=20 b. n=8

Name:

Class:

Date:

Chapter 08 - Sampling Variability and Sampling Distributions c. n=50 d. n=150 ANSWER: d 17. The standard deviation of the distribution of

decreases as n increases.

a. True b. False ANSWER: True 18. As the sample size increases, which of the following is true regarding the sampling distribution of ? a. The sampling distribution becomes more spread out b. The sampling distribution becomes less spread out c. The sampling distribution is not affected by changes in sample size d. The sampling distribution will become less spread out, but only if p is close to 0.5 ANSWER: b 19. The standard deviation

of the sampling distribution of the sample proportion

proportion p and the sample size n by the following expression:

is related to the population

. Based on this expression, which of the

following is true regarding the relationship between and n? a. increases as n increases because n is under the radical (square root operator) b.

decreases as n increases because n is under the radical (square root operator)

c.

increases as n increases because n is in the numerator

d.

decreases as n increases because n is in the denominator

ANSWER: d 20. For which of the following would you expect the sampling distribution for tightly clustered about the population proportion p?

I) large sample size n II) large population proportion p III) small sample size n IV) population proportion near 0.5 a. I only b. I and II c. I and IV d. II only ANSWER: a

to be the least spread out and more

21. A random sample is to be selected from a population that has a proportion of success p = 0.50. Determine the mean and standard deviation of the sampling distribution for the sample size n = 100. a. Mean b. Mean

; standard deviation ; standard deviation

Name:

Class:

Date:

Chapter 08 - Sampling Variability and Sampling Distributions c. Mean d. Mean

; standard deviation ; standard deviation

ANSWER: c 22. Many colleges allow students to rent textbooks for an academic term. Suppose that 73% of all students enrolled at a particular college would rent textbooks if they had the option. If the campus bookstore uses a random sample size 40 to estimate the proportion of students at the college who would rent textbooks, then what are the standard deviation and mean

of the sampling distribution of

?

a. Standard deviation =0.070, mean = 0.73 b. Standard deviation =0.135, mean = 0.27 c. Standard deviation = 0.082, mean = 0.73 d. Standard deviation = 0.265, mean = 0.27 ANSWER: a 23. You’re a biologist measuring the length of frogs in seasonal ponds. You’re interested in the proportion of frogs longer than 2 inches. Suppose that extensive studies previously conducted in your area of study have shown that the population proportion of frogs over 2 inches in length is 0.110. If you used a sample size of 10 frogs, then what are the standard deviation and mean of the sampling distribution of (the per-sample proportion of frogs over 2-inches in length)? a. Standard deviation = 0.099, mean = 0.110 b. Standard deviation = 0.099, mean = 0.220 c. Standard deviation = 0.105, mean = 0.110 d. Standard deviation = 0.298, mean = 0.110 ANSWER: a 24. Suppose that a particular candidate for public office is favored by 33.0% of all registered voters in a district. If a polling organization took random samples of 60 voters, what would be the standard deviation and mean of the sampling distribution of (the per-sample proportion of voters favoring the candidate)? a. Standard deviation = 0.061, mean = 67.0% b. Standard deviation = 0.061, mean = 33.0% c. Standard deviation = 0.106, mean = 67.0% d. Standard deviation = 0.272, mean = 33.0% ANSWER: b 25. Suppose the proportion of sunny days in a beachside tourist area is known to be 0.550. You survey groups of 12 tourists per group who visit the area regarding the proportion of their stay which was sunny. What is the standard deviation and mean of the sampling distribution of (the proportion of sunny days during each tourist group’s visit)? a. Standard deviation = 0.214, mean = 0.550 b. Standard deviation = 0.021, mean = 0.450 c. Standard deviation = 0.144, mean = 0.550 d. Standard deviation = 0.194, mean = 0.450

Name:

Class:

Date:

Chapter 08 - Sampling Variability and Sampling Distributions ANSWER: c 26. The closer the population proportion p is to 0 or 1, the larger n must be for the distribution of the sample proportion to be approximately normal. a. True b. False ANSWER: True 27. If p = 0.90 then a sample size n = 10 is large enough for the sampling distribution to be approximated by a normal distribution. a. True b. False ANSWER: False 28. When the sample size n is “large enough”, the sampling distribution of has an approximately normal sampling distribution. How does one determine what n is considered sufficiently large for this to be true? What information regarding the population is needed to make this determination?

ANSWER: To determine if a sample size n is sufficiently large for the sampling distribution of to be approximately normal, you need to know the population proportion of success p. The sample size n will be large enough to approximate the sampling distribution of as normal if and if . Another way to say this is that the sample size is large enough to expect at least 10 successes and at least 10 failures in the sample.

29. You’re researching the proportion of homes that sell within one month of being offered for sale. The housing market in the area you’re researching has more home buyers than sellers, so the population proportion is 0.85. If you used a sample size of 20, would the sampling distribution of have an approximately normal distribution? a. Yes, the sampling distribution of

would be approximately normal.

b. No, the sampling distribution of

would not be approximately normal.

c. The extent to which a sampling distribution can be approximated as normal is unrelated to n and p. d. Cannot tell from the information given.

ANSWER: b 30. You’re evaluating four sampling distributions of to determine which ones can be approximated as normal distributions. All of them have sample sizes of 60. The corresponding population proportions are given below: I) p = 0.50 II) p = 0.20 III) p = 0.95 IV) p = 0.15 a. I only b. I and II c. III and IV only d. I, II, and IV only ANSWER: b 31. As n grows larger, the values of

are clustered closer to the population proportion p.

Name:

Class:

Date:

Chapter 08 - Sampling Variability and Sampling Distributions a. True b. False ANSWER: True 32. The mean value

of the sampling distribution is equal to the population value p, regardless of sample size n.

a. True b. False ANSWER: True 33. Consider sampling from a population whose proportion of successes is p = 0.1. As the sample size n increases, some characteristics of the sampling distribution of change. Which of the following characteristics will change as n increases and how does it affect the ability to use the sampling distribution of to predict the population p? a) The mean of the sampling distribution of b) The standard deviation of the sampling distribution of c) The shape of the sampling distribution of ANSWER:

a) As the sample size increases, the mean of the sampling distribution of stays the same. Since is equal to p regardless of n, increasing n does not change the ability to use the sampling distribution of to predict p. b) As the sampling size increases, the standard deviation of the sampling distribution decreases.

With a smaller , the for any given sample will be closer to the population proportion p. c) As the sample size increases, the sampling distribution of becomes less skewed and more normal.

34. Suppose you want to estimate the population proportion, but only have the proportion of a random sample size n.

Which of the following characteristics of the sampling distribution proportion would permit you to determine how well estimates p?

I. II. III.

Proportions of individual samples

cluster around the population proportion p

can be used in place of p to calculate can be used in place of p to verify that the sampling distribution of

is approximately normal

a. I and II only b. II and III only c. I and III only d. I, II, and III ANSWER: d 35. The distribution of the sampling proportion being sampled. a. True b. False ANSWER: False

will always have the same shape as the distribution of the population

36. Suppose that the actual proportion of people at a particular company who use their bicycles to travel to work is 0.35.

Name:

Class:

Date:

Chapter 08 - Sampling Variability and Sampling Distributions In a study of bicycle parking needs, the company’s administration would like to estimate this proportion. They plan to take a random sample of 50 employees and use the sample proportion who use bicycles, , as an estimate of the population proportion. Estimate the standard deviation of the sample distribution. Suppose that another sample of different size has been selected and the standard deviation of this new sample distribution = 0.13. Would you expect more or less sample-to-sample variability in the sample proportions than for when n = 50? Is the sample size that resulted in = 0.13 larger or smaller than 50? a. The standard deviation for the initial sample of the size n = 50 is 0.067. A standard deviation of 0.13 is greater than a standard of 0.067, indicating lower sample-to-sample variability. The new sample size is smaller. b. The standard deviation for the initial sample of the size n = 50 is 0.67. A standard deviation of 0.13 is less than a standard of 0.67, indicating lower sample-to-sample variability. The new sample size is larger. c. The standard deviation for the initial sample of the size n = 50 is 0.067. A standard deviation of 0.13 is greater than a standard of 0.067, indicating higher sample-to-sample variability. The new sample size is smaller. d. The standard deviation for the initial sample of the size n = 50 is 0.067. A standard deviation of 0.13 is greater than a standard of 0.067, indicating lower sample-to-sample variability. The new sample size is larger.

ANSWER: c 37. Determine the mean and standard deviation of the sampling distribution of when n = 100 and p = 0.650. Determine whether or not the sampling distribution of is approximately normal. If the distribution is normal, what is the probability of a sample proportion = 0.600? a.

= 0.650,

= 0.047, sampling distribution is approximately normal, probability of

= 0.600 is 0.144.

b.

= 0.650,

= 0.059, sampling distribution is approximately normal, probability of

= 0.600 is 0.198.

c.

= 0.650,

= 0.081, sampling distribution is approximately normal, probability of

= 0.600 is 0.269.

d.

= 0.650,

= 0.094, sampling distribution is approximately normal, probability of

= 0.600 is 0.297.

ANSWER: a 38. Suppose you have a population with proportion p = 0.88. How does the standard deviation of the sampling distribution change for a sample size of n = 20 vs. a sample size of n = 100? For which is the sampling distribution approximately normal? a. For n = 20, = 0.0727; for n = 100, = 0.0325; the sampling distribution is approximately normal for n = 100, but not for n = 20 b. For n = 20, = 0.2098; for n = 100, = 0.0325; the sampling distribution is approximately normal for both n = 100 and for n = 20 c. For n = 20, = 0.0727; for n = 100, = 0.0938; the sampling distribution is approximately normal for n = 100, but not for n = 20 d. For n = 20, = 0.0775; for n = 100, = 0.1803; the sampling distribution is approximately normal for neither n = 100, nor for n = 20 ANSWER: a 39. Suppose two sampling distributions are created from a single population. For one sampling distribution, n = 25 and for the other, n = 100. The population proportion is p = 0.52. For which of the two sampling distributions would there be a 95% chance of randomly selecting a sample with = 0.40?

I.

Sampling distribution with n = 25

Name:

Class:

Date:

Chapter 08 - Sampling Variability and Sampling Distributions II.

Sampling distribution with n = 100

a. I only b. II only c. Neither I nor II d. Both I and II ANSWER: b 40. The principal at a High School has been asked to estimate the proportion of students who drive to school and use the school parking lot. They take a random sample of size n = 32 students and calculate a sample proportion = 0.8. The principal concludes that, since the sample size was greater than 30, the sampling distribution would be approximately normal. Why is this conclusion incorrect?

ANSWER: The principal’s statement is not accurate since only one of the two checks was used. Although the product is greater than 10., the product is less than 10 41. One method for estimating the availability of office space in large cities is to conduct a random sample of offices, and calculate the proportion of offices currently being used. Suppose that real estate agents believe that p = 0.70 of all offices are currently occupied, and decide to take a sample to assess their belief. They are considering a sample size of n = 40. a) Show that this sample size is large enough to justify using the normal approximation to the sampling distribution of . b) What is the mean of the sampling distribution of if the real estate agents are correct? c) What is the standard deviation of the sampling distribution of if the real estate agents are correct? d) If the real estate agents are correct, what is the probability that a sample proportion, , would differ from p = 0.70 by as much as 0.05?

ANSWER: a) b)

= 0.70

c)

d)

The probability that

42. Some biologists believe the evolution of handedness is linked to complex behaviors such as tool-use. Under this theory, handedness would be genetically passed on from parents to children. That is, left-handed parents would be more likely to have left-handed children than right-handed parents. An alternate theory asserts that handedness should be random, with left- and right-handedness equally likely. In a recent study using a simple random sample of n = 76 righthanded parents, 50 of the children born were right-handed ( = 0.658). Suppose handedness is a random occurrence with either hand equally likely to be dominant, implying that the probability of a right-handed offspring is p = 0.50. a) Show that it is reasonable to approximate the sampling distribution of p using a normal distribution. b) Assuming left- and right-handed children are equally likely from right-handed parents, what is the probability of observing a sample proportion of at least = 0.658.

ANSWER:

a)

which is greater than or equal to 10.

is also greater than or equal to 10. b) The probability that is greater than or equal to 0.658 is equal to

which is also equal to 38 and

Name:

Class:

Date:

Chapter 08 - Sampling Variability and Sampling Distributions

43. The first large-scale study of the human sex ratio involved over 6,000 families each having 12 children and was conducted in the 19th century, when large families were common. 52% of the children they observed were boys. Suppose that 21st century researchers wish to replicate this observational study. In order to see if this proportion of boys might have changed in the intervening years, suppose the researchers track down 50 families with 12 children. From these 600 children, a random sample of 50 children is taken. 30 of 50 children were boys ( = 0.6). a) Show that it is reasonable to approximate the sampling distribution using a normal distribution. b) If the modern true population proportion of newborn boys is p = 0.52, what is the probability of observing a sample proportion of at least = 0.6?

ANSWER:

a) equal to 10. b) The probability that

which is greater than or equal to 10. is greater than or equal to 0.6 is equal to

which is also greater than or

Name:

Class:

Date:

Chapter 09 - Estimating a Population Proportion 1. Which of the following properties of a statistic make it a good estimator of a population characteristic?

I. It is unbiased (or nearly unbiased) II. It has a large standard error a. I only b. Neither I nor II c. II only d. Both I and II ANSWER: a 2. Under which of the following conditions does the standard deviation good estimator of ?

I. II. III.

Under all conditions, because When the is close to 0.5 When sampling size is large

of the sampling distribution of

become a

is an unbiased estimator

a. Neither I nor II nor III b. I only c. II only d. III only ANSWER: d 3. Which of the following are characteristics of a statistic that is a good estimator of a population characteristic?

I. II.

Its sampling distribution is centered at the actual value of the population characteristic Its values are closely clustered around its center

a. I only b. II only c. Both I and II d. Neither I nor II ANSWER: c 4. A statistic that is unbiased with a small standard error is likely to result in an estimate that is close to the actual value of the population characteristic. a. True b. False ANSWER: True 5. Three different statistics are being considered for estimating a population characteristic. The sampling distributions for all three statistics are shown below.

Name:

Class:

Date:

Chapter 09 - Estimating a Population Proportion

Which statistic would you recommend using to estimate the population characteristics? a. Statistic I only b. Statistic II only c. Statistic III only d. Statistics I and II ANSWER: a 6. When choosing a statistic for calculating an estimate, what factors should be considered?

ANSWER: Two factors should be considered. First, the statistic should be unbiased, meaning that the statistic should have a long-term average equal to the population parameter being estimated. Second, the standard deviation of the sampling distribution of the statistic should be as small as possible, making typical estimates more accurate.

7. Using an unbiased statistic guarantees both that there will be no systemic tendency to under- or overestimate the value of the population characteristic and that estimates will almost always be relatively close to the true value. a. True b. False ANSWER: False 8. An unbiased statistic is one that: a. Is closely approximated by a normal curve b. Does not consistently tend to over- or underestimate the value of the population characteristic c. Is mound-shaped and has a small variance d. Is nearly symmetric ANSWER: b 9. What is the difference between an unbiased statistic and a biased statistic?

ANSWER: An unbiased statistic is one for which its average value over all possible samples is exactly equal to the value of the population parameter it is estimating. A biased statistic, on the other hand, will average to a value that is different from the population parameter.

Name:

Class:

Date:

Chapter 09 - Estimating a Population Proportion 10. The sampling distributions for three different statistics are shown in the figure below. Which of them are unbiased estimators of the population characteristic?

a. Statistics I and II b. Statistics II and III c. Statistics I and III d. Statistics I, II, and III ANSWER: b 11. The sampling distributions for three different statistics are shown in the figure below. Which of them are unbiased estimators of the population characteristic?

a. Statistics I and II b. Statistics II and III c. Statistics I and III d. Statistics I, II, and III ANSWER: d 12. The sampling distribution of

tends to be more spread out for larger sample sizes than for smaller sample sizes.

a. True b. False ANSWER: False 13. A random sample will be selected from the population of all adult residents of a particular city. The sample proportion

Name:

Class:

Date:

Chapter 09 - Estimating a Population Proportion will be used to estimate , the proportion of all adult residents who are registered to vote. For which of the following situations will the estimate tend to be the closest to the actual value of ?

I. II. III. a. I only b. II only c. III only d. I and III will be equally close to the actual value of ANSWER: c 14. Under which of the following conditions does I. II. III.

the standard deviation of the sampling distribution of

decrease

decreases increases approaches 0.5

a. I only b. II only c. I and III d. II and III ANSWER: b 15. A random sample will be taken of all the employees of a particular company. The sample proportion will be used to estimate the proportion of all employees who use mass transit to commute to work. For which of the following situations will the estimate tend to be the closest to the actual value of p?

I. II. III. a. I only b. II only c. III only d. I and III will be equally close to the actual value of p ANSWER: c 16. A random sample will be taken of all the students at a particular university. The sample proportion will be used to estimate p, the proportion of all students who plan to graduate within the next 12 months. For which of the following situations will the estimate tend to be the closest to the actual value of p?

I. II. III.

Name:

Class:

Date:

Chapter 09 - Estimating a Population Proportion a. I only b. II only c. III only d. I and III will be equally close to the actual value of p ANSWER: c 17. Suppose you would like to use the sample proportion large, which of the following will also be true?

I. II.

to estimate the population proportion p. If your sample size is

You can approximate the sampling distribution of by a normal distribution The standard deviation about the mean of the sampling distribution will be small

a. I only b. Neither I nor II c. Both I and II d. II only ANSWER: c 18. For a given value of population proportion p, if the sample size following best describes the resultant change in margin of error? a. Margin of error increases by a factor of two b. Margin of error decreases by a factor of two c. Margin of error decreases by a factor of four d. Margin of error does not change ANSWER: b

is increased by a factor of four, then which of the

19. For a given value of population proportion if the sample size following best describes the resultant change in margin of error? a. Margin of error increases by a factor of two b. Margin of error decreases by a factor of two c. Margin of error decreases by a factor of four d. Margin of error does not change ANSWER: a

is decreased by a factor of four, then which of the

20. Suppose you have a population with a proportion of interest If the sampling size is large, which of the following is true regarding the likelihood that the proportion of any given sample will differ from p by more than 1.96 times the standard error of ? a. It is likely that b. It is unlikely that

will differ from by more than 1.96 times the standard error of will differ from

by more than 1.96 times the standard error of

c. It is necessary to know the value of population proportion p to answer this question. d. The likelihood that will be with a given interval around is unrelated to the sample size .

ANSWER: b 21. Suppose you have a population with a proportion of interest

If the sampling size

is large, which of the following

Name:

Class:

Date:

Chapter 09 - Estimating a Population Proportion is true regarding the likelihood that the proportion standard error of ? a. It is likely that b. It is unlikely that

of any given sample will differ from

by more than 1.96 times the

will differ from by more than 1.96 times the standard error of will differ from

by more than 1.96 times the standard error of

c. It is necessary to know the value of population proportion d. The likelihood that will be with a given interval around

to answer this question. is unrelated to the sample size .

ANSWER: a 22. The proportion of students at a particular university who commute to campus by bicycle is 0.68. If you sampled 100 students, what is the margin of error for any sampled proportion of students who commute to campus by bicycle? (95% confidence level) a. 9.1% b. 4.7% c. 16.2% d. 11.1% ANSWER: a 23. You’re interested in the proportion of residents of your town who use a wood-burning appliance as the exclusive heat source for their home in the winter. To estimate this population proportion , you take a sample of 1500 households and find that 26% of them use a wood-burning appliance as their sole home heating source. What is the margin of error associated with using to estimate p? (95% confidence level) a. Margin of error using

to estimate

is 0.022

b. Margin of error using

to estimate

is 0.044

c. Margin of error using

to estimate

is 0.011

d. Margin of error using

to estimate

is 0.026

ANSWER: a 24. You’re interested in the proportion of college students who have used cell phones to cheat on an exam. To estimate this population proportion , you take a sample of 151 students and find that 48% of them have used a cell phone to cheat on an exam. What is the margin of error associated with using to estimate p? (95% confidence level) a. Margin of error using

to estimate

is 0.056

b. Margin of error using

to estimate

is 0.080

c. Margin of error using

to estimate

is 0.115

d. Margin of error using

to estimate

is 0.041

ANSWER: b 25. You’re interested in the proportion of college students who have used cell phones to cheat on exams. You would like to estimate this proportion for the population of students enrolled at a particular large college. What would the margin of error be if you surveyed 500 randomly selected students and 250 responded that they had used their cell phones to cheat on an exam? (95% confidence level) a. Margin of error = 0.0438 b. Margin of error = 0.0860

Name:

Class:

Date:

Chapter 09 - Estimating a Population Proportion c. Margin of error = 0.0214 d. Margin of error = 0.127 ANSWER: a 26. You’re interested in the proportion of dog owners in your city who regularly make use of professional grooming services to care for their dog’s coat. To estimate this population proportion p, you take a sample of 550 dog owners in your city and find that 88% of them make regular use of professional grooming services for their dogs’ coats. What is the margin of error associated with using to estimate p? (95% confidence level) a. Margin of error using

to estimate

is 0.033

b. Margin of error using

to estimate

is 0.078

c. Margin of error using

to estimate

is 0.014

d. Margin of error using

to estimate

is 0.027

ANSWER: d 27. You’re interested in the proportion of residents in your neighborhood who engage in daily exercise. To estimate this population proportion , you take a sample of 128 residents of your neighborhood and find that 68% of them exercise daily. What is the margin of error associated with using to estimate ? (95% confidence level) a. Margin of error using

to estimate

is 0.041

b. Margin of error using

to estimate

is 0.081

c. Margin of error using

to estimate

is 0.143

d. Margin of error using

to estimate

is 0.050

ANSWER: b 28. Which of the following are conditions for use of the margin of error formula when estimating a population proportion from a sample proportion?

I) The sample is selected from a convenient portion of the population II) The sample is selected in a way that makes it reasonable to think that the sample is representative of the population III) For a given value of , the products of are both less than or equal to 10 a. I only b. II only c. III only d. I and III only ANSWER: b 29. Which of the following should be true for the sampling method when using the margin of error formula to estimate a population proportion from a sample proportion?

I. II. III.

The sample is a random sample from the population of interest The sample is selected in a way that makes it reasonable to think that the sample is representative of the proportion of the population with the lowest values.

The sample is selected in a way that makes it reasonable to think that the sample is representative of the proportion of the population with the highest values. a. Neither I nor II nor III

Name:

Class:

Date:

Chapter 09 - Estimating a Population Proportion b. I only c. II only d. III only ANSWER: b 30. Suppose you have a population with the proportion p of some characteristic of interest. If you take a random sample from the population with = 0.95, for which of the following sampling sizes could you use the margin of error formula for as an estimate of ? a. = 25 b. = 100 c. = 150 d. = 250 ANSWER: d 31. Suppose you’re estimating the proportion p of vacationers to a particular area who prefer rainy weather vs. sunny weather. You would like to use the margin of error formula (95% confidence level) to estimate p from a random sample of 500 vacationers. Which of the following is the smallest value of for which you could use the margin of error formula? a. 5% b. 10% c. 1% d. 2% ANSWER: d 32. Suppose you’re estimating the proportion of vacationers to a particular area who prefer hot, sunny weather vs. cool, rainy weather. You would like to use the margin of error formula (95% confidence level) to estimate p from a random sample of 500 vacationers. Which of the following is the largest value of for which you could use the margin of error formula? a. 95% b. 90% c. 99% d. 98% ANSWER: d 33. A representative sample of 5000 Americans was surveyed regarding their personal weekly physical fitness routines.

Based on the results of this survey a proportion = 0.060 engaged in fitness routines on par with those of athletes training to compete in the Olympics. Which of the following could you use to express an estimate of the population proportion?

(95% confidence level) a. Within 0.0066 of 0.060 b. Within 0.0034 of 0.060 c. Within 0.0068 of 0.030 d. Within 0.0023 of 0.060 ANSWER: a 34. A representative sample of 150 residents of a particular suburban neighborhood were surveyed regarding their use of

Name:

Class:

Date:

Chapter 09 - Estimating a Population Proportion environmentally toxic lawn chemicals. Based on the result of the survey, a proportion = 0.93 reported no use of environmentally toxic lawn chemicals. Which of the following could you use to express an estimate of the population proportion? (95% confidence level) a. Within 0.041 of 0.93 b. Within 0.21 of 0.07 c. Within 0.11 of 0.93 d. Within 0.41 of 0.07 ANSWER: a 35. A representative sample of 55 employees of a small company were surveyed regarding their satisfaction with their compensation. Based on the survey results, a proportion = 0.90 reported satisfaction with their compensation. Which of the following could you use to express an estimate of the population proportion? (95% confidence level) a. Within 0.08 of 0.90 b. Within 0.04 of 0.90 c. Within 0.08 of 0.10 d. Cannot calculate the margin of error since the sampling distribution for cannot be approximated by a normal distribution.

ANSWER: d 36. A representative sample of 55 patients of a knee therapy clinic were surveyed regarding their adherence to a daily therapeutic exercise regimen. Based on the survey results, a proportion = 0.52 reported adherence to a daily therapeutic exercise regimen. Which of the following could you use to express an estimate of the population proportion? (95% confidence level) a. Within 0.132 of 0.52 b. Within 0.067 of 0.52 c. Within 0.132 of 0.48 d. Cannot calculate the margin of error since the sampling distribution for cannot be approximated by a normal distribution.

ANSWER: a 37. A representative sample of 152 performing arts students at an urban university in a major metropolitan area were surveyed regarding their success in securing internships with municipal performing arts companies. Based on the survey results, a proportion = 0.12 reported success in securing internships. Which of the following could you use to express an estimate of the population proportion? (95% confidence level) a. Within 0.052 of 0.12 b. Within 0.026 of 0.12 c. Within 0.052 of 0.88 d. Cannot calculate the margin of error since the sampling distribution for cannot be approximated by a normal distribution.

ANSWER: a 38. Which of the following affects the width of a confidence interval for a population proportion? a. Confidence level b. Sample size

Name:

Class:

Date:

Chapter 09 - Estimating a Population Proportion c. Sample proportion value d. All of the these ANSWER: d 39. Holding all other elements equal, an increase in sample size will result in a wider confidence interval. a. True b. False ANSWER: False 40. Which of the following has the effect of reducing the confidence interval? a. Decreasing the sample size b. Increasing the sample size c. For

, increasing the value of

d. For

, reducing the value of

ANSWER: b 41. Which of the following changes to the value of the sample proportion , increasing the value of I) For , reducing the value of II) For , decreasing the value of III) For , increasing the value of IV) For

reduce the confidence interval?

a. I and II b. III and IV c. I and III d. II and IV ANSWER: b 42. All else being equal, the higher the confidence level, the wider the confidence interval. a. True b. False ANSWER: True 43. A researcher has decided to decrease the confidence level in their estimation of a population proportion. What is the effect on the width of the associated confidence interval? a. The width of the confidence interval increases b. The width of the confidence interval decreases c. The width of the confidence interval is unchanged d. There is not enough information to determine ANSWER: b 44. Which of the following is true regarding the confidence level associated with a confidence interval?

I.

The confidence in a particular value

Name:

Class:

Date:

Chapter 09 - Estimating a Population Proportion II.

The confidence one can have in the method used to construct the interval

a. I only b. II only c. Neither I nor II d. Both I and II ANSWER: b 45. A scientist has decided to increase the size of the sample they use to estimate a population proportion. What is the effect on the width of the associated confidence interval? a. The width of the confidence interval increases b. The width of the confidence interval decreases c. The width of the confidence interval is unchanged d. There is not enough information to determine ANSWER: b 46. Briefly define the following terms in your own words: a) Confidence interval b) Confidence Level associated with a confidence interval ANSWER: (a) The interval for which you can have a set percent confidence that the actual value of the population characteristic is included in the interval. (b) A method has been used to produce the confidence interval that is successful in capturing the actual population proportion a set percentage of the time.

47. The large-sample confidence interval formula for estimating can always be safely used if

.

a. True b. False ANSWER: False 48. Which of the following conditions must be met to use the large-sample confidence interval formula when estimating a population proportion?

I. II.

The sample is a random sample from the population of interest or selected in a way that makes it reasonable to think that the sample is representative of the population The sample is sufficiently large to include at least 10 successes and 10 failures

a. I only b. II only c. Neither I nor II d. Both I and II ANSWER: d 49. Suppose you want to use a large-sample 95% confidence interval to estimate the population proportion p using a random sample from the population of interest with proportion . Which of the following additional conditions must be met? a. The sample size must be greater than 100 b. The product must be greater than or equal to 10

Name:

Class:

Date:

Chapter 09 - Estimating a Population Proportion c. The product

must be equal to or less than 10

d. None of these ANSWER: b 50. Suppose you want to estimate the population proportion using a conveniently collected sample of interest with proportion with a sample size = 100. Can you use a large-sample 95% confidence interval? a. No, because the sampling method was not collected randomly b. Yes, because c. Yes, because d. Yes, because the sample size ANSWER: a

is large

51. Suppose you want to estimate the population proportion p using a random sample from the population of interest with proportion and a sample size of 30. Have you met the conditions to use a large-sample 95% confidence interval for the population proportion? a. Yes, because the sampling method was random b. Yes, because c. No, because d. Yes, because the sample size ANSWER: c

is large

52. Which of the following answers to the four key QSTN questions leads to the selection of a large-sample confidence interval for a population proportion as the appropriate method? a. Q=: hypothesis testing, S = experimental data, T = two numerical variables, N = one treatment b. Q = estimation, S = experimental data, T = two numerical variables, N = one sample c. Q = hypothesis testing, S = experimental data, T = one numerical variable, N = one treatment d. Q = estimation, S = sampling, T = one categorical variable, N = one sample ANSWER: d 53. You’re using the data from a survey of 500 randomly selected customers from your local coffee shop regarding the proportion who prefer coffee with cream for an afternoon beverage ( ). Part one: Would a large-sample confidence interval be an appropriate method for population proportion? Part Two: Would the large-sample confidence interval be appropriate if you wanted to know the relative proportions of customers who prefer coffee with cream, milk tea, and green tea? a. Part one: yes, because the survey was based on a random sample sufficiently large to include at least 10 successes and 10 failures. Part two: yes, because it involves estimation from sampled data. b. Part one: no, because the survey was based on a sample insufficiently large to include at least 10 successes and 10 failures. Part two: yes, because it involves estimation from categorical data. c. Part one: yes, because the survey was based on a random sample sufficiently large to include at least 10 successes and 10 failures. Part two: yes, because it involves estimation from a single sample. d. Part one: yes, because the survey was based on a random sample sufficiently large to include at least 10 successes and 10 failures. Part two: no, because it involves estimation from sampled data of multiple categorical variables.

ANSWER: d

Name:

Class:

Date:

Chapter 09 - Estimating a Population Proportion 54. Suppose you would like to test your hypothesis that more than half of the customers at a particular coffee shop prefer cream vs. milk with their coffee. You run an experiment in which you offer milk or cream to 250 customers and record how many select cream. 150 of the 250 customers select cream. Can you use an = 250 and to apply the large-confidence method to estimate the population proportion? a. Yes, because a single variable was involved b. Yes, because the variable is categorical c. No, because the question was a hypothesis test rather than an estimation d. No, because there were two rather than one treatment or sample ANSWER: c 55. Suppose you would like to know what proportion of graduates from your university accepts a job in the local area.

You conduct two surveys, each with 500 students, which give values of and . Can you use the largeconfidence method to estimate the population proportion?

I. II. III.

No, because the data includes two variables No, because the data are numerical rather than categorical No, because there are two samples rather than one

a. Neither I nor II nor III b. I only c. II only d. III only ANSWER: d 56. In a survey of 800 randomly-selected restaurant managers, 486 said that they would choose locally-produced produce over produce that required shipping, even if the price for the local produce was higher. Which of the following steps would you use in applying the EMC3 method?

I) Recognize that you will estimate the value of , the proportion of restaurant managers who chose locally-grown produce.

II) Select a large-sample 95% confidence interval method since it involves estimation using sampling data involving one categorical variable and a single sample.

III) Check conditions of random sampling, sample size: IV) Calculate the confidence interval of (0.574, 0.643) and communicate it as the interval over which you can be 95% confident that the actual proportion of restaurant managers who choose local produce is somewhere between 0.574 and 0.643. a. I only b. I and II only c. I, II, and III only d. I, II, III, and IV ANSWER: d 57. In a survey of 200 random students, 8 said that they would attempt to bribe another student to help them cheat on an exam. Which of the following steps would you use in applying the EMC3 method?

I) Recognize that you will estimate the value of p, the proportion of students would bribe another student to help them cheat.

II) Select a large-sample 95% confidence interval method since it involves estimation using sampling data involving one

Name:

Class:

Date:

Chapter 09 - Estimating a Population Proportion categorical variable and a single sample.

III) Check conditions of random sampling, sample size: .

IV) Calculate the confidence interval of (0.013, 0.067) and communicate it as the interval over which you can be 95% confident that the actual proportion of students who would bribe another student to help them cheat lies somewhere between 0.013 and 0.067. a. I only b. I and II only c. I, II, and III only d. I, II, III, and IV ANSWER: c 58. In a survey of 100 randomly-selected travelers, 55 said that they prefer non-stop flights to connecting flights. Which of the following steps would you use in applying the EMC3 method?

I) Recognize that you will estimate the value of , the proportion of travelers who prefer non-stop flights.

II) Select a large-sample 95% confidence interval method since it involves estimation using sampling data involving one categorical variable and a single sample.

III) Check conditions of random sampling, sample size: IV) Calculate the confidence interval of (0.452, 0.648) and communicate it as the interval over which you can be 95% confident that the actual proportion of travelers who prefer non-stop flights is somewhere between 0.452 and 0.648. a. I only b. I and II only c. I, II, and III only d. I, II, III, and IV ANSWER: d 59. Suppose that a random sample of 85 high school classrooms in the state of Iowa is selected and a 95% confidence interval for the proportion that has Internet access is (0.73, 0.79). Which of the following is a correct interpretation of the 95% confidence level? a. The method used to construct the interval will produce an interval that includes the value of the population proportion about 95% of the time in repeated sampling. b. You can be 95% confident that the sample proportion is between 0.73 and 0.79. c. There is a 95% chance that the proportion of all high school classrooms in Iowa that have Internet access is between 0.73 and 0.79. d. You can be 95% confident that the proportion of all high school classrooms in Iowa that have Internet access is between 0.73 and 0.79.

ANSWER: a 60. An understanding of birds’ choices of habitat is a crucial element in understanding avian biology and ecology. One aspect of habitat choice is the pattern of their preferred vertical height when feeding in forests. In a study of small birds in an old-growth forest in the Pacific Northwest, researchers observed the landings of kinglet birds. They found that 78 of the 163 landings were in the “mid” height region, 21-40 meters above the ground. a) Compute an estimate of the population proportion of all landings of these kinglet birds that are in the 21-40 meter height range. b) Construct and interpret a 95% confidence interval for p, the population proportion of all landings of these kinglet birds that are in the 21-40 meter height range.

Name:

Class:

Date:

Chapter 09 - Estimating a Population Proportion ANSWER:

a) b) The 95% confidence interval is given by

which

can be interpreted that one can be 95% confident that the true proportion of kinglet bird landings in the midrange is between 0.4018 and 0.5552.

61. A recent study investigated the effects of a child safety campaign encouraging parents to ensure that their children used seatbelts in vehicles. Investigators observed a simple random sample of parents in a large city and found that 192 out of 594 parents ensured that their children used seat belts. a) Compute an estimate of the population proportion of all parents who ensure that their children use seat belts. b) Construct and interpret a 95% confidence interval for p, the population proportion of all parents who ensure that their children use seat belts.

ANSWER: (a) ; (b) The 95% confidence interval is given by which can be interpreted that one can be 95% confident that the true proportion of parents who ensure that their children use seat belts is between 0.2856 and 0.3608.

62. One difficulty in measuring the nesting success of birds is that the researchers must count the eggs in the nest, which is disturbing to the parents. Even though the researcher does not harm the birds, the flight of the bird might alert predators to the presence of a nest. To see if researcher activity might degrade nesting success, the nest survival of 102 nests that had their eggs counted was recorded. Sixty-four (64) of the nests failed (i.e., the parent abandoned the nest). a) Construct and interpret a 95% confidence interval for the proportion of nest failure in the population. b) The “normal” nest failure rate of these birds is 29%. Based on the confidence interval from part (a), do you think that the researcher’s activity affects nesting success? Justify your answer with an appropriate statistical argument.

ANSWER: This setting meets the condition that , so a 95% confidence interval can be

calculated. The confidence interval is

which means that

one can be 95% confident that the true proportion of nest failures in the population is between 0.5336 and 0.7213. On this basis, it appears that the researcher’s activities affected nesting success since the expected failure rate of 0.29 is not within the confidence interval calculated for the sample.

63. Suppose that a newspaper conducts a survey of a random sample of 120 registered voters to predict the winner of a local election. The candidate of political party A was favored by 62 of the respondents. a) Construct and interpret a 99% Confidence Interval for the true proportion of voters who prefer the political party A candidate. b) If a candidate needs a simple majority of votes to win the election, can the political party A candidate be confident of victory? Justify your response with an appropriate statistical argument.

ANSWER: This setting meets the condition that , so a 99% confidence interval can be

Name:

Class:

Date:

Chapter 09 - Estimating a Population Proportion

calculated. The confidence interval is

which means that

one can be 99% confident that the true level of support for political party candidate A is between 0.3990 and 0.6344. Given that a significant portion of the confidence interval lies below 50% of votes, the political party A candidate cannot be completely confident of victory.

64. Suppose you have been asked to estimate the proportion of college students who have used cell phones to cheat on an exam. You have no prior knowledge of the population proportion , nor do you have any prior studies from which you could obtain a . Your supervisor suggests that you include 151 students in the survey. If you assume a 95% confidence level, which of the following is an estimate of the margin of error under these conditions? a. b. c. d. Cannot tell from the information given ANSWER: b 65. A manufacturer of small appliances purchases plastic handles for coffeepots from an outside vendor. If a handle is cracked, it is considered defective and cannot be used. A large shipment of plastic handles is received. What is the smallest number of handles from the shipment that should be inspected to estimate p, the proportion of defective handles in the shipment, with a margin of error of 0.13 or less? (Assume a confidence level of 95%). a. 4 handles b. 57 handles c. 113 handles d. 228 handles ANSWER: b 66. You’re planning a survey of residents in your community to determine how many would be interested in participating in a government-sponsored program to improve the energy efficiency of their homes. You want to ensure that your margin of error will be no greater than 0.060 with a 95% confidence level. Which of the following is the minimum sample size should you use? a. 267 b. 534 c. 133 d. 387 ANSWER: a 67. You’re planning a survey of students in your university to determine how many would be interested in working on a sponsored research project. What is the minimum number of students you should include in your survey if you want a margin of error no greater than 0.025 with a 95% confidence level? a. 1537 b. 3012 c. 784

Name:

Class:

Date:

Chapter 09 - Estimating a Population Proportion d. 1269 ANSWER: a 68. You’re running a preliminary screening test to determine the effectiveness of a new, injection-delivered osteoarthritis treatment. You plan to survey patients who have received the new treatment to determine what proportion of them felt that their joint function was improved by the treatment. You would like your results to estimate the long-run proportion of patients who feel improved by the treatment with a margin of error no greater than 0.10 with 95% confidence. What is the minimum number of patients you should include in your survey? a. 49 b. 97 c. 180 d. 154 ANSWER: b 69. You’re planning a survey of students in your university to determine how many would be interested in volunteering for a community service project. What is the minimum number of students you should include in your survey if you want a margin of error no greater than 0.16 with a 99% confidence level? a. 66 b. 38 c. 45 d. 132 ANSWER: a 70. You’re planning a survey of students in your university to determine how many of them plan to study abroad for at least one academic term of their undergraduate program. What is the minimum number of students you should include in your survey if you want a margin of error no greater than 0.12 with a 90% confidence level? a. 58 b. 47 c. 65 d. 67 ANSWER: b 71. Suppose you’re a human resources manager concerned about the use of social media background checks to screen job candidates. You have read a published study in which the proportion of 500 randomly selected hiring managers who disqualified candidates based on social media background checks was 395, which gave and a 95% confidence interval of (0.755,0.825). You decide to use a bootstrap method as an alternate way to find a 95% confidence interval for p using the published study data as input. Using the Shiny app (or equivalent statistical software) with 1000 simulated samples, calculate a 95% bootstrap confidence interval and interpret the results. a. The 95% bootstrap confidence interval for the proportion of hiring managers who would disqualify a job candidate on the basis of social media background checks is (0.754,0.824). You can be 95% confident that the actual proportion of hiring managers who disqualify job candidates on the basis of social media background checks is between 75.4% and 82.4%. b. The 95% bootstrap confidence interval for the proportion of hiring managers who would disqualify a job candidate on the basis of social media background checks is (0.688,0.923). You can be 95% confident that the actual proportion of hiring managers who disqualify job candidates on the basis of social media background checks is between 68.8% and 92.3%.

Name:

Class:

Date:

Chapter 09 - Estimating a Population Proportion c. The 95% bootstrap confidence interval for the proportion of hiring managers who would disqualify a job candidate on the basis of social media background checks is (0.789,0.811). You can be 95% confident that the actual proportion of hiring managers who disqualify job candidates on the basis of social media background checks is between 78.9% and 81.1%. d. The 95% bootstrap confidence interval for the proportion of hiring managers who would disqualify a job candidate on the basis of social media background checks is (0.705,0.848). You can be 95% confident that the actual proportion of hiring managers who disqualify job candidates on the basis of social media background checks is between 70.5% and 84.8%.

ANSWER: a 72. Suppose you’re a medical researcher interested in injuries newborn babies sustain during invasive intensive care procedures. You review a published study that reported that 9 of 1081 newborns developed catheter-associated liver injuries. Due to the small size of , a large-sample confidence interval is not appropriate. Use the Shiny app (or equivalent statistical software) to create a bootstrap 95% confidence interval for the published data using 1000 simulated sample proportions and interpret the results. a. The 95% bootstrap confidence interval for the proportion of newborns sustaining catheter-induced liver injuries is (0.004,0.014). You can be 95% confident that the actual proportion of newborns sustaining catheterinduced liver injuries is 0.004 and 0.014. b. The 95% bootstrap confidence interval for the proportion of newborns sustaining catheter-induced liver injuries is (0.008,0.022). You can be 95% confident that the actual proportion of newborns sustaining catheterinduced liver injuries is 0.008 and 0.022. c. The 95% bootstrap confidence interval for the proportion of newborns sustaining catheter-induced liver injuries is (0.002,0.032). You can be 95% confident that the actual proportion of newborns sustaining catheterinduced liver injuries is 0.002 and 0.032. d. The 95% bootstrap confidence interval for the proportion of newborns sustaining catheter-induced liver injuries is (0.006,0.011). You can be 95% confident that the actual proportion of newborns sustaining catheterinduced liver injuries is 0.006 and 0.011.

ANSWER: a 73. Suppose you’re a medical researcher interested in injuries newborn babies sustain during invasive intensive care procedures. You review a published study that reported that 9 of 1081 newborns developed catheter-associated liver injuries. You used 1000 simulations to create a bootstrap 95% confidence interval of (0.004, 0.014). How does this bootstrap confidence interval compare to the 95% large-sample confidence interval calculated with ? Would it be more appropriate to use the bootstrap method or the large-sample method to create a 95% confidence interval? a. Large-sample 95% confidence interval = (0.003, 0.014); large-sample confidence interval is more appropriate. b. Large-sample 95% confidence interval = (0.009, 0.017); bootstrap confidence interval is more appropriate. c. Large-sample 95% confidence interval = (0.009, 0.017); large-sample confidence interval is more appropriate. d. Large-sample 95% confidence interval = (0.003, 0.014); bootstrap confidence interval is more appropriate.

ANSWER: d

Name:

Class:

Date:

Chapter 10 - Population Proportion 1. If the null hypothesis is not rejected, there is strong statistical evidence that the null hypothesis is true. a. True b. False ANSWER: False 2. Which of the following accurately describes the null and alternative hypotheses in a hypothesis test?

I. II. III. IV.

The null hypothesis is initially presumed to be the correct one The alternative hypothesis is initially presumed to be the correct one Data is considered in light of whether it supports the null hypothesis Data is considered in light of whether it supports the alternative hypothesis

a. I and II b. I and IV c. II and III d. II and IV ANSWER: b 3. Under which conditions will the null hypothesis be rejected in a hypothesis test?

I. II. III.

Lack of convincing evidence in favor of the null hypothesis Evidence in favor of the alternative hypothesis Convincing evidence against the null hypothesis

a. Neither I nor II nor III b. I only c. II only d. III only ANSWER: d 4. Suppose you’re conducting a hypothesis test. Your data does not provide convincing evidence that the null hypothesis is false. Which of the following can you conclude?

I. II. III.

You fail to reject the null hypothesis You reject the alternative hypothesis You support the hull hypothesis

a. Neither I nor II nor III b. I only c. II only d. III only ANSWER: b 5. In choosing between null and alternative hypotheses, which of the following is initially assumed? a. The alternative hypothesis is true b. The null hypothesis is true c. Neither the alternative nor the null hypothesis is true

Name:

Class:

Date:

Chapter 10 - Population Proportion d. Both the alternative and the null hypotheses are true ANSWER: b 6. Explain in your own words the distinction between a null and alternative hypothesis.

ANSWER: The null hypothesis is the claim about a population characteristic that is initially assumed to be true. The alternative is the competing claim about the population characteristic.

7. If you have data that provides convincing evidence that the null hypothesis is false, then which of the following conclusions can you make in a hypothesis test?

I. II. III.

Reject the null hypothesis Support the null hypothesis Reject the alternative hypothesis

a. Neither I nor II nor III b. I only c. II only d. III only ANSWER: b 8. Suppose you’re conducting a hypothesis test. The data you gather might or might not occur if the null hypothesis were true. Which of the following can you conclude?

I. II. III.

Fail to reject the null hypothesis because you did not have convincing evidence against it Fail to reject the null hypothesis because you have strong evidence that it was true Reject the null hypothesis because you had convincing evidence against it.

a. Neither I nor II nor III b. I only c. II only d. III only ANSWER: b 9. Suppose you’re conducting a hypothesis test. The data you gather would not be considered surprising if the null hypothesis were true.

I. II. III.

Fail to reject the null hypothesis because you did not have convincing evidence against it Fail to reject the null hypothesis because you have strong evidence that it was true Reject the null hypothesis because you had convincing evidence against it.

a. Neither I nor II nor III b. I only c. II only d. III only ANSWER: b 10. Under which of the following conditions will the null hypothesis fail to be rejected in a hypothesis test?

Name:

Class:

Date:

Chapter 10 - Population Proportion I. II. III.

Data is equivocal Data provides some evidence against the null hypothesis, but the evidence is not convincing Data does not present convincing evidence against the null hypothesis

a. I and II only b. II and III only c. I and III only d. I, II, and III ANSWER: d 11. You are interested in determining whether there is strong evidence in support of the claim that less than 40% of adults who have retired from full-time employment have part-time employment. To answer this question, what null and alternative hypothesis should you test? a. b. c. d.

ANSWER: b 12. You are interested in determining if more than 20% of students prefer to study in the early morning as opposed to other times of the day. Which of the following represents the null and alternative hypothesis you should test? a. b. c. d.

ANSWER: a 13. You’re interested in determining if sample data supports a claim that more than 45% of students in a particular program make regular use of an on-campus tutoring center. Which of the following represents the null and alternative hypothesis you would test? a. b. c. d.

ANSWER: a 14. You’re determining if fewer than 25% of graduates from the community colleges in your state incur debt to graduate with an Associate’s degree. Which of the following represents the null and alternative hypothesis you would test? a. b. c. d.

ANSWER: c

Name:

Class:

Date:

Chapter 10 - Population Proportion 15. You’re evaluating a new injection-based treatment for restoring ligament integrity. The current standard treatment has a success rate of 55%. If p represents the proportion of success of the new treatment, which of the following represents the hypothesis you would test? a. b. c. d.

ANSWER: a 16. You’re evaluating a new physical therapy treatment for cervical spine pain. The current standard treatment has a success rate of 75%. If p represents the proportion of success of the new treatment, which of the following represents the hypothesis you would test? a. b. c. d.

ANSWER: a 17. A type II error is made by failing to reject a false null hypothesis. a. True b. False ANSWER: True 18. Describe the two types of errors that might be made when a hypothesis test is carried out. a. A Type I error is rejecting H0 when Ho is true. A Type II error is failing to reject H0 when H0 is false. b. A Type I error is rejecting H0 when H0 is false. A Type II error is failing to reject H0 when H0 is true. c. A Type I error is failing to reject H0 when H0 is true. A Type II error is rejecting H0 when H0 is true. d. A Type I error is rejecting H0 when H0 is true. A Type II error is failing to reject H0 when H0 is true.

ANSWER: a 19. An engineer is interested in the proportion of threaded fasteners in a bulk purchase lot that exceeds the minimum break strength requirements. To accept the purchase lot, more than 80% of the fasteners must meet the minimum break strength. Random samples of fasteners were tested in the lab and the test results were used as a basis for choosing between H0 = 0.08 and Ha 0.08, which of the following describes a Type I error for this hypothesis test?

I. II.

It is concluded that more than 80% of the fasteners in the purchase lot met the minimum break strength when the actual proportion that met the minimum break strength was less than or equal to 80%.

It is concluded that 80% or fewer of the fasteners met the minimum break strength when the actual proportion that met the minimum break strength was more than 80%. a. Neither I nor II b. I only c. Both I and II d. II only

Name:

Class:

Date:

Chapter 10 - Population Proportion ANSWER: b 20. A city bus scheduler is interested in whether the proportion of intercity express buses arriving at the central station exceeds 75%. They randomly sample the arrival timeliness of a sample of intercity buses and use the data as a basis for choosing between: H0 = 0.75, Ha 0.75 which of the following describes a Type I error for this hypothesis test?

I. II.

It is concluded that more than 75% of intercity buses arrive on time when the actual proportion which arrives on time is equal to or less than 75%.

It is concluded that 75% or fewer buses arrived on time when the actual proportion of on-time arrivals exceeded 75%.

a. Neither I nor II b. I only c. Both I and II d. II only ANSWER: d 21. Which of the following are true regarding Type I and Type II errors associated with hypothesis testing?

I) Both Type I and Type II errors result from the rejection of a true H0 II) Both Type I and Type II errors are the consequences of decisions based on sample data III) Both Type I and Type II errors result in similar consequences a. I only b. II only c. III only d. II and III only ANSWER: b 22. The level of significance of a test is the probability of making a Type I error, which is rejecting a true null hypothesis. a. True b. False ANSWER: True 23. One of the earliest decisions that must be made when performing a hypothesis test is the choice of significance level.

Briefly describe the considerations that go into making this decision.

ANSWER: To decide on the significance level, the consequences of Type I and II errors should be considered. If a Type I error has worse consequences, a small significance level should be chosen, such as α < 0.05. If a Type II error has worse consequences, a large significance level should be chosen, such as α > 0.05.

24. Suppose you’re a test engineer in charge of ensuring the acceptability of materials used for structural aircraft parts. In determining whether or not to approve materials for use, you adopt the following null and alternative hypotheses: H0: material is not acceptable for use versus Ha: new material is acceptable for use The consequence of a Type I error would be the use of an inadequate material in an aircraft, potentially failing in the aircraft and loss of human life. The consequence of a Type II error is acceptable material being scrapped, resulting in higher costs. Which of the following are the most appropriate significance level and associated rationale? a. α = 0.10, since the consequence of a Type II error is more significant than that of a Type I error b. α = 0.05, since the consequence of Type I and Type II errors are similar

Name:

Class:

Date:

Chapter 10 - Population Proportion c. α = 0.025, since the consequence of a Type I error is somewhat more significant than that of a Type II error d. α = 0.01, since the consequence of a Type I error is much more significant than that of a Type II error.

ANSWER: d 25. Patients with serious, life-threatening diseases are likely to be more willing to accept the risk of an ineffective treatment than forego a potentially life-saving treatment. Patients with mild, chronic disease are more concerned about the risk of side effects and the cost of ineffective drugs. In approving new drugs, the FDA uses the following null and alternative hypotheses: H0: new drug is not effective versus, Ha: new drug is effective. If the standard significance level for approval in an FDA clinical trial is α = 0.05, which of the following would represent the most likely opinions of patients regarding significance levels for FDA drug approval?

I. II. III.

Patients with a serious, life-threatening disease would favor a lower significance level since the consequence of a Type I error is high for them.

Patients with a mild, chronic disease would favor a higher significance level since the consequence of a Type I error is high for them.

Patients with a serious, life-threatening disease would favor a higher significance level since the consequence of a Type II error is higher for them.

a. Neither I nor II nor III b. I only c. II only d. III only ANSWER: d 26. All other things being equal, choosing a smaller value of α will increase the probability of making a type II error. a. True b. False ANSWER: True 27. Assuming the same sample size is used, how does changing the significance level from 0.2 to 0.05 affect the probability of rejecting the null hypothesis when the alternative hypothesis is true? a. Probability decreases b. Probability increases c. Probability does not change d. Probability changes, but it might either decrease or increase ANSWER: a 28. Which of the following is an initial assumption in a hypothesis test? a. The null hypothesis is false b. The proportion of the sample used to test the hypothesis is close to 0.5 c. The alternate hypothesis is true d. The null hypothesis is true ANSWER: d 29. Which of the following can we say about the sampling distribution if the null hypothesis p = 0.8 is true?

I.

It has a large standard error

Name:

Class:

Date:

Chapter 10 - Population Proportion II. III.

It can be approximated by a normal distribution It is centered on 0.8

a. Neither I nor II nor III b. I only c. II only d. III only ANSWER: d 30. If a null hypothesis p = 0.65 is true, and we know the standard error of the sampling distribution for

, and we know

that the sampling distribution can be approximated as a normal distribution, which of the following can we also determine?

I.

The z-statistic for any known sample proportion

II.

The probability of observing a z-value is at least as unusual as the z-statistic for

III.

The chance of seeing a sample proportion

at a given distance from p = 0.65

a. I and II b. II and III c. I and III d. I, II, and III ANSWER: d 31. Which of the following provides a rationale for the rejection of the null hypothesis H0 I. II. III.

Data from an observed sample would have been likely to occur if the null hypothesis were true.

The sample size n for the observed sample is large The sampling distribution for the observed sample can be approximated as a normal distribution

a. Neither I nor II nor III b. I only c. II only d. III only ANSWER: a 32. In a hypothesis test, you begin by assuming which of the following?

I. II. III.

The null hypothesis is false The alternative hypothesis is true The null hypothesis is true a. Neither I nor II nor III b. I only c. II only d. III only

Name:

Class:

Date:

Chapter 10 - Population Proportion ANSWER: d 33. In a hypothesis test, how do you determine whether or not your initial premise was correct?

I. II.

Consider the observed data (sample values) and ask if they are surprising given your initial premise.

If the observed data would have been surprising given your initial premise, then your initial premise was incorrect.

If the observed data would not have been surprising given your initial premise, then your initial premise was correct.

III.

a. I and II only b. II and III only c. I and III only d. I, II, and III ANSWER: d 34. Every year on Groundhog Day (February 2), the famous groundhog Punxsutawney Phil tries to predict whether there will be 6 more weeks of winter. Suppose that you plan to take a random sample of 23 years and use weather data to determine the proportion of these years that the groundhog’s prediction was correct. If the groundhog has a 50-50 chance of making a correct prediction, which of the following is for samples of size 23 ?: a.

= 0.1474

b.

= 0.1043

c.

= 0.2085

d.

= 0.0870

ANSWER: b 35. Small P - values indicate that the observed sample is inconsistent with the null hypothesis. a. True b. False ANSWER: True 36. Define, in your own words, a test statistic.

ANSWER: A test statistic is a measure of how much the sample differs from the null hypothesis.

37. In your own words, what is a P - values?

ANSWER: A P - values is a probability of observing a test statistic as or more extreme than the one observed in the sample assuming that the null hypothesis is true.

38. Which of the following describes what a z-statistic measures in the context of hypothesis testing?

I.

The distance between the sample statistic

and the population proportion p

II.

The distance between the sample statistic

and the value predicted by the alternative hypothesis in terms of the

standard error of

Name:

Class:

Date:

Chapter 10 - Population Proportion III.

The distance between the sample statistic

and the null hypothesis value in terms of the standard error of

a. Neither I nor II nor III b. I only c. II only d. III only ANSWER: d 39. Suppose you’re conducting a hypothesis test with a null hypothesis p = 0.35. If you calculate a z-statistic of 4.00 for a particular sample proportion , then which of the following is true?

I.

The sample proportion

was 4.00 standard errors below the 0.35.

II.

The sample proportion

was 4.00 standard errors above 0.35

III.

The sample proportion

was within 4.00 standard errors of 0.35

a. Neither I nor II nor III b. I only c. II only d. III only ANSWER: c 40. Which of the following describes what a P - measures in the context of hypothesis testing? a. The distance between the value predicted by the null hypothesis and a given sample statistic

in terms of the

standard error of b. The probability of obtaining a test statistic less extreme than the one observed if the null hypothesis were true c. A measure of the correlation between the null hypothesis and observed sample d. A measure of the inconsistency between the null hypothesis and the observed sample ANSWER: d 41. The sample size affects the standard error and, hence the test statistic. Assuming the same significance level is used, how does increasing the sample size from 50 to 100 affect the probability of rejecting the null hypothesis when the alternative hypothesis is true? a. Decreases the probability b. Increases the probability c. The probability does not change d. The probability changes, but it might either decrease or increase ANSWER: b 42. In a test of H0: p = 0.45 versus H0: p < 0.45, the value of the z-statistic was calculated to be z = 0.55. If the significance level for the test was α = 0.2, should the null hypothesis be rejected? a. P = 0.3020, reject the null hypothesis b. P = 0.3020, reject the null hypothesis

Name:

Class:

Date:

Chapter 10 - Population Proportion c. P = 0.3020 reject the null hypothesis d. P = 0.3020, fail to reject the null hypothesis ANSWER: b 43. For a given significance level α, under which conditions would you reject the null hypothesis? a. P - value = α b. P - value ≥ α c. P - value is unrelated to α d. P - value < α ANSWER: d 44. Suppose you’re conducting a hypothesis test with H0 = 0.68, Ha > 0.68, α = 0.15. You take a random sample with n = 200 and get a = 0.72. Which of the following can we say regarding the null hypothesis? a. P - value = 0.113, reject the null hypothesis since P - value < α b. P - value = 0.887, fail to reject the null hypothesis since P - value > α c. P - value = 0.389, reject the null hypothesis since P - value > α d. P - value = 0.611 , fail to reject the null hypothesis since P - value > α ANSWER: a 45. Suppose you’re conducting a hypothesis test with H0 = 0.38, Ha > 0.38, α = 0.05. You take a random sample and use the n and from that sample to determine a P-value of 0.12. Which of the following can we say regarding the null hypothesis?

I. II. III.

Reject the null hypothesis since the P - value is greater than the α - valuee Fail to reject the null hypothesis since the P - value is greater than the α - value Reject the alternative hypothesis since P - value is greater than the α - value

a. Neither I nor II nor III b. I only c. II only d. III only ANSWER: c 46. Suppose you’re conducting a hypothesis test with H0 = 0.38, Ha > 0.38, α = 0.15. You take a random sample and use the n and from that sample to determine a P-value of 0.15. Which of the following can we say regarding the null hypothesis?

I. II. III.

Reject the null hypothesis since the P - value is not greater than the α - valuee Fail to reject the null hypothesis since the P - value is greater than or equal to the α - value Reject the null hypothesis since P - value is greater than or equal to the α - value a. Neither I nor II nor III b. I only c. II only

Name:

Class:

Date:

Chapter 10 - Population Proportion d. III only ANSWER: c 47. The null hypothesis can be rejected when the P - value is smaller than α. a. True b. False ANSWER: True 48. Children as young as 2 years of age, upon seeing an object placed under a pillow in a familiar setting at home, will understand to look for it after some time and be able to find it. Investigators believe this capability will be less pronounced in a laboratory setting, where the child is away from the familiar setting of home. Let p denote the proportion of 2-yearolds that have this understanding of the home situation, and suppose that p = 0.35. The investigators wish to determine whether the proportion that remembers is less when the child is away from home. a) What is the null hypothesis? b) What is the appropriate alternative hypothesis? c) In your own words, distinguish between a Type I and a Type II error in this context.

ANSWER: a) H0 : p = 0.35, b) Ha : p < 0.35, c) A type I error is to decide that children remember less when outside of the home environment, when in fact, they remember equally well. A type II error is to decide that children remember as well in the laboratory setting as in the home setting, when in fact they remember less when away from home.

49. As children grow, they develop what is known as “representational insight”, a connection between an object and a symbol for that object. A random sample of youngsters 24 months old was shown a video of someone putting a toy under 1 of 4 randomly placed boxes in a room familiar to the child. They were then taken to the room and asked to “find the toy”. The investigators reasoned that a child with representational insight should pick the correct box on the first try. If the children were to overturn the boxes randomly, they would find the toy on the first turn 25% of the time. Thirty (30) out of the 57 subjects found the toy by turning over the correct box on the first try. Does this sample provide sufficient evidence that the proportion of 24-month-old children who choose the correct box on the first try is greater than 0.25? Use a significance level of α = 0.05 to test the appropriate hypothesis.

ANSWER: (1) p0 = the true proportion of 24-month-old children who pick the correct box on the first try; (2) H0: p0 = 0.25; (3) Ha: p0 > 0.25; (4) is large-sample z appropriate? (57)(0.25) greater than or equal to 10, yes; (4) ; (5) P-value for z = 4.81 is approximately zero; (6) since the P - value < α,

the null hypothesis can be rejected. This can be interpreted that the true proportion of 24-month-old children who pick the correct box is greater than 0.25. That is, it appears from the sample that 24-month-old children have representational insight.

50. One criticism of reading comprehension tests is that while they may measure reading comprehension, they also measure other factors not related to reading comprehension. A reading comprehension (RC) test on a major college entrance exam provides short English prose passages, and the examinees answer a set of multiple-choice items about the passage. To see if particular items measure something other than RC, investigators gave the RC test without the reading passages to a random sample of psychology students. The investigators reasoned that if questions were measuring knowledge or memory rather than just RC, students would answer questions at a higher rate than chance (20% since there were 5 choices for each question). Suppose that on one question, 30 out of 100 examinees answered the question correctly. Is this sufficient evidence that students are using more than just reading comprehension to answer this question?

Name:

Class:

Date:

Chapter 10 - Population Proportion Test the relevant hypothesis using α = 0.05.

ANSWER: (1) H0: p0 = 0.20, Ha: p0 > 0.20 where p0 is the proportion of psychology students who answer the question correctly; (2) determine if a large-sample z test is appropriate (100)(0.20) is greater than or equal to 10; (3) calculate the test statistic

; P (z > 2.50) = 0.0062 which is less than the α value

of 0.05, so we reject the null hypothesis and conclude that the true proportion of psychology students who answer the question correctly is greater than 0.20. From this we further conclude from the sample that the students are using more than reading comprehension to answer the test question.

51. Researchers conducted a survey in which each person in a representative sample of 2135 software developers had been asked about the main priorities when choosing a new job. When asked about the ability to work remotely, 1238 of the software developers in the sample said that this is one of the main priorities in the search for work. This data was used to test the hypothesis H0: p = 0.5 versus Ha: p > 0.50, where p = the proportion of software developers who feel that the ability to work remotely is one of their main priorities. Test the hypothesis using α = 0.10.

ANSWER: (1) determine if a large-sample z test is appropriate (0.5)(2135) is greater than 10; (2) calculate the test statistic with p = 0.5,

= 0.580,

P(z>1.597) = 0.056; since the P -

value is less than the α = 0.10, the null hypothesis is rejected. We can conclude that for more than half of the software developers remote work is one of their main priorities in a work search.

52. For the scenario below, which of the following represents the correct answer to the four key (QSTN) questions and whether or not a large-sample z-test for a population proportion is appropriate?

Researchers conducted a survey in which each person in a representative sample of 2135 software developers had been asked about the main priorities when choosing a new job. When asked about the ability to work remotely, 1238 of the software developers in the sample said that this is their main priority in the work search. Does this support the claim that over half of software developers feel that the ability to work remotely is their main priority in the work search? a. Q = estimation, S = experiment, T = one numerical variable, N = one sample; large-sample z-test for a population proportion is appropriate. b. Q = hypothesis testing, S = experiment, T = two categorical variables, N = one treatment; large-sample z-test for a population proportion is not appropriate. c. Q = estimation, S = experiment, T = one categorical variable, N = one treatment; large-sample z-test for a population proportion is appropriate. d. Q = hypothesis testing, S = sample, T = one categorical variable, N = one sample; large-sample z-test for a population proportion is appropriate.

ANSWER: d 53. For the scenario below, which of the following represents the correct answer to the four key (QSTN) questions and whether or not a large-sample z-test for a population proportion is appropriate.

One criticism of reading comprehension tests is that while they may measure reading comprehension, they also measure other factors not related to reading comprehension. A reading comprehension (RC) test on a major college entrance exam provides short English prose passages, and the examinees answer a set of multiple-choice items about the passage. To see if particular items measure something other than RC, investigators gave the RC test without the reading passages to a random sample of psychology students. The investigators reasoned that if questions were measuring knowledge or memory rather than just RC, students would answer questions at a higher rate than chance (20% since there were 5

Name:

Class:

Date:

Chapter 10 - Population Proportion choices for each question). Suppose that on one question, 30 out of 100 examinees answered the question correctly. Is this sufficient evidence that students are using more than just reading comprehension to answer this question? a. Q = estimation, S = experiment, T = one numerical variable, N = one sample; a large-sample z-test for a population proportion is not appropriate b. Q = hypothesis testing, S = experiment, T = two categorical variables, N = one treatment; a large-sample z-test for a population proportion is not appropriate c. Q = estimation, S = experiment, T = one categorical variable, N = one treatment; a large-sample z-test for a population proportion is appropriate d. Q = hypothesis test, S = sample, T = one categorical variable, N = one sample; a large-sample z-test for a population proportion is appropriate ANSWER: d 54. For the scenario below, which of the following represent the correct answer to the four key (QSTN) questions and whether or not a large-sample z-test for a population proportion is appropriate.

A group of Canadian researchers conducted an experiment that queried a group of subjects regarding the time it took them to reach for their cell phones if nothing else occupied their attention. The experiment showed that 77% of the subjects took fewer than 20 seconds from the time they entered the distraction-free room to when they reached for their cell phones. Do the results of this experiment support the claim that more than 75% of cell phone users would reach for their phones if nothing else occupied their attention. a. Q = estimation, S = experiment, T = one numerical variable, N = one sample; a large-sample z-test for a population proportion is appropriate b. Q = hypothesis testing, S = experiment, T = two categorical variables, N = one treatment; a large-sample z-test for a population proportion is not appropriate c. Q = hypothesis testing, S = sampling, T = one categorical variable, N = one treatment; a large-sample z-test for a population proportion is appropriate d. Q = estimation, S = sample, T = one categorical variable, N = one sample; a large-sample z-test for a population proportion is not appropriate ANSWER: c 55. Assuming a random sample from a large population, for which of the following null hypotheses and sample sizes is the large-sample z test appropriate? a. H0: p0 = 0.10, n = 75 b. H0: p0 = 0.15, n = 50 c. H0: p0 = 0.6, n =200 d. H0: p0 = 0.3, n =20 ANSWER: c 56. Assuming a random sample from a large population, for which of the following null hypotheses and sample sizes would the large-sample z test not be appropriate? a. H0: p0 = 0.9, n = 200 b. H0: p0 = 0.10, n = 150 c. H0: p0 = 0.08, n = 100 d. H0: p0 = 0.8, n = 100 ANSWER: c

Name:

Class:

Date:

Chapter 10 - Population Proportion 57. In a hypothesis test, the null hypothesis is p = 0.44. What is the minimum random sample size which will still permit you to use a large-sample z-test? a. 23 b. 17 c. 53 d. 77 ANSWER: a 58. Suppose you’re conducting a hypothesis test with a null hypothesis p = 0.40. You take a random sample sized n = 20.

Which of the following would permit you to use a large-sample z-test?

I. = 0.5 II.

= 0.6

III.

= 0.7

a. Neither I nor II nor III b. I only c. II only d. III only ANSWER: d 59. For the following scenario, which of the following accurately summarize the HMC3 process?

The article reports that in a random sample of 1760 residents of the city, 597 answered “yes” to the following question: “Are you satisfied with the ecological situation in your city?” The authors were interested in using these data to determine if there is convincing evidence that less than 40% of the residents of the city are satisfied with the ecological situation in the city. a. Hypothesis H0: p = 0.40 versus Ha: p < 0.40; Q = hypothesis test, S = sample, T = one categorical variable, N = one sample; method = large-variable test for a population proportion; check: np = (1760)(0.40) ≥ 10; P (z < 5.2067) ≈ 0 so null hypothesis can be rejected; the sampled data support the hypothesis that fewer than 40% of the city’s residents are satisfied with the ecological situation in the city. b. Hypothesis H0: p = 0.40 versus Ha: p > 0.40; Q = hypothesis test, S = sample, T = one categorical variable, N = one sample; method = large-variable test for a population proportion; check: np = (1760)(0.40) ≥ 10; P (z> 5.2067) ≈ 0 so null hypothesis can be rejected; the sampled data support the hypothesis that more than 40% of the city’s residents are satisfied with the ecological situation in the city. c. Hypothesis H0: p = 0.40 versus Ha: p < 0.40; Q = hypothesis test, S = sample, T = two categorical variables, N = one sample; the large-variable test for a population proportion is not an appropriate method d. Hypothesis H0: p = 0.40 versus Ha: p < 0.40; Q = hypothesis test, S = sample, T = one categorical variable, N = one sample; method = large-variable test for a population proportion; check: np = (0.34)(0.40) ≤ 10, largesample z-test is not appropriate ANSWER: a 60. For the following scenario, which of the following accurately summarize the HMC3 process?

A group of Canadian researchers conducted an experiment in which they placed a group of 100 subjects in a distractionfree room and measured the time it took them to reach for their cell phones. The experiment showed that 77% of the subjects took fewer than 20 seconds from the time they entered the distraction-free room to when they reached for their cell phones. Do the results of this experiment support the claim that more than 75% of cell phone users would reach for

Name:

Class:

Date:

Chapter 10 - Population Proportion their phones if nothing else occupied their attention a. Hypothesis H0: p = 0.75 versus Ha: p < 0.75; Q = hypothesis test, S = sample, T = one categorical variable, N = one sample; method = large-variable test for a population proportion; check: np = (100)(0.25) ≥ 10; P (z < 461888) ≈ 33.3% so null hypothesis cannot be rejected; the sampled data do not support the hypothesis that more than 75% of cell phone users would reach for their cell phones if nothing else occupied their attention. b. Hypothesis H0: p 0.75 versus Ha: p > 0.75; Q = hypothesis test, S = sample, T = one categorical variable, N = one sample; method = large-variable test for a population proportion; check: np = (100)(0.25) ≥ 10; P (z> 0.46188) ≈ 0.667 so null hypothesis cannot be rejected; the sampled data do not support the hypothesis that more than 75% of cell phone users would reach for their cell phones if nothing else occupied their attention. c. Hypothesis H0: p = 0.75 versus Ha: p < 0.75; Q = hypothesis test, S = sample, T = two categorical variables, N = one sample; the large-variable test for a population proportion is not an appropriate method d. Hypothesis H0: p = 0.75 versus Ha: p < 0.75; Q = hypothesis test, S = sample, T = one categorical variable, N = one sample; method = large-variable test for a population proportion; check: np = (0.25)(25) ≤ 10, largesample z-test is not appropriate ANSWER: a 61. Which of the following are potential mistakes that can be made when applying the HMC3 process for hypothesis testing and conclusion interpretation?

I. II. III.

Incorrect expression of the null and alternative hypothesis Use of the sampled proportion rather than the null hypothesis proportion in calculating the sampling distribution standard error Combination of sample size and null hypothesis proportion which don’t meet the requirements for large-sample testing

a. I and II b. II and III c. I and III d. I, II, and III ANSWER: d 62. Which of the following is a reason to use a randomization test as opposed to a large-sample z test for hypothesis testing of population proportions? a. The sampling distribution of is well approximated by a normal distribution b. Your sample was not random nor was it representative of the population c. Your sample proportion is close in value to the proportion represented by the null hypothesis d. When your sample size is too small to assume that the sampling distribution of

is normal

ANSWER: d 63. Which of the following are essential assumptions and steps in conducting a randomization test for one proportion?

I. II.

Assume that the population proportion is equal to the value specified in the null hypothesis Simulate random samples of an appropriate size and use them to create a sampling distribution.

Name:

Class:

Date:

Chapter 10 - Population Proportion III.

Use the simulation-based sampling distribution to find an approximate P-value

a. I and II only b. II and III only c. I and III only d. I, II, and III ANSWER: d 64. Suppose that you are interested in deciding if there is evidence that a majority of the inhabitants of your city have a pet. You take a random sample of 16 inhabitants and find that 10 of the 16 inhabitants of the sample have a pet. Use a randomization test to select the appropriate output for one set of 1000 simulated proportions and carry out a hypothesis test for a population proportion with a significance level α = 0.05. a.

b.

Name:

Class:

Date:

Chapter 10 - Population Proportion c.

d.

ANSWER: b 65. Which of the following is a reason to use an exact binomial test as opposed to a large-sample z test for hypothesis testing of population proportions? a. The sampling distribution of is well approximated by a normal distribution b. Your sample was not random nor was it representative of the population c. Your sample proportion is close in value to the proportion represented by the null hypothesis d. When your sample size is too small to assume that the sampling distribution of

is normal

ANSWER: d 66. Use the Exact Binomial Test for One Proportion to determine the binomial probability for the following scenario: A group of Canadian researchers conducted an experiment in which they placed a group of 800 subjects in a distraction-free room and measured the time it took them to reach for their cell phones. The experiment showed that 77% of the subjects took fewer than 20 seconds from the time they entered the distraction-free room to when they reached for their cell phones. Do the results of this experiment support the claim that more than 75% of cell phone users would reach for their

Name:

Class:

Date:

Chapter 10 - Population Proportion phones if nothing else occupied their attention. a. P - value = 0.102 b. P - value = 0.096 c. P - value = 0.127 d. P - value = 0.083 ANSWER: a 67. Data from a random sample of 12 women from the Northern Territory of Australia was used to test the claim that more than 50% of women of age 13 to 26 had received at least one dose of the HPV vaccine. The sample proportion was 0.667. Use the exact binomial distribution to test the hypothesis H0: p = 0.5 and Ha: p > 0.5 where p represents the proportion of women aged 13 to 26 who received at least one dose of the HPV vaccine. a. P - value = 0.194, since the P - value is large, the null hypothesis would not be rejected b. P - value = 0.02, since the P - value is small, the null hypothesis would be rejected c. P - value=0.04, since the P - value is small, the null hypothesis would be rejected d. P - value = 0.187, since the P - value is large, the null hypothesis would not be rejected ANSWER: a

Name:

Class:

Date:

Chapter 11 - Difference Between Two Proportions 1. Two samples are said to be independent when the selection of the individuals in one sample has no bearing on the selection of those in the other sample. a. True b. False ANSWER: True For which of the following sample sizes and

2.

values would it be appropriate to use to estimate a difference in population proportion?

I) II) III) a. I only b. II only c. II and III only d. III only ANSWER: b 3. Which of the following conditions would permit you to use a large-sample confidence interval for a difference in population proportion?

I) The sample size for one of the two populations must be large enough to include at least 10 successes and 10 failures II) The sample size for both of the two populations must be large enough to include at least 10 successes and 10 failures III) The samples from both populations must be randomly selected IV) The samples from one of the two populations must be selected in a way that it is reasonable to regard each sample as representative of the corresponding population. a. I and III b. II and III c. II and IV d. I and IV ANSWER: b 4. Suppose you are interested in the proportion of two populations. You gather a random sample from each population.

What else must you do if you would like to use a large sample confidence interval to express the difference in the population proportions?

I. II. III.

Ensure that the sample size you use for one population is large Ensure that the sample size you use for one population is sufficiently large to allow for at least 10 successes and 10 failures Ensure that the sample sizes you use for both populations are sufficiently large to allow for at least 10 successes and 10 failures a. Neither I nor II nor III b. I only

Name:

Class:

Date:

Chapter 11 - Difference Between Two Proportions c. II only d. III only ANSWER: d 5. of

When constructing a confidence interval for the difference of two population proportions, the appropriate standard error is

a. True b. False ANSWER: True 6. A 90% confidence interval for

is (-0.05, -0.002). Which of the following is the 95% confidence interval

calculated from the same data? a. (-0.058, 0.005) b. (-0.055, 0.003) c. (0.003, 0.055) d. (0.005, 0.058) ANSWER: b 7. A 99% confidence interval for

is (0.020, 0.150). Which of the following is the 95% confidence interval

calculated from the same data? a. (0.036, 0.134) b. (0.044, 0.126) c. (-0.020,0.075) d. (0.068, 0.169) ANSWER: a 8. A 95% confidence interval for

is (0.036, 0.134). Which of the following is the 90% confidence interval

calculated from the same data? a. (0.036, 0.134) b. (0.044, 0.126) c. (-0.020,0.075) d. (0.068, 0.169) ANSWER: b 9. Suppose you’re interested in determining the difference in the proportions of a variable of interest for two different populations: population A and population B. You take a random sample size of 200 from both populations. The sample proportion from populations A and B are as follows: . Which of the following represent a 95% confidence interval for a. (-0.064, 0.124) b. (-0.094, 0.154)

?

Name:

Class:

Date:

Chapter 11 - Difference Between Two Proportions c. (-0.049, 0.109) d. (-0.022, 0.098) ANSWER: a 10. A marketing strategist would like to estimate the difference between the proportion of men who list “Action” as their favorite movie genre and the proportion of women who list “Action” as their favorite genre. The strategist gathers a random sample of 300 men and 200 women. Of the men, 156 indicate that “Action” is their favorite genre; of the women, 87 indicate that “Action” is their favorite. (a) Determine if the large sample confidence interval procedures can be used for estimation. (b) Create a 95% confidence interval for the difference in the population proportions. (c) Interpret the confidence interval. (d) Based on the confidence interval, is it possible that the two population proportions are equal?

ANSWER: (a) There are at least 10 successes and failures in each group, so the large sample confidence interval procedure can be used for estimation. (b) The 95% confidence interval is given by:

(c) We are 95% confident that the actual difference in proportions is between -0.004 and 0.174. (d) Because this confidence interval contains 0, the two proportions may be equal 11. Suppose the proportions for random samples taken from populations A and B and the confidence interval for is determined to be (0.15, 0.27). Which of the following can you say regarding the relative values of

and

?

I. II. III.

You think that is greater than and the interval (0.15, 0.27) gives an estimate of how much greater.

You think that is less than and the interval (0.15, 0.27) gives an estimate of how much less. and could be equal.

a. Neither I nor II nor III b. I only c. II only d. III only ANSWER: b 12. Suppose the proportions for random samples taken from populations A and B and the confidence interval for is determined to be (-0.54, -0.38). Which of the following can you say regarding the relative values of ?

I. II. III.

You think that is greater than and the interval (-0.54, -0.38) gives an estimate of how much greater.

You think that is less than and the interval (-0.54, -0.38) gives an estimate of how much less. and could be equal a. Neither I nor II nor III b. I only c. II only d. III only

and

Name:

Class:

Date:

Chapter 11 - Difference Between Two Proportions ANSWER: c 13. Suppose the proportions for random samples taken from populations A and B and the confidence interval for is determined to be (-0.50, 0.15). Which of the following can you say regarding the relative values of

and

?

I. II. III.

You think that is greater than B and the interval (-0.54,-0.38) gives an estimate of how much greater.

You think that is less than and the interval (-0.54,-0.38) gives an estimate of how much less. and could be equal.

a. Neither I nor II nor III b. I only c. II only d. III only ANSWER: d 14. An article describes the results of an experiment. Students were randomly assigned to the two groups. One group was a control group of students who used source A while preparing for the test. Of the 54 students in this group, 31 passed the test. Those in the second group used source B while preparing for the test. Of the 48 students in the supplement group, 17 passed the test.

Construct and interpret a 95% confidence interval for the difference in the proportion of students who passed the test using source A and the proportion of students who passed the test using source B. a. Confidence Interval = (-0.310, -0.139); because both endpoints of the interval are negative, you would conclude that the proportion of students who passed the test using source B is greater than the proportion of students who passed the test using source A by somewhere between 0.139 and 0.301. b. Confidence Interval -= (-0.409, -0.031); because both endpoints of the interval are negative, you would conclude that the proportion of students who passed the test passed the test using source B is greater than the proportion of students who passed the test using source A by somewhere between 0.031 and 0.409. c. Confidence Interval = (-0.409, 0.031); because 0 is included in the confidence interval, you can conclude that the proportion of students who passed the test using source A and the proportion of students who passed the test using source B could be equal. d. Confidence Interval = (0.031, 0.409); because both endpoints of the interval are positive, you could conclude that the proportion of students who passed the test using source A is greater than the proportion of students who passed the test using source B by somewhere between 0.031 and 0.409.

ANSWER: d 15. The hypothesis

is equivalent to the hypothesis

.

a. True b. False ANSWER: True 16. A study was carried out to see if seniors were more likely than freshmen to favor banning cell phones at school.

Which of the following hypothesis should be tested to answer this question? The proportion of seniors in favor of banning cell phones , and the proportion of freshmen in favor of banning cell phones . a. b.

Name:

Class:

Date:

Chapter 11 - Difference Between Two Proportions c. d.

ANSWER: a 17. Suppose you’re interested in whether graduate students were less likely than undergraduate students to complete assigned projects on time. Which of the following hypothesis should be tested to answer this question? The proportion of graduate students who complete assignments on time g, and the proportion of undergraduate students who complete assignments on time . a. b. c. d.

ANSWER: b 18. Suppose you’re interested in whether or not there is a difference in the proportion of bus trips or taxi trips taken in a particular metropolitan area that are completed within the expected travel time. Which of the following hypothesis should be tested to answer this question? The proportion of on-time bus trips is , and the proportion of on-time taxi trips is . a. b. c. d.

ANSWER: c 19. A hotel chain is interested in evaluating reservation processes. Guests can reserve a room by using either a telephone system (T) or an online system (O) that is accessed through the hotel’s website. Independent random samples of 90 guests who reserved a room by phone and 68 guests who reserved a room online were selected. Of those who reserved by phone, 61 reported that they were satisfied with the reservation process. Of those who reserved online, 44 reported that they were satisfied. Which of the following hypotheses should be tested to conclude that the proportion who are satisfied is greater for those who reserve a room online? a. b. c. d.

ANSWER: b 20. Suppose you’d like to use a large-sample test of a hypothesis regarding a difference in the proportions of two populations. The samples from each population included at least 10 successes and 10 failures. What else is required in order to use the large-sample test of the hypothesis?

I. II.

Samples from both populations were taken randomly Samples from both populations were representative of their respective populations a. Either I or II b. Neither I nor II

Name:

Class:

Date:

Chapter 11 - Difference Between Two Proportions c. I only d. II only ANSWER: a 21. Suppose you’d like to use a large-sample test of a hypothesis regarding a difference in the proportions of two populations. You take random samples from both populations. What else is required in order to use the large-sample test of the hypothesis?

I. II. III.

Ensure that the sample from one of the populations includes at least 10 successes and 10 failures Ensure that the samples from both of the populations include at least 10 successes and 10 failures Ensure that the sample from one of the populations is large

a. Neither I nor II nor III b. I only c. II only d. III only ANSWER: c 22. Which of the following conditions would permit you to use a large-sample test of a hypothesis regarding a difference in the proportions of two populations?

I) The sample size for one of the two populations must be large enough to include at least 10 successes and 10 failures II) The sample size for both of the two populations must be large enough to include at least 10 successes and 10 failures III) The samples from both populations must be randomly selected IV) The samples from one of the two populations must be selected in a way that it is reasonable to regard each sample as representative of the corresponding population. a. I and III b. II and III c. II and IV d. I and IV ANSWER: b 23. The for a hypothesis test concerning the difference in two population proportions is always calculated by finding the area to the right of the test statistic, regardless of the alternative hypothesis. a. True b. False ANSWER: False used in the large sample test of 24. The standard deviation of in the large sample confidence interval for a. True b. False ANSWER: False

is the same as the standard deviation used

25. A study is conducted to determine whether the proportion of airline passengers complaining of post-flight respiratory symptoms is larger for flights that do not circulate cabin air than for flights that do circulate the air. After checking to

Name:

Class:

Date:

Chapter 11 - Difference Between Two Proportions make sure that all of the necessary conditions were met, the following is the associated with this test?

statistic was calculated to be 0.84. Which of the

a. 0.2005 b. 0.4010 c. 0.7995 d. 0.5990 ANSWER: a 26. Each person in a random sample of 200 students and a random sample of 150 faculty at a large university was asked whether they take public transportation to campus. Fifty-eight percent of the students and 46% of the faculty responded “yes”. This data was used to carry out a test of the hypotheses: The value of the test statistic was

. For a significance level of 0.01, which of the following is correct?

a.

should be rejected; there is convincing evidence that the proportion of people who take public transportation to campus is different for students and faculty. b. should be rejected; there is convincing evidence that the proportion of people who take public transportation to campus is the same for students and faculty. c. should not be rejected; there is no convincing evidence that the proportion of people who take public transportation to campus is different for students and faculty. d. should not be rejected; there is no convincing evidence that the proportion of people who take public transportation to campus is the same for students and faculty.

ANSWER: c 27. A study seeks to determine whether the proportion of Dutch boys who listen to music at high volume is greater than this same proportion for Dutch girls. After checking to make sure that all of the necessary conditions were met, we calculated the value of the statistic to be . Which of the following is associated with this test?

If , what can we conclude? a.

, reject the null hypothesis and conclude that the proportion of Dutch boys who listen to music at high volume is greater than this same proportion for Dutch girls. b. , fail to reject the null hypothesis and conclude that there is no convincing evidence that the proportion of Dutch boys who listen to music at high volume is greater than this same proportion for Dutch girls. c. , reject the null hypothesis and conclude that the proportion of Dutch boys who listen to music at high volume is greater than this same proportion for Dutch girls. d. , fail to reject the null hypothesis and conclude that there is no convincing evidence that the proportion of Dutch boys who listen to music at high volume is greater than this same proportion for Dutch girls.

ANSWER: a 28. Suppose you conduct an experiment in which subjects are randomly assigned to two treatment groups. The proportion of successes in treatment group #1 is 0.75, while the proportion of successes in treatment group #2 is 0.68. Which of the following could have contributed to the difference?

I.

Effect of the treatments

Name:

Class:

Date:

Chapter 11 - Difference Between Two Proportions II.

Response variability

a. I only b. Both I and II c. II only d. Neither I nor II ANSWER: b 29. Suppose you conduct an experiment in which you randomly assign gardeners to two groups. One group uses compost as a fertilizer, while the other group uses synthetic fertilizer. Gardeners from each group report whether or not the growth rate of their garden plants met a pre-determined standard. If the proportion of gardeners using the compost whose plants met the standard was 0.89 and the proportion of gardeners using the synthetic fertilizer was 0.70, which of the following can you conclude?

I. II. III.

The difference of 0.17 between the proportions of the two groups is due to the difference in fertilizers.

The compost fertilizer results in faster plant growth.

The difference of 0.17 between the proportions of the two groups is due to random variability.

a. Neither I nor II nor III b. I only c. II only d. III only ANSWER: a 30. Which of the following is true regarding differences in proportions for outcomes of experiments performed on randomly assigned subjects? a. They can be generalized to a larger population b. They are due to the treatment difference c. They are due to variability in the random assignment d. They could have contributions from both the treatment difference and variability in response.

ANSWER: d 31. Suppose you’re interested in the proportion of undergraduate students who study in the library vs. the number of graduate students who study in the library. Which of the following data types would be appropriate? a. Sample data b. Experimental data c. Either sample data or experimental data would be appropriate d. Cannot tell from the information given ANSWER: a 32. Suppose you’re interested in whether or not treatment with a new drug reduces asthma symptoms more than breathing exercises alone. Which of the following data types would be appropriate? a. Sample data b. Experimental data c. Either sample data or experimental data would be appropriate d. Cannot tell from the information given

Name:

Class:

Date:

Chapter 11 - Difference Between Two Proportions ANSWER: b 33. Suppose you’re interested in the effect of class starting time on the proportion of students who earn a C-grade or higher in the class. For one academic term, you randomly assign ten students each to an early-morning vs. afternoon session of the same course and compare grades at the end of the term. Which of the following data types would you use to draw your conclusions? a. Sample data b. Experimental data c. A combination of sample data and experimental data d. Cannot tell from the information given ANSWER: b 34. Suppose you’d like to use a large-sample to draw conclusions about a difference in treatment proportions. The number of individuals in each treatment group is large enough to ensure that each group has at least 10 successes and 10 failures. What else is required to use the large-sample test of the hypothesis?

I. II.

Individuals were selected randomly from a larger group Individuals were randomly assigned to treatment groups

a. I only b. II only c. Neither I nor II d. Both I and II ANSWER: b 35. Suppose you’d like to use a large-sample z-test to draw conclusions about a difference in treatment proportions. You randomly assign individuals to treatment groups. What else is required to use the large-sample z-test?

I. II. III.

Ensure that the number of individuals assigned to one treatment group is sufficiently large to ensure at least 10 successes and 10 failures Ensure that the number of individuals assigned to both treatment groups is sufficiently large to ensure at least 10 successes and 10 failures Ensure that the individuals from both groups are randomly drawn from a larger group

a. Neither I nor II nor III b. I only c. II only d. III only ANSWER: c 36. Which of the following conditions would permit you to use a large-sample - confidence interval to draw conclusions about a difference in treatment proportions.

I) The size for one of the two treatment groups must be large enough to include at least 10 successes and 10 failures II) The size for both of the two treatment groups must be large enough to include at least 10 successes and 10 failures III) Individuals for both treatment groups must be randomly assigned. a. I only b. II only

Name:

Class:

Date:

Chapter 11 - Difference Between Two Proportions c. II and III d. I and III ANSWER: c 37. A researcher would like to determine if the proportion of patients who indicate that they are happy with a hospital emergency room service is significantly different for those who receive treatment from a female nurse rather than a male nurse. As patients are admitted for treatment, they are randomly assigned to a nurse and before discharge are asked to indicate if they were happy or unhappy with the treatment they received. The following results were obtained: Female nurse: = 35, number happy = 21; male nurse: =35, number happy = 22 Perform a hypothesis test to determine if a significant difference exists.

ANSWER: The hypothesis test is The assumptions for a z-test are met, so the test statistic is:

The is 0.803, so we fail to reject the null hypothesis. There is evidence that there are no differences in the proportion of happy patients with either gender of the nurse.

38. A study is conducted at a university to determine if its test preparation seminar improves the proportion of students who pass the licensing exam. The following summary data were obtained: Group that attended the seminar: = 35, number who passed = 16 Group that did not attend the seminar: = 76, number who passed = 19 Is there evidence to support the claim that the proportion of passing grades is higher for those who attended the seminar?

Assume an .

ANSWER: The hypothesis test is The value for

which gives a test statistic is 2.182. The

of 0.0143 is less than 0.05, therefore the

null hypothesis is rejected. The proportion of seminar-attending students who passed the exam is significantly greater than that of non-seminar-attending students.

39. One of the most striking human accomplishments is the achievement of intelligible speech by age five. Children who suffer from speech delays can frequently benefit from therapeutic exercises guided by a speech therapist. Researchers ran an experiment investigating the effectiveness of guided exercises in childhood speech development. Children were randomly assigned to treatments with 468 receiving guided therapy exercises and 171 receiving only instructions for selfdirected exercises. Of the children who worked with a therapist, 404 showed speech improvement. Of the children who performed self-directed exercises, 135 showed speech improvement.

At the 0.05 significance level, do the data provide evidence that the guidance of a speech therapist improved childhood speech development? Provide statistical evidence for your conclusion.

ANSWER: Subjects were randomly assigned, and treatment group sizes met the conditions of the z-test

Test statistic z = 2.275; P-value (z > 2.275) = 0.0116 Since this P-value is less than 0.005, reject the null hypothesis. There is evidence that children who perform exercises with the guidance of a speech therapist show more speech improvement than those who engage in self-exercise alone.

Name:

Class:

Date:

Chapter 11 - Difference Between Two Proportions 40. A researcher would like to determine if the proportion of patients who indicate that they are happy with a hospital emergency room service is significantly different for those who receive treatment from a female nurse rather than a male nurse. As patients are admitted for treatment, they are randomly assigned to a nurse and before discharge are asked to indicate if they were happy or unhappy with the treatment they received. The following results were obtained: Female nurse: = 35, number happy = 21; male nurse: n35, number happy = 22 Find a 99% confidence interval for the difference in treatment proportions.

ANSWER: The confidence interval is:

Therefore, we are 99% confident that the true difference in treatment proportions lies in the interval (0.327,0.269).

41. A study compared flu vaccines administered by injection and flu vaccines administered as a nasal spray. Each of the 4,000 children under the age of 5 who participated in the study received both a nasal spray and an injection, but onlyone was the real vaccine and the other was salt water. In other words, a child could receive a real vaccine injection plus a salt water nasal spray or a salt water injection and a real vaccine nasal spray. At the end of the flu season, it was determined that of the 2,000 children receiving the real vaccine by nasal spray, 10.1% got the flu. Of the 2,000 children receiving the real vaccine by injection, 15.6% got the flu. The 95% confidence interval for the difference in treatment proportions is: a. 0.00 ± 0.021 b. 0.055 ± 0.017 c. 0.055 ± 0.024 d. 0.055 ± 0.021 ANSWER: d 42. An article describes an experiment that investigated if car following behavior for motorcyclists in conditions A is less dangerous than in conditions B. Motorcyclists were randomly assigned to one of two groups. The 60 participants in the first group were placed in condition A while driving in a simulator. The 60 participants in the second group were placed in condition B while driving in a simulator. The motorcyclists were instructed to pay attention to neighboring traffic, maintain two car lengths from a virtual lead vehicle, and avoid crashes. Of the motorcyclists from group A, 38 avoided crashes. Of the motorcyclists from group B, 17 avoided crashes.

Use the given information to construct and interpret a 95% confidence interval for the difference in the proportions of motorcyclists who would avoid crashes. a. Confidence Interval: (0.083, 0.517) Because both endpoints of the interval are positive, you would conclude that the proportion of motorcyclists who avoided crashes while driving in conditions A is greater than the proportion of motorcyclists who avoided crashes while driving in conditions B by somewhere between 0.0803 and 0.517. b. Confidence Interval: (-0.183, 0.517) Because 0 is included in the confidence interval, you would conclude that the proportion of motorcyclists who avoided crashes while driving in conditions A is greater than the proportion of motorcyclists who avoided crashes while driving in conditions B could be equal. c. Confidence Interval: (-0.517, 0.083) Because 0 is included in the confidence interval, you would conclude that the proportion of motorcyclists who avoided crashes while driving in conditions A is greater than the proportion of motorcyclists who avoided crashes while driving in conditions B could be equal. d. Confidence Interval: (0.183, 0.517) Because both endpoints of the interval are positive, you would conclude that the proportion of motorcyclists who avoided crashes while driving in conditions A is greater than the proportion of motorcyclists who avoided crashes while driving in conditions B by somewhere between 0.0803 and 0.517.

ANSWER: a

Name:

Class:

Date:

Chapter 11 - Difference Between Two Proportions 43. An article describes the results of an experiment. Students of computer programming courses were randomly assigned to two groups. One group was a control group of students who were trained by teacher A. Of the 69 students who trained with teacher A, 17 passed the final exam. Those in the second group were trained by teacher B. Of the 131 students who trained with teacher B, 9 passed the final exam.

Based on the given data, what can you learn about the difference in the proportion of students who passed the exam after being trained by teacher A and those who passed the exam after being trained by teacher B? Calculate and interpret a 95% bootstrap confidence interval for the difference in proportions. a. The 95% confidence interval based on the bootstrap resampling is (0.068, 0.288). Based on the data from this experiment, you can be 95% confident that the actual difference in the proportions of students who passed the exam after being trained by teacher A and those who passed the exam after being trained by teacher B is between 0.068 and 0.288. Both endpoints of the interval are positive, and you can conclude that the proportion of students who passed the exam after being trained by teacher A is greater than the proportion of students who passed the exam after being trained by teacher B. b. The 95% confidence interval based on the bootstrap resampling is (-0.068, 0.288). Based on the data from this experiment, you can be 95% confident that the actual difference in the proportions of students who passed the exam after being trained by teacher A and those who passed the exam after being trained by teacher B is between -0.068 and 0.288. Zero is contained in this interval, so it is plausible that there is no difference in the population proportions. c. The 95% confidence interval based on the bootstrap resampling is (-0.288, 0.068). Based on the data from this experiment, you can be 95% confident that the actual difference in the proportions of students who passed the exam after being trained by teacher A and those who passed the exam after being trained by teacher B is between -0.288 and 0.068. Zero is contained in this interval, so it is plausible that there is no difference in the population proportions. d. The 95% confidence interval based on the bootstrap resampling is (-0.068, -0.288). Based on the data from this experiment, you can be 95% confident that the actual difference in the proportions of students who passed the exam after being trained by teacher A and those who passed the exam after being trained by teacher B is between 0.068 and 0.288. Both endpoints of the interval are positive, and you can conclude that the proportion of students who passed the exam after being trained by teacher A is greater than the proportion of students who passed the exam after being trained by teacher B. ANSWER: a 44. Under which of the following conditions would you use a bootstrap confidence interval to determine a difference in proportions?

I) Subjects are randomly assigned to treatment groups II) Treatment groups include sufficient subjects to allow for at least 10 successes and 10 failures III) Sample size conditions necessary for the large-sample z confidence interval are not met a. I only b. I and II c. II and III d. III only ANSWER: d 45. Under which conditions would a bootstrap confidence interval not be appropriate?

I. II. III.

You have ready access to the technology needed to perform the simulation Subjects in the study were not randomly assigned to treatment groups The sample size conditions are appropriate for a large-sample z-confidence interval

Name:

Class:

Date:

Chapter 11 - Difference Between Two Proportions a. Neither I nor II nor III b. I only c. II only d. III only ANSWER: d 46. An article describes the results of an experiment. Patients suffering from chronic somatic diseases were randomly assigned to two groups. One group was a control group of patients who received treatment A. Of the 58 patients in this group, 9 reported improvements at the end of the study period. Patients in the second group received treatment B. Of the 33 patients in this group, 4 reported improvements at the end of the study period.

Do these data provide evidence that the proportion of success for patients who received treatment A differs from the proportion of success for patients who received treatment B? Use a randomization test to select the appropriate output for one set of 1000 simulated proportions and carry out a hypothesis test for a difference in proportions. Use a significance level of 0.05. a.

b.

Name:

Class:

Date:

Chapter 11 - Difference Between Two Proportions c.

d.

ANSWER: b 47. Which of the following are essential assumptions and steps in conducting a randomization test for a difference in proportions?

I. II.

Pool the two original samples together into one hypothetical collection Draw samples equal to the sample sizes for each of the two groups from the combined pool with replacement. Use each pair of samples to calculate a simulated

III.

Repeat the simulated sampling and use the values of a. I and II

to create a sampling distribution.

Name:

Class:

Date:

Chapter 11 - Difference Between Two Proportions b. II and III c. I and III d. I, II, and III ANSWER: d 48. Under which of the following conditions would you use a randomization test to determine a difference in proportions?

I) Subjects are randomly assigned to treatment groups II) Treatment groups include sufficient subjects to allow for at least 10 successes and 10 failures III) Sample size conditions necessary for the large-sample confidence interval are not met a. I only b. I and II c. II and III d. III only ANSWER: d

Name:

Class:

Date:

Chapter 12 - Population Mean 1. As

grows larger, the mean of the sampling distribution of

gets closer to the population mean µ.

a. True b. False ANSWER: False 2. The standard deviation of the sampling distribution of

decreases as n increases.

a. True b. False ANSWER: True 3. The spread of the sampling distribution of

decreases when:

a. The population mean increases b. The sample size decreases c. The population standard deviation increases d. The sample size increase ANSWER: d 4. You’re constructing a sampling distribution for a population with the following could you do?

I. II.

. If you needed a

, which of

provided that is always less than provided that

a. I only b. Neither I nor II c. II only d. Both I and II ANSWER: c 5. If you are using the sampling distribution of to estimate population parameters, which of the following are advantages of using a large sample size ?

I) As increases, the mean of the sampling distribution approaches the population mean.

II) As increases, the standard deviation of the sampling distribution approaches the standard deviation of the population.

III) As increases, the standard deviation of the sampling distribution decreases. a. I only b. I and II c. I and III d. III only ANSWER: d 6. If represents the mean of the sampling distribution and represents the population mean, what can be done to reduce the difference between and ? a. Nothing needs to be done since for any population distribution b. Increase sample size

Name:

Class:

Date:

Chapter 12 - Population Mean c. Decrease the population standard deviation d. Decrease sample size ANSWER: a 7. What is the standard deviation of the sampling distribution of mean of 48 and a standard deviation of 11? a. 0.138 b. 0.371 c. 11 d. 1.23 ANSWER: d

for random samples of size 80 from a population with a

8. The population of voting citizens in a particular small town who favor candidate A has a mean of 250 and a standard deviation of 58. If you created a sampling distribution using sample size , what would the standard deviation of your sampling distribution be? a. 58 b. 2.32 c. 11.6 d. 4.31 ANSWER: c 9. The population of voting citizens in a particular small town who favor candidate A has a mean of 250 and a standard deviation of 58. If you created a sampling distribution using sample size , what would the mean of your sampling distribution be? a. 250 b. 50 c. Cannot tell from the information given d. 290 ANSWER: a 10. Commute distances for employees of a large company have a distribution that is quite skewed. Suppose the mean commute distance is 20 miles and the standard deviation for the commute distance is 7 miles. What can be said about the sampling distribution of the mean commute distance for random samples of size 49 employees from this plant? a. and will be 20 and 1, respectively, but the sampling distribution of will not be normal. b. The sampling distribution for

will be approximately normal with mean 20 and standard deviation 7.

c. The sampling distribution for

will be approximately normal with mean 20 and standard deviation 1.

d.

and

will be 20 and 7, respectively, but the sampling distribution of

will not be normal.

ANSWER: c 11. How are the qualities ANSWER:

and

12. The sampling distribution of

related?

will always have the same shape as the distribution of the population being sampled.

Name:

Class:

Date:

Chapter 12 - Population Mean a. True b. False ANSWER: False 13. For n sufficiently large, the distribution of

is approximately a standard normal distribution.

a. True b. False ANSWER: True 14. The sampling distribution of

is normal if the population is normal.

a. True b. False ANSWER: True 15. For a random sample from a skewed population, for which of the following sample sizes would the sampling distribution of be closest to normal in shape? a. b. c. d.

ANSWER: d 16. Consider sampling from a skewed population. As the sample size n increases, some characteristics of the sampling distribution of change. How does increasing sample size change the following characteristics of the sampling distribution? (a) The mean of the sampling distribution (b) The standard deviation of the sampling distribution (c) The shape of the sampling distribution ANSWER: (a) as the sample size increases, the mean of the sampling distribution remains the same; (b) as the sample size increases, the standard deviation of the sampling distribution decreases; (c) as the sample size increases, the sampling distribution becomes less skewed and more normal.

17. Which of the following factors affect the width of a confidence interval estimation of a population mean? a. Sample size b. Population mean c. Sample mean for any single sample d. All of these ANSWER: a 18. Which of the following factors affect the width of a confidence interval estimation of a population mean?

I) Choice of confidence level II) Value of population standard deviation III) Value of population mean IV) Sample size

Name:

Class:

Date:

Chapter 12 - Population Mean a. I only b. I and IV only c. II and III only d. I, II, and IV only ANSWER: d 19. Suppose you’re using a confidence interval to estimate a population mean. Which of the following are actions you can take to reduce the width of your confidence interval?

I) Decrease the sample size II) Decrease the population standard deviation III) Increase the sample size IV) Decrease the confidence level a. II, III, and IV only b. III and IV only c. I and II only d. III only ANSWER: b 20. The confidence interval formula for estimating the population mean when the sample size is large is based on the Central Limit Theorem. a. True b. False ANSWER: True 21. The width of the confidence interval for the population mean decreases as the sample size grows larger. a. True b. False ANSWER: True 22. Under what conditions is it reasonable to use the z confidence interval to estimate a population mean?

ANSWER: When (1) the data are from a random sample of the population, (2) either the sample size is greater than or equal to 30 or it is reasonable to believe that the population distribution is normal, and (3) the population standard deviation is known.

23. Under what conditions is it reasonable to use the t confidence interval to estimate a population mean?

ANSWER: When (1) that data are from a random sample of the population and (2) either the sample size is greater than or equal to 30 or it is reasonable to believe that the population distribution is normal 24. Suppose you’re using a single sample mean and confidence interval to estimate a population mean. Although it is not typical to know the population standard deviation, in this case, you do know it. What are the conditions for the appropriate use of the confidence interval formula?

I) The population distribution must be normal.

II) The sample size must be equal to or greater than 30.

III) If the population distribution is not normal, the sample size must be equal to or greater than 30.

IV) The sample must have been selected randomly or in a way that would result in a sample that is representative of the population a. I and IV

Name:

Class:

Date:

Chapter 12 - Population Mean b. II and IV c. I, II, and IV d. III and IV ANSWER: d 25. Suppose you’re using a single, random sample and a confidence interval to estimate a population mean. You don’t know the population standard deviation. Which of the following are conditions for the appropriate use of the confidence interval formula?

I) The population distribution is normal.

II) The sample size is large (greater than or equal to 30). a. I only b. II only c. Either I or II d. Neither I nor II ANSWER: c 26. Suppose you’re planning to use a t critical value in calculating the confidence interval to estimate a population mean from a single-sample mean. Which of the following conditions must also be true?

I. II. III.

You must know the standard deviation of the population.

Your sample must have been randomly selected or be representative of the population.

Your sample size must be less than or equal to 30.

a. I only b. II only c. III only d. I and II and III ANSWER: b 27. The t confidence interval formula for estimating approximately normally distributed. a. True b. False ANSWER: False 28. How are the quantities,

should only be used when the population being sampled is at least

related?

ANSWER:

29. Suppose you are estimating the mean number of visitors to an organic cherry farm on a typical summer. According to historical records, the number of summer visitors ranges from 100 to 300. If n = the number of years of historical records sampled, what is the minimum n needed to give a margin of error of 33 visitors or less? Assume 95% confidence. a. 9 years b. 3 years c. 21 years d. 15 years

Name:

Class:

Date:

Chapter 12 - Population Mean ANSWER: a 30. Suppose you would like to estimate the number of airline passengers who transit a given large airport every day wearing masks to protect against disease transmission. Records from the local health authorities state that the daily number of mask-wearing passengers ranges from 500 to 1200. What is the minimum number of passengers you must sample in order for your margin of error to be 35 passengers? Assume 95% confidence. a. 343 b. 96 c. 32 d. 18 ANSWER: b 31. If you know that the population standard deviation of a particular population is 15 and the sample size is 36, what is the margin of error for estimating the population mean? Assume 95% confidence. a. 4.9 b. 2.5 c. 0.8 d. 9.6 ANSWER: a 32. Suppose you’re estimating the mean of a population and require a particular margin of error M. Suppose further that you have the population standard deviation, or can estimate it from the anticipated population range. How would a confidence of 99% change the required sample size compared to that of a 95% confidence? a. Sample size smaller for 99% confidence b. Sample size smaller for 95% confidence c. Sample size not affected by confidence d. Cannot tell from the information given ANSWER: b 33. You want to predict the mean number of days per year that a particular coastal area experiences early morning fog.

Given that fog in this area generally occurs only in winter months, you can assume that the anticipated days per year with early morning fog will be 20 to 120. You can sample recent weather records to find the days per year in which early morning fog was recorded. What sample size (# years of weather records) must you use if you would like to predict the mean number of days with early morning fog with a margin of error of 10 days? a. 385 b. 25 c. 100 d. 245 ANSWER: b 34. The foraging capability of Downey Woodpeckers can be compromised if part of their habitat disappears due to significant human encroachment. These creatures eat insects in trees, and if they cannot find enough food due to a decreasing forest area, their body mass may decrease. A 20-year-old study of Downy Woodpeckers indicates that for male Downy Woodpeckers, the average mass is about 28 g, with a standard deviation of approximately 1.5 g. Suppose it is desired to estimate the population mean for the mass of male Downy Woodpeckers in a local forest preserve. If the 20year-old values are taken as reasonable estimates, determine the sample size necessary to estimate to within 0.2 grams

Name:

Class:

Date:

Chapter 12 - Population Mean with 95% confidence.

ANSWER:

35. What sample size would you need if you wanted to estimate the mean number of first-time skiers who visit a particular resort in a given year? Data from a local skier club indicates that the annual number of first-time skiers to this particular resort ranges from 40 to 80. You would like a minimum margin of error 4 skiers per year. Assume 95% confidence. a. 25 b. 7 c. 385 d. 97 ANSWER: a 36. Suppose you would like to estimate mean real estate prices for a given area. You have a good estimate of the population standard deviation from historical records on price variability. What size sample would you need if you wanted to estimate the population mean with a minimum margin of error of $9,000? Assume = $33,500 and 95% confidence. a. 54 b. 14 c. 450 d. 198 ANSWER: a 37. According to internal testing done by an apple grower, the mean firmness of their apples, as measured on the Mohs hardness scale is 7.0, with a standard deviation of 0.3. (a) If the claim by the apple grower is true, what is the mean of the sampling distribution of for samples of size n = 16? (b) If the claim by the apple grower is true, what is the standard deviation of the sampling distribution of for samples of size n = 16?

ANSWER: (a) The sampling distribution mean is equal to the population mean of 7.0; (b) the standard deviation of the sampling distribution of the sample mean is 38. According to internal testing done by a tire manufacturer, the mean lifetime of tires sold on new cars is 23,000 miles with a standard deviation of 2,500 miles. (a) If the claim by the tire manufacturer is true, what is the mean of the sampling distribution of for samples of size n = 4? (b) If the claim by the tire manufacturer is true, what is the standard deviation of the sampling distribution of for samples of size n = 4?

ANSWER: (a) The sampling distribution mean is equal to the population mean of 23,000 miles; (b) the standard deviation of the sampling distribution of the sample mean is 39. A new species of sea crab has been discovered, and an experiment is conducted to determine whether or not the animal can regulate its temperature. That the animal can maintain a body temperature different from the surroundings would be considered evidence of this regulating capability. Ten of these sea crabs were exposed to ambient temperatures

Name:

Class:

Date:

Chapter 12 - Population Mean of 24ºC. Their body temperatures were measured with the results below: 24.33, 24.61, 24.67, 24.64, 24.42, 24.97, 25.23, 24.73, 24.90, 24.44 For purposes of this example, assume that it is reasonable to regard these 10 crabs as a random sample from the population of crabs in this species. (a) Calculate an estimate of the population mean. (b) Construct and interpret a 99% confidence interval for the population mean. (c) Does it appear from these data that the crabs are able to regulate their body temperature? Provide statistical justification for your response.

ANSWER: (a) The population mean is equal to the sample mean of 24.694. (b) Confidence interval: (c) Since the confidence interval of the crab’s temperature does not include the temperature of seawater, this is evidence that the crabs must be regulating their temperatures to some other value.

40. A random sample of houses in a particular city is selected and the level of radon gas is measured for each house in the sample. The values collected are given below in parts per million (ppm). Experience has shown that radon gas level is approximately normally distributed for this population.

4, 18, 13, 6, 7, 3, 9, 8, 11, 8 (a) Calculate an estimate of the population mean of radon gas levels. (b) Construct and interpret a 99% confidence interval for the population mean. (c) The city standard for radon calls for no more than a level of 6 ppm. From these data, does it appear that the mean radon level for the city houses is under 6 ppm? Provide statistical justification for your response.

ANSWER: (a) The population mean is equal to the sample mean of 8.7 ppm. (b) Confidence interval: (c) This data leaves the question open. The estimate is above the 6-ppm upper limit, however, the confidence interval includes a range of values that are under 6. The data is consistent with some acceptable levels of radon, as well as some unacceptable levels.

41. At a particular high school a popular achievement test is used for college placement. Counselors selected a random sample of 100 students from the high school and scored their tests by hand before sending them in for computer processing. For this sample, the mean was 525 and standard deviation was 25. Construct and interpret a 99% confidence interval for the population mean.

ANSWER: This setting has a random sample with a sample size > 30, so a 99% confidence interval can be safely constructed.

Based on this sample, you can be 99% confident that the mean of the high school students’ test scores is between 518.5 and 531.6.

42. The Environmental Protection Agency (EPA) is charged with monitoring the environment. One aspect of this is keeping track of “acid rain”, a broad term describing the fall of water through an acidic atmosphere. Acidity is measured on the pH scale, where pure water has a pH of 7.0. Normal rain is slightly acidic because carbon dioxide dissolves in it, and thus has a pH of about 5.5 (lower pH indicating greater acidity). Suppose the EPA wishes to determine whether a particular area is subject to acid rain. Let denote the true average pH for rain in the area.

(A) What is the appropriate null hypothesis?

(B) What is the appropriate alternative hypothesis?

(C) In your own words, distinguish between a Type I and Type II error in this context.

Name:

Class:

Date:

Chapter 12 - Population Mean ANSWER: (A) and (B) (C) a Type I error would include determining that the area is subject to acid rain when in fact the area is not subject to acid rain. A type II error would include deciding that the area is not subject to acid rain when in fact the area is subject to acid rain.

43. Psychologists have noted that people tend to make classifications based on their “typicality”. For example, a dog is more readily classified as a mammal than is a whale. Previous large-scale studies have established the following for songbirds such as robins: when young children are shown a picture of a songbird and asked if it is a bird, they respond “yes” in an average of 750 milliseconds. Do children regard chickens as representative of birds? If so, are they more representative or less representative of birds than songbirds? Let µ represent the mean time it takes children to respond to a question about whether a chicken is a bird. The investigators wish to determine whether the classification time differs from the time needed to classify songbirds.

(A) What is the appropriate null hypothesis?

(B) What is the appropriate alternative hypothesis?

(C) In your own words, distinguish between a Type I and Type II error in this context.

ANSWER: (a) and (b) (c) a Type I error would include deciding that the average classification time for chickens is different from that of songbirds when it is, in fact, the same. A type II error would include deciding that the average classification time for chickens is the same as for songbirds when in fact it is different.

44. In cities and towns on the borders between states there is a significant amount of travel across state lines to avoid high state taxes on gasoline. Some states have large rivers for borders and tolls to cross the bridges. Do these tolls impede traffic bound to neighboring states to get cheaper gasoline? To test this hypothesis, an experimental Toll-Free Week will be instituted on a particular bridge where, currently (with tolls in place), 50 cars per day drive out of the state. Let µ denote the true average number of bridge crossings per day in the absence of a toll.

(A) What is the appropriate null hypothesis?

(B) What is the appropriate alternative hypothesis?

(C) In your own words, distinguish between a Type I and Type II error in this context.

ANSWER: (a) and (b) (c) a Type I error would include deciding that the average number of crossings would be greater than 50 if there were no toll when, in fact, the average number is still 50. A type II error would include deciding that the number of crossings would stay the same (50 per day) if there were no toll, when in fact the average number of crossings would increase.

45. Suppose residents of a particular neighborhood are concerned about the arsenic level in their tap water. Health authorities have established that arsenic levels in tap water should be kept below 10 parts per million (ppm). Which of the following hypothesis could the residents test in order to determine if their drinking water has unsafe levels of arsenic? Let µ represent the arsenic levels of the neighborhood tap water. a. b. c. d.

ANSWER: a 46. Suppose residents of a mountain town are concerned about the level of airborne particulates from wood stoves on the local air quality. Health authorities have established maximum levels of 15 micrograms per cubic meter for smoke particulates. Which of the following hypothesis could the residents test in order to determine if their air quality was unhealthy? Let µ represent the smoke particulate levels in micrograms per cubic meter in the local air. a.

Name:

Class:

Date:

Chapter 12 - Population Mean b. c. d.

ANSWER: d 47. A company provides portable walkie-talkies to construction crews. Their batteries last, on average, 55 hours of under continuous use conditions. The purchasing manager receives a brochure advertising a new brand of batteries with a lower price, but suspects that the lifetime of the new brand of batteries may be shorter than the brand current in use. To test this, the new brand is installed in 8 randomly selected radios. The results for the battery life (hours) are: 45 52 56 55 51 57 48 52 Is there sufficient evidence to conclude that the purchasing manager is correct in his conjecture that the new brand has a shorter average life?

ANSWER: Start by writing the hypothesis test based on µ = battery life in hours Next, assign a significance based on relative risks of a type I or II error Choose a one-sample t-test method. Since the sample size is small, use a graphical representation of the distribution of sample values to estimate the normality of the population:

Based on the histogram and box plot, the sample value distribution appears normal, so it is reasonable to assume that the population is approximately normal and a t-test is appropriate.

Next, calculate the t based on the sample mean, sample standard deviation, and sample size:

Since the P-value is less than α, we reject the null hypothesis and conclude that the true mean lifetime of the batteries is less than 55 hours, thereby justifying the suspicions of the purchasing manager.

48. An important part of any dispensing process is statistical quality control. At a particular restaurant, machines are set to dispense 600 ml of soda into every customer’s glass. Over time the machines can get “out of control” and dispense too much soda or too little. At a random point in time each clock hour, the owner dispenses and checks a glass of dispensed soda and determines the actual volume of soda dispensed. One day the volumes of dispensed soda were: 600.15 599.92 599.85 599.92 599.81 600.14 600.04 599.98 Is there sufficient evidence to conclude that the dispensing machine needs adjustment?

ANSWER: Start by writing the hypothesis test based on = soda volume in milliliters Next, assign a significance based on relative risks of a type I or II error Choose a one-sample t-test method. Since the sample size is small, use a graphical representation of the distribution of sample values to estimate normality of the population:

Name:

Class:

Date:

Chapter 12 - Population Mean

Based on the histogram and box plot, the sample value distribution appears normal, so it is reasonable to assume that the population is approximately normal and a t-test is appropriate.

Next, calculate the t based on the sample mean, sample standard deviation, and sample size:

Since the P-value is not less than α, we fail to reject the null hypothesis and cannot conclude that the true mean volume of soda dispensed is different from 600 mL. The sample does not give convincing evidence that the machine needs adjusting.

49. A boat manufacturer claims that a particular boat and motor combination will burn less than 4.0 gallons of fuel per hour. Fuel consumption for a random sample of 10 similar boats resulted in the data below: 4.06 4.29 4.26 4.64 4.23 3.93 3.64 4.13 3.93 3.86 Is there sufficient evidence to conclude that the manufacturer’s claim is correct? Use α = 0.05.

ANSWER: Start by writing the hypothesis test based on µ = fuel consumption in gallons/hour Choose a one-sample t-test method. Since the sample size is small, use a graphical representation of the distribution of sample values to estimate normality of the population:

Based on the histogram and box plot, the sample value distribution appears normal, so it is reasonable to assume that the population is approximately normal and a t-test is appropriate.

Next, calculate the t based on the sample mean, sample standard deviation, and sample size:

Name:

Class:

Date:

Chapter 12 - Population Mean Since the P-value is not less than α, we fail to reject the null hypothesis and cannot conclude that the mean fuel consumption is less than 4.0 gallons per hour. The sample does not give sufficient evidence that the manufacturer is correct.

50. In your own words, distinguish between “statistical” and “practical” significance.

ANSWER: If observing a difference between a sample and a null hypothesis is unlikely to happen by chance alone, the results are called statistically significant. If the difference is enough to justify a different decision that would be the case were the hypothesis true, the results are called practically significant.

51. Which of the following best describes a situation in which the results of a hypothesis test conclude rejection of the null hypothesis and whether or not such a situation would necessarily justify a different decision?

I. II. III.

Statistically significant different; necessarily justifies a different decision Practically significant different; necessarily justifies a different decision Statistically significant different; does not necessarily justify a different decision

a. I only b. II only c. III only d. Neither I nor II nor III ANSWER: c 52. Researchers conducting a particular study wanted to determine if the weight loss in kilograms for obese patients on a particular diet and exercise program was more than 5 kg. Patients were assigned randomly to each group and a hypothesis test was conducted where: The mean weight loss for the study participants was 5.02 kg which, given the chosen significance level, number of participants (n), and sample standard deviation meant that the null hypothesis was rejected.

From a practical health standpoint, the difference between a 5.00 kg weight loss and a 5.02 kg weight loss is inconsequential.

Which of the following best describes the significance of the study results? a. Practical, but not significant b. Significant, but not practical c. Significant and Practical d. Neither significant nor practical ANSWER: b 53. Suppose you need to create a confidence interval to estimate the mean of a population. You know that your population is very skewed. Which of the following approaches is appropriate?

I. II.

Use a large-sample confidence interval provided that your sample size is greater than or equal to 30.

Use a bootstrapping confidence interval estimate regardless of your sample size

a. I only b. II only c. Either I or II d. Neither I nor II ANSWER: c

Name:

Class:

Date:

Chapter 12 - Population Mean 54. Which of the following are reasons you would choose to use a bootstrap confidence interval rather than a large-sample confidence interval to estimate a population mean? a. Your population is not approximately normal and your sample size is too small. b. Your sample standard deviation is large c. You have too many degrees of freedom d. You don’t know the population standard deviation.

ANSWER: a 55. Researchers studied how much time people spend in the reading room of the city’s library. They determined that the mean time spent by readers in the reading room of the library for a representative sample of 8 readers was 84.125 minutes.

The original sample data values are:

Select the most appropriate 95% bootstrap confidence interval for a population mean time spent by readers in the reading room of the library and provide an interpretation of your results. a. The bootstrap confidence interval is (71.25, 96.75). You can be 95% confident that the population mean time spent in the reading room is between 71.25 and 96.75 minutes. b. The bootstrap confidence interval is (74.50, 93.75). You can be 95% confident that the population mean time spent in the reading room is between 74.50 and 93.75 minutes. c. The bootstrap confidence interval is (65.55, 102.95). You can be 95% confident that the population mean time spent in the reading room is between 65.55 and 102.95 minutes. d. The bootstrap confidence interval is (77.63, 90.50). You can be 95% confident that the population mean time spent in the reading room is between 71.25 and 96.75 minutes.

ANSWER: a 56. Suppose that you need to conduct a hypothesis test regarding the mean of a population. You know that your population is very skewed. Which of the following approaches is appropriate?

I. II.

Use a one-sample t test provided that your sample size is greater than or equal to 30.

Use a randomization-based test method regardless of your sample size

a. I only b. II only c. Either I or II d. Neither I nor II ANSWER: c 57. Which of the following are reasons you would choose to use a randomization-based test rather than a one-sample t test to evaluate a hypothesis regarding a population mean? a. Your population is not approximately normal and your sample size is too small. b. Your sample standard deviation is large. c. You have too many degrees of freedom. d. You don’t know the population standard deviation.

ANSWER: a

Name:

Class:

Date:

Chapter 12 - Population Mean 58. Researchers studied how many steps a day adult residents of the city make. They determined that the mean number of steps per day for a representative sample of 10 adult residents of the city was 5,139 steps. The original data values are shown in the table below:

Researchers are interested in deciding if there is evidence that adult residents of the city make more than 5,000 steps per day. Use a randomization test to select the appropriate output for one set of 1,000 simulated sample means and carry out a hypothesis test for a population mean. a.

b.

c.

Name:

Chapter 12 - Population Mean

d.

ANSWER: a

Class:

Date:

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means 1. Suppose you plan to take two samples from a population. If, in selecting individuals for sample #1, you don’t affect the selection of individuals for sample #2, which of the following describes your samples?

I. II. III.

Paired samples Random samples Independent samples

a. I only b. II only c. III only d. Neither I nor II nor III ANSWER: c 2. Suppose you’re taking random samples from two different populations. Which of the following best describes your samples?

I. II. III.

Representative Independent Paired

a. I only b. II only c. III only d. Neither I nor II nor III ANSWER: b 3. Suppose you plan to take two samples from one or more populations. It is important that observations from the first sample be matched up in some meaningful way with observations from the second sample. Which of the following best describes your samples?

I. II. III.

Paired samples Random samples Independent samples

a. I only b. II only c. III only d. Neither I nor II nor III ANSWER: a 4. Suppose a researcher is collecting data to compare the average amount of soda consumed daily by men and women.

The researcher will ask participants to state the amount of soda they consumed on the previous day. The researcher would like to determine if differences exist in the amount of soda consumed by men vs. by women. Should the researcher use a procedure for two independent samples or paired data?

ANSWER: The two groups are independent, therefore the procedure for independent samples should be used.

5. Which of the following are strategies for using paired data to rule out confounding effects?

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means I) Record measurements (samples) of the same individuals before and following an event of interest.

II) Construct study pairs from naturally occurring pairs such as twins.

III) Construct study pairs from pairs of individuals with a shared environment such as married couples or roommates.

IV) Select pairs where both individuals in the pair share a characteristic that might otherwise obscure the effect being studied between two populations. a. I and II only b. I, II, and III only c. I, II, III, and IV d. II, III, and IV only ANSWER: c 6. Suppose you conduct observations of samples from two populations assuming that the samples are independent. You apply an analysis method and reach a conclusion. If you later learned that your samples were paired, which of the following actions should you take? a. None, since the analysis methods for paired and unpaired data are the same b. Repeat your analysis using a method based on paired samples only if your analysis involved confidence intervals. c. Repeat your analysis using a method based on paired samples only if your analysis involved hypothesis testing. d. None of these ANSWER: d 7. An article describes a study on the effectiveness of a fabric device that acts as a support stocking for a weak or damaged human heart. In the study, 94 people who consented to treatment were assigned at random to either a standard treatment (S) consisting of drugs or to an experimental treatment € that consisted of drugs plus surgery to install the stocking. After two years, 36% of the 61 patients receiving the stocking had improved, while 23% of the patients receiving the standard treatment had improved. Which of the following hypotheses should be tested to determine whether the proportion of patients who improve is significantly higher for the experimental treatment than for the standard treatment? a. H0: PE PS < 0 versus Ha: PE PS > 0 b. H0: PE

PS = 0 versus Ha: PE

PS > 0

c. H0: PE

PS = 0 versus Ha: PE

PS < 0

d. H0: PE

PS = 0 versus Ha: PE

PS ≠ 0

ANSWER: b 8. When a surgeon repairs injuries, sutures (stitched knots) are sometimes used to hold together and stabilize the injured tissues. If these knots elongate and loosen, the injury may not heal properly. Researchers at the University of California, San Francisco, tied a particular type of knot with two types of suture material, material A and material B. Suppose that 112 tissue specimens were available and that each specimen and type of suture material were randomly assigned. The investigator tested the knots to see how much they elongated. For purposes of this exercise, you can assume that it is reasonable to regard the elongation distributions as approximately normal. Which of the following hypotheses should be tested to determine if there is a significant difference in mean elongation between the two thread materials? a. H0: μA μB < 0 versus Ha: μA μB > 0 b. H0: μA

μB = 0 versus Ha: μA

μB ≠ 0

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means c. H0: μA

μB = 0 versus Ha: μA

μB > 0

d. H0: μA

μB = 0 versus Ha: μA

μB < 0

ANSWER: b 9. In weight-bearing joints such as knees, damage to articular cartilage and subchondral bone can be difficult to heal and frequently lead to the need for a joint prosthesis. Recently, both surgical and injection-based methods have been developed to treat articular cartilage lesions using a patient’s bone marrow aspirates. Both the surgical and injection-based methods rely on the same fundamental mechanism to accomplish cartilage repair, but each method has different advantages from the standpoint of versatility and invasiveness. Researchers investigated the effectiveness of surgical vs. injection-based bone marrow aspirate delivery for the repair of knee articular cartilage lesions. For the study, 200 patients were recruited and randomly assigned to either an injection treatment group or a surgical treatment group. Following treatment and appropriate recovery periods, patients were evaluated with imaging to determine the quality of repaired cartilage which is rated on a scale of 0 to 100. For the purpose of this exercise, you can assume that it is reasonable to regard the repair cartilage quality score distributions as approximately normal. Which of the following hypotheses should be tested to determine if there is a significant difference in repair cartilage quality for the surgical vs. injection groups?

The I subscript in the following hypotheses tests refers to injection treatment while the S subscript refers to surgical treatment. a. H0: μI μS < 0 versus Ha: μI μS > 0 b. H0: μI

μS = 0 versus Ha: μI

μS > 0

c. H0: μI

μS = 0 versus Ha: μI

μS ≠ 0

d. H0: μI

μS = 0 versus Ha: μI

μS < 0

ANSWER: c 10. In a recent paper, the authors distinguished between spending money on experiences (such as travel) and spending money on material possessions (such as a car). In an experiment to determine if the type of purchase affects how happy people are after the purchase has been made, 155 college students were randomly assigned to one of two groups. The students in the “experiential” group were asked to recall a time when they spent about $250 on an experience. They rated this purchase on three different happiness scales that were then combined into an overall measure of happiness. The students assigned to the “material” group recalled a time that they spent about $250 on an object and rated this purchase in the same manner. The mean happiness score was 5.62 for the experiential group and 5.44 for the material group. Which of the following hypotheses should be tested to determine whether the authors’ conclusion that, on average, “experiential purchases induced more reported happiness”? The E subscript in the following hypotheses tests refers to experiential while the P subscript refers to object purchases. a. H0: μE μP < 0 versus Ha: μE μP > 0 b. H0: μE

μP = 0 versus Ha: μE

μP > 0

c. H0: μE

μP = 0 versus Ha: μE

μP ≠ 0

d. H0: μE

μP < 0 versus Ha: μE

μP > 0

ANSWER: b 11. Chefs from a group of restaurants in a small city collaborated in a study to determine the proportion of customers who expressed higher satisfaction with a meal if the ingredients for that meal were fresh and locally produced. The chefs conducted a study in which 120 customers who ordered the daily lunch special were randomly assigned to receive a meal prepared from local vs. imported ingredients. Preparation methods and seasonings for each meal (local vs. imported ingredients) were the same. After the meal, customers gave a satisfaction rating of 1 through 5. Satisfaction ratings for the local-ingredient meals were averaged and found to be 4.26. Satisfaction ratings for the imported-ingredient meals were averaged and found to be 3.41. Which of the following hypotheses should be tested to determine whether the chefs’

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means conclusion that, on average, “customers were more satisfied with meals prepared using local ingredients than meals prepared with imported ingredients”? The L subscript in the following hypotheses tests refers to meals prepared with local ingredients while the I subscript refers to meals prepared with imported ingredients. a. H0: μL μI < 0 versus Ha: μL μI > 0 b. H0: μL

μI = 0 versus Ha: μL

μI > 0

c. H0: μL

μI = 0 versus Ha: μL

μI < 0

d. H0: μL

μI = 0 versus Ha: μL

μI ≠ 0

ANSWER: b 12. Which of the following are conditions for using the paired-samples t-test?

I) The population distribution of sample differences is normal or the number of sample differences is large II) The samples are independent III) The n sample differences can be viewed as random samples from a population of sample differences a. I and III only b. I and II only c. II and III only d. I, II, and III ANSWER: a 13. You’re conducting hypothesis testing using sample data with one numerical variable and two paired samples. Which of the following conditions would permit you to use the paired-samples t-test?

I) The number of sample differences is large (n 30) II) The n sample differences in your study can be viewed as a random sample from a population of differences III) The population distribution of the sample differences is approximately normal IV) It is reasonable to regard the sample of differences as representative of population differences a. I and II only b. III and IV only c. I, II, and III only d. Either I and II or III and IV ANSWER: d 14.

are always equal.

a. True b. False ANSWER: True 15. Which of the following are conditions for using the paired-samples t-Confidence Interval to estimate a difference in population means?

I) The population distribution of sample differences is normal or the number of sample differences is large II) The samples are independent III) The n sample differences can be viewed as random samples from a population of sample differences a. I and III only b. I and II only

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means c. II and III only d. I, II, and III ANSWER: a 16. You’re estimating the difference in population means using sample data with one numerical variable and two paired samples. Which of the following conditions would permit you to use the paired-samples t-Confidence Interval?

I) The number of sample differences is large (n ≥ 30) II) The n-sample differences in your study can be viewed as a random sample from a population of differences III) The population distribution of the sample differences is approximately normal IV) It is reasonable to regard the sample of differences as representative of population differences a. I and II only b. III and IV only c. I, II, and III only d. Either I and II or III and IV ANSWER: d 17. Body fat and lean body mass can be estimated in living animals by measuring the total body electrical conductivity (TOBEC). Evaluation of diet drugs is often conducted on rats, with the use of the TOBEC method to measure the effectiveness of the diet drugs on body fat content. One problem frequently encountered in testing with rats is that some test subject rats are so big that their tails must be tucked under their bodies for the rats to be placed in the measurement chamber. This problem is causing concern among the researchers because there is a possibility that the tail position might alter measurements. To see if the TOBEC measurement is altered by tail position, an experiment was run on 16 rats ranging in weight from 210 to 505 grams. The rats were measured first in the tail-under position, then in the tail-extended position. The data for the lean mass measures, and the differences, are presented below:

Test the hypothesis that there is no difference between the population mean TOBEC measurements of rats in the tailunder vs. tail-extended positions. Assume that these rats are a random sample of laboratory rats. Write a short paragraph based on your analysis explaining your results. Assume α = 0.05.

ANSWER: The first step is expressing in writing the hypothesis, where µd is the population mean of the difference in TOBEC measurements for the two tail positions.

H0: μd = 0 versus Ha: μd ≠ 0 The second step is selecting a method appropriate for a hypothesis test using sample data involving one numerical variable and two paired samples. The appropriate method is the paired-sample t-test.

The third step is checking that the requirements for the paired-sample t-test have been met in this case. The sample is random, but since it is small (n = 16), the sample data should be plotted to see if they are approximately normal, thereby indicating that the population is also approximately normal.

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means

The plot shows reasonable symmetry, consistent with a normal distribution.

The fourth step is calculation of a test-statistic and P-value and comparison to the significance level:

Since the P-value is less than 0.05, the null hypothesis is rejected. The tail position does make a difference in rat body fat measurement using the TOBEC method.

18. The number of degrees of freedom of the paired t test statistic is equal to the number of sample pairs minus one. a. True b. False ANSWER: True 19. The State Test of Basic Skills is a collection of various achievement tests given to students in grades 1 – 8. Student achievement levels are reported on a scale that runs from 0 to 13. The schools in one particular community are evaluating their reading program for students whose native language is not English. In one part of the study the reading comprehension of 10 students, randomly selected from a large population of students in the program, take the Reading Comprehension test in the 3rd and 4th grades. Their scores for each year, in grade equivalents, are listed below:

“Normal” growth, by definition, is a change of 1.0. Using the data above, test the hypothesis that the difference in means for 3rd and 4th grade students in this program for non-native English speakers is equal to 1.0. Assume α = 0.05.

ANSWER: The first step is expressing in writing the hypothesis, where µd is the population mean of the difference in TOBEC measurements for the two tail positions.

H0: μd = 1 versus Ha: μd ≠ 1 The second step is selecting a method appropriate for a hypothesis test using sample data involving one numerical variable and two paired samples. The appropriate method is the paired-sample t-test.

The third step is checking that the requirements for the paired-sample t-test have been met in this case. The sample is random, but since it is small (n = 10), the sample data should be plotted to see if they are approximately normal, thereby indicating that the population is also approximately normal.

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means The plot shows reasonable symmetry, consistent with a normal distribution.

The fourth step is calculation of a test-statistic and P-value and comparison to the significance level:

Since the P-value is less than 0.05, the null hypothesis is rejected. There is evidence that the mean gain in reading comprehension between the 3rd and 4th grades is not equal to 1.

20. A map publishing company is interested in the effectiveness of a new contour display method in the time needed for map readers to identify elevations at particular points of interest. The company’s researchers conducted a study in which 40 randomly selected map users identified points of interest first without and later with the new contour display. The time needed to find the points of interest were recorded and the difference in the time needed to find each point of interest with and without the new contour display was calculated for each person. Test results are summarized below: • •

Sample size n = 40 Mean of the sample differences for (time to locate points of interest without the new contour display) minus (time to locate points of interest with the new contour display) =

•

Standard deviation of the sample differences =

seconds

seconds

The researchers wanted to know if the time to locate a point of interest without the new contour display was greater than the time with the new contour display. Assume α = 0.05.

Which of the following are the appropriate P value and conclusion? a. P(t > 3.16) = 0.002, null hypothesis rejected, there is convincing evidence that the time to identify a point of interest without the new contour display is greater than the time to identify a point of interest with the new contour display. b. P(t > 1.88) = 0.032, null hypothesis rejected, there is convincing evidence that the time to identify a point of interest without the new contour display is greater than the time to identify a point of interest with the new contour display. c. P(t < 3.16) = 0.001, fail to reject the null hypothesis, there is no convincing evidence that the time to identify a point of interest without the new contour display is greater than the time to identify a point of interest with the new contour display. d. P(t > 0.92) = 0.187, fail to reject the null hypothesis, there is no convincing evidence that the time to identify a point of interest without the new contour display is greater than the time to identify a point of interest with the new contour display.

ANSWER: a 21. A group of researchers investigated the role of natural daylight exposure on sleep quality for 49 randomly selected individuals. For two weeks, the participants refrained from the use of any artificial lighting and used natural daylight for all of their task lighting needs. Sleep-related hormone levels were measured at the start and end of the test. The researchers believe that if sleep hormone levels decreased as a result of the natural daylight regimen, there was evidence that natural daylight improved sleep quality. The following sample statistics were reported for the difference in sleep hormone levels (before minus after): n= 49 Which of the following are the appropriate P value and conclusion? Assume α = 0.05. a. P(t < -1.51) = 0.070, null hypothesis rejected, there is convincing evidence that the sleep hormone levels decreased as a result of the natural daylight regimen, confirming the researchers’ hypothesis that natural

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means daylight improved sleep quality. b. P(t < -0.51) = 0.310, null hypothesis rejected, there is convincing evidence that the sleep hormone levels decreased as a result of the natural daylight regimen, confirming the researchers’ hypothesis that natural daylight improved sleep quality. c. P(t < -0.51) = 0.310, fail to reject the null hypothesis, there is no convincing evidence that the sleep hormone levels decreased as a result of the natural daylight regimen, the researchers’ hypothesis that natural daylight improved sleep quality is not confirmed. d. P(t < -1.51) = 0.70, fail to reject the null hypothesis, there is no convincing evidence that the sleep hormone levels decreased as a result of the natural daylight regimen, the researchers’ hypothesis that natural daylight improved sleep quality is not confirmed.

ANSWER: d 22. Viruses are infectious agents that often cause diseases in plants. Different viruses have different potency levels, and this fact can be used to detect whether a new virus is infecting plants in the field. In a potency comparison experiment, two viruses were placed on a tobacco leaf of 10 randomly selected tobacco plants in a field. The viruses were randomly assigned to one-half of each of the leaves. The table below presents the potency of the viruses, as measured by the number of lesions appearing on the leaf half. For this problem, you can assume that the population distribution of difference is approximately normal.

Test the hypothesis that there is no difference in the mean number of lesions for Virus X and Virus Y. Assume α = 0.05.

ANSWER: The first step is expressing in writing the hypothesis, where µd is the mean difference in the number of lesions for virus X – virus Y. H0: μd = 0 versus Ha: μd ≠ 0 The second step is selecting a method appropriate for a hypothesis test using sample data involving one numerical variable and two paired samples. The appropriate method is the paired-sample t-test.

The third step is checking that the requirements for the paired-sample t-test have been met in this case. The sample is random, but since it is small (n = 10), we rely on the fact that we know that we can assume that population distribution of difference is approximately normal.

The fourth step is calculation of a test-statistic and P-value and comparison to the significance level:

Since the P-value is less than 0.05, the null hypothesis is rejected. There is evidence that the mean number of lesions for Virus X is less than the number of lesions for Virus Y. 23. In 1992 Hurricane Andrew struck Florida causing widespread devastation. Since the eye of the hurricane passed directly over a site where scientists were studying the ecology of white-tailed deer, investigators felt that the home ranges of the deer would change, but were unsure of the direction of change. Home ranges of animals usually do not change much unless an area is under ecological stress.

The home range data for a random sample of 18 white-tailed radio-collared deer are shown in the table below. The raw area of the home range for each of the deer is reported in hectares for the pre-hurricane year of 1992 and post hurricane year of 1993.

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means

(a) Use graphical displays of your choice, show that the assumptions necessary for determining any change in the mean home ranges are plausible. (b) Construct a 95% confidence interval for the difference in means of the home ranges from before Andrew to after Andrew. (c) Do the data provide evidence of a change in the size of the home ranges after Hurricane Andrew? Provide statistical justification for your response.

ANSWER: There is no information that the deer with the collars are a random sample of the deer population, so this must be assumed. With n = 18, we need to find evidence that the distribution of changes in the home range are normally distributed. The histogram below shows reasonable symmetry, suggesting that a normal distribution can be assumed.

Confidence interval: This data does not provide evidence that there was a change in the size of the home range for the deer after Hurricane Andrew. The confidence interval calculated includes 0, so it is reasonable to believe that the hurricane made no difference.

24. Energy efficiency researchers conducted a study in which 50 randomly selected single-family dwelling occupants rated their winter comfort level before and following the installation of floor insulation. The comfort rating scale goes from 0 to 100 with 100 being the most comfortable. The mean and standard deviation of the difference in comfort rating after insulation minus the comfort rating before insulation are: μd = 28, sd = 33 Which of the following is the 95% confidence interval for the difference in comfort rating from before to after insulation installation? a. Confidence Interval (18.6, 37.4) you can be 95% confident that the actual difference between the winter comfort rating of dwellings before vs. after insulation installation is somewhere between 18.6 and 37.4.

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means b. Confidence Interval (9.3, 17.9) you can be 95% confident that the actual difference between the winter comfort rating of dwellings before vs. after insulation installation is somewhere between 9.3 and 17.9. c. Confidence Interval (-3.96, 4.58) since the confidence interval includes zero, there may be no difference between winter comfort ratings before vs. after insulation installation. d. Confidence Interval (-37.4, -18.6) you can be 95% confident that the actual difference between the winter comfort rating of dwellings before vs. after insulation installation is somewhere between -37.4 and -18.6.

ANSWER: a 25. Student volunteers conducted a study in which 60 randomly selected incoming freshmen were given an intensive weekend mathematics course partway through their first academic term and asked to rate their personal perception of readiness for their technical courses before and following the weekend course. Ratings were on a scale of 0 to 20 with twenty representing a high degree of readiness. The mean and standard deviation of the difference in readiness scores after the weekend course vs. before the weekend course are: μd = 9, sd = 15 Which of the following is the 99% confidence interval for the difference in comfort rating from before to after insulation installation? a. Confidence Interval (8.3., 12.2) you can be 99% confident that the actual difference in readiness scores before vs. after the weekend course is somewhere between 8.3 and 12.2. b. Confidence Interval (-3.8, -1.4) you can be 99% confident that the actual difference in readiness scores before vs. after the weekend course is somewhere between -3.8 and -1.4. c. Confidence Interval (3.8, 14.2) you can be 99% confident that the actual difference in readiness scores before vs. after the weekend course is somewhere between 3.8 and 14.2. d. Confidence Interval (-0.6, 2.7) because the confidence interval includes zero, there may be no difference between readiness scores before vs. after the weekend course.

ANSWER: c 26. A particular company is interested in reducing daily commutes for its workers. The company ran a study in which 40 randomly selected employees were offered a free pass for express mass transit services and asked to record their commute times before and following use of the express mass transit service. The mean and standard deviation for the difference in commute times (hours) before vs. after use of the express mass transit are: μd = 0.56, sd = 0.68.

Which of the following is a 95% confidence interval for the difference in commute times before vs. after use of the express mass transit? a. Confidence Interval (0.34, 0.78) You can be 95% confident that the actual difference in commute times before vs. after use of express mass transit was between 0.34 and 0.78. b. Confidence Interval (-0.07, 0.12) Because the confidence interval includes zero, there may be no difference in commute times before vs. after use of express mass transit. c. Confidence Interval (0.64, 0.78) You can be 95% confident that the actual difference in commute times before vs. after use of express mass transit was between 0.64 and 0.78. d. Confidence Interval (0.21, 0.83) You can be 95% confident that the actual difference in commute times before vs. after use of express mass transit was between 0.21 and 0.83.

ANSWER: a 27. Of the residents of a particular community who make regular use of air travel from an airport in a nearby city, 10 were randomly selected to participate in a study in which study participants were given a free pass on an intercity shuttle bus and asked to record their travel times before and following use of the shuttle bus. The mean and standard deviation for the difference in travel times (hours) before vs. after use of the shuttle bus are: μd = 1.8, sd = 1.3.

Which of the following is a 99% confidence interval for the difference in travel times before vs. after use of the shuttle bus?

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means a. Confidence Interval (0.46, 3.14) You can be 99% confident that the actual difference in travel times before vs. after use of the shuttle bus was between 0.46 and 3.14. b. Confidence Interval (-0.88, 1.45) Because the confidence interval includes zero, there may be no difference in travel times before vs. after use of the shuttle bus. c. Confidence Interval (1.20, 4.23) You can be 99% confident that the actual difference in travel times before vs. after use of the shuttle bus was between 1.20 and 4.23. d. Confidence Interval (0.76, 2.56) You can be 99% confident that the actual difference in travel time before vs. after use of the shuttle bus was between 0.76 and 2.56.

ANSWER: a 28. Traffic safety researchers investigated the time drivers needed to recognize a stop sign based on the design of the sign. They would like to know if there is a difference in recognition time for the new vs. old sign design. Which of the following hypotheses represents the researcher’s question? a. H0: μd = 0 versus Ha: μd < 0 b. H0: μd = 0 versus Ha: μd > 0 c. H0: μd = 0 versus Ha: μd ≠ 0 d. H0: μd ≠ 0 versus Ha: μd = 0 ANSWER: c 29. Suppose you’re the owner of a pastry shop and are interested in whether the sales of vanilla cream cake had exceeded the sales of dark chocolate cake. Which of the following hypothesis represents your question? For this question, µd represents the mean sales of vanilla cream cake minus the mean sales of dark chocolate cake. a. H0: μd = 0 versus Ha: μd < 0 b. H0: μd = 0 versus Ha: μd > 0 c. H0: μd = 0 versus Ha: μd ≠ 0 d. H0: μd ≠ 0 versus Ha: μd = 0 ANSWER: b 30. Recruiters for a community college are interested in whether a recent change in financial aid allocation has improved enrollment at the college. μbefore = the mean enrollment prior to the financial aid allocation change μafter = the mean enrollment after the financial aid allocation change μd = μafter μbefore Which of the following hypothesis represents the recruiters’ question? a. H0: μd = 0 versus Ha: μd < 0 b. H0: μd = 0 versus Ha: μd > 0 c. H0: μd = 0 versus Ha: μd ≠ 0 d. H0: μd ≠ 0 versus Ha: μd = 0 ANSWER: b 31. Suppose you’re planning a community vegetable garden and are interested in whether a new soil treatment will reduce the number of potato plants lost to root rot. If µd represents the difference in mean number of potato plants lost to root rot

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means without the soil treatment minus the mean number of potato plants lost to root rot after the soil treatment, which of the following hypotheses represents your question? a. H0: μd = 0 versus Ha: μd < 0 b. H0: μd = 0 versus Ha: μd > 0 c. H0: μd = 0 versus Ha: μd ≠ 0 d. H0: μd ≠ 0 versus Ha: μd = 0 ANSWER: b 32. City planners are interested in the effect of new state subsidies for electric vehicles on the air quality in areas of high traffic congestion. One planner states that they feel that pollution has decreased following the implementation of the subsidies. μbefore = the mean pollution level prior to subsidy implementation μafter = the mean pollution level after subsidy implementation μd = μafter μbefore Which of the following hypothesis represents the recruiters’ question? a. H0: μd = 0 versus Ha: μd < 0 b. H0: μd = 0 versus Ha: μd > 0 c. H0: μd = 0 versus Ha: μd ≠ 0 d. H0: μd ≠ 0 versus Ha: μd = 0 ANSWER: a 33. Instructors at a particular college feel that student engagement did not change with the resumption of onsite course offerings. Supposing student engagement is regularly assessed with a numerical score, which of the following hypotheses represents the instructors’ statement if µd is the difference in mean levels of student engagement before and following the resumption of onsite classes? a. H0: μd = 0 versus Ha: μd < 0 b. H0: μd = 0 versus Ha: μd > 0 c. H0: μd = 0 versus Ha: μd ≠ 0 d. H0: μd ≠ 0 versus Ha: μd = 0 ANSWER: c 34. Which of the following are conditions for use of a two-sample t test to determine a difference in population means?

I) The population distribution of sample differences is normal or the number of sample differences is large.

II) The samples are paired.

III) Each sample is a random sample from the population of interest. a. I and III only b. I and II only c. II and III only d. I, II, and III ANSWER: a 35. Which of the following are conditions for using a two-sample t test for determining a difference in population means?

I) The population distribution of sample differences is normal or the number of sample differences is large

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means II) The samples are independent III) Each sample is a random sample from the population of interest a. I and III only b. I and II only c. II and III only d. I, II, and III ANSWER: a, d 36. You’re conducting hypothesis testing using sample data with one numerical variable and two independent samples.

Which of the following conditions would permit you to use the two-sample t-test?

I) The number of sample differences is large (n ≥ 30).

II) Each sample is a random sample from the populations of interest..

III) The population distributions are approximately normal.

IV) The samples are independently selected in a way that would result in samples that are representative of the populations. a. I and II only b. III and IV only c. I, II, and III only d. Either I and II or III and IV ANSWER: d 37. Which of the following are conditions for using the two-sample t Confidence Interval to estimate a difference in population means?

I) The population distribution of sample differences is normal or the number of sample differences is large.

II) The samples are paired.

III) Each sample is a random sample from the population of interest. a. I and III only b. I and II only c. II and III only d. I, II, and III ANSWER: a 38. You’re estimating the difference in population means using sample data with one numerical variable and two independent samples. Which of the following conditions would permit you to use the two-sample t-Confidence Interval?

I) The number of sample differences is large (n ≥ 30).

II) Each sample is a random sample from the population of interest.

III) The population distributions are approximately normal.

IV) The samples are independently selected in a way that would result in samples that are representative of the populations. a. I and II only b. III and IV only c. I, II, and III only d. Either I and II or III and IV ANSWER: d 39. A software developer is interested in determining whether two random number generators have the same population mean. Random number generator A has a population standard deviation of 1.00 and random number generator B has a

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means population standard deviation of 1.25. The developer took a sample of 10 trials from each generator. The results are summarized below.

Find the P-value for the test of the difference between the population means for these two generators. a. 0.171 b. 0.169 c. 0.086 d. 0.095 ANSWER: a 40. The data below give the weights in ounces of randomly-selected bars of bath soap produced by two different molding machines.

The question of interest is whether these two molding machines produce soap bars of differing average weights. Find the P-value for this test assuming that weight distributions for soap bars produced by the two machines are approximately normal. a. 0.014 b. 0.311 c. 0.0388 d. 0.054 ANSWER: a 41. Researchers have hypothesized that female Downy Woodpeckers avoid the feeding areas of socially dominant males; that is, the males chase them away from prime spots. An alternative opinion is that there are important physical characteristics of males and females that might lead them to choose different foraging locations. One such characteristic could be the bill length of the males and females; it may be that the longer bills let one gender or the other drill deeper into a tree and thus get more food per tree. The data in the table below are the bill lengths (cm) of 12 male and 12 female randomly selected Downy Woodpeckers caught and released in a banding survey. The investigators would like to know whether these data provide evidence that the males and females differ in bill size.

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means

Is there sufficient evidence to conclude that there is a difference in mean bill lengths for males and females? Support your conclusions with statistical analysis and appropriate interpretation of analysis results. Assume α = 0.05.

ANSWER: First, state the hypothesis where µm = population mean for male bill lengths and µf = population mean for female bill lengths: H0: μm μf = 0 versus Ha: μm μf ≠ 0 Second, select the two-sample t test for a difference in population means based on the fact that the scenario involves hypothesis testing, sample data, one numerical variable, and two independently selected samples.

Third, given that the sample size is not large, ensure that population distributions for both males and females are approximately normal. The sample boxplots below show reasonably symmetric distributions, suggesting normal population distributions.

Fourth, calculate the test statistic

Since the P-value is more than α = 0.05, fail to reject the null hypothesis. There is not enough evidence to say that the bills of males are larger than those of females.

42. Researchers hypothesize that anatomical features are different for male and female foraging animals. The results of a study of beak width of males and females of a particular bird species are summarized in the table below. For this question, assume that study subjects were randomly selected and that the male and female beak width populations are approximately normal.

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means

Test the hypothesis the male beaks are wider than female beaks with α = 0.05.

ANSWER: First, state the hypothesis where μm = population mean for male bill widths and μf = population mean for female bill widths: H0: μm μf = 0 versus Ha: μm μf > 0 Second, select the two-sample t test for a difference in population means based on the fact that the scenario involves hypothesis testing, sample data, one numerical variable, and two independently selected samples.

Third, given that the sample size is not large, it is important that we have been told that population distributions for both males and females are approximately normal.

Fourth, calculate the test statistic

Since the P-value is more than α = 0.05, fail to reject the null hypothesis. There is not enough evidence to say that the bills of males are wider than those of females.

43. Researchers conjecture that the anatomical features of male and female foraging animals are different. The results of a study of beak width of males and females of a particular bird species are summarized in the table below. For the purpose of this question, assume that study subjects were randomly selected and that the male and female beak width populations are approximately normal.

Construct a 95% confidence interval for the difference in bill widths for males vs. females and answer the question of whether the bill widths differ with statistical justification.

ANSWER: The 95% CI for the difference in bill width is, with approximate df = 16.97 (rounded down to 16 in the table):

Confidence Interval = (-0.036, 0.116). Since the confidence interval includes zero, there is not enough evidence to say that the bill depths differ between males and females.

44. Samples from two independent, normally distributed populations produced the following results.

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means

Calculate the 95% confidence interval for the difference between the mean of population 1 and the mean of population 2. a. (-9.65, 15.65) b. (-8.26, 14.86) c. (-10.10, 16.74) d. (-0.55, 2.54) ANSWER: a 45. The data below give the weights in ounces of randomly-selected bars of bath soap produced by two different molding machines.

Weight (ounces) Machine 1 11.4 12.4 12.1 11.8 11.7 12.3 12.0 11.8 Machine 2 13.0 12.4 12.4 12.3 12.1 12.5 12.0 12.1 The question of interest is whether these two molding machines produce soap bars of differing weight. Find a 95% confidence interval for the population difference assuming that the weights for the two machines are approximately normal. a. (-1.760, -0.091) b. (-1.200, -0.464) c. (-0.354, 0.173) d. (-1.280, -0.384) ANSWER: d 46. Suppose that you wish to compare two treatments for preventing baldness in men. In some circumstances, you may be able to randomly assign the treatments to the men, and in some circumstances, you may not be able to randomly assign the treatments to the men. Respond to the following questions in a few sentences. a) If you are testing the hypothesis that the means are equal for the populations, how would your statistical procedures differ, if at all, depending on whether you randomly assigned subjects to treatments or whether you merely observed differences in men who chose one treatment or the other? b) How would your interpretation of the results differ, if at all, depending on whether you randomly assigned subjects to treatments or whether you merely observed differences in men who chose one treatment or the other?

ANSWER: a) The procedures for testing if the means are different for the two treatments would not differ. In each case, a two-sample t-test would be used. b) The interpretation of the results would differ. If the subjects are randomly assigned to each of the treatments, then any significant differences can be attributed to the different effect of the treatment.

On the other hand, if the subjects have chosen the treatments, the difference might be due either to the treatments to some other unknown confounding variable, which affects the results.

47. When testing hypotheses involving treatment effects in an experiment, the conclusions of any inference test should be worded in terms of what quantities?

ANSWER: The conclusions to any inference test should be worded in terms of treatment effects, including treatment

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means means or treatment proportions.

48. The perception of danger is an important characteristic for survival of animals. In a field experiment in Cost Rica, investigators located and directly approached black iguanas. Two treatments were randomly assigned to the individual iguanas. In one treatment the investigator gazed at the iguana while approaching. In a second treatment, the investigator did not gaze at the iguana while approaching. The outcome measure was the distance of the investigator from the iguana when it decided to run away. The researchers believe that eye contact is noticed by the iguana, leading to a longer approach distance. Data for the approach distance (meters) at which the iguana first runs is given below:

Test the researcher’s hypothesis that there is a longer mean approach distance for the “Eye Contact” group with a significance level of 0.05.

ANSWER: Step One: Identify the hypothesis where µ1 = mean approach distance for the eye contact, µ2 = mean approach distance for the no eye contact H0:μ1 μ2 μ2 = 0 versus Ha: μ1 μ2 > 0 Step Two: Select the two-sample t procedure based on the fact that the scenario involves a hypothesis test based on experimental data with a single numerical variable and two independent samples.

Step Three: Since samples sizes are not large, it is necessary to plot the sample data to see if it shows reasonably normal behavior, suggesting that the two populations can be approximated as normal. . The boxplots below show a reasonably symmetric distribution, suggesting normality.

Step Four: Calculate the test statistic t = 0.27, and determine the P-value = 0.395 via calculator or >0.10 via table.

Step Five: Since the P-value is more than 0.05, fail to reject the null hypothesis. There is insufficient evidence to say that the approach distance is greater with eye contact.

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means 49. A common memory task is classification of objects into categories. Researchers studied this classification capability by randomly selecting subjects and randomly assigning them to one of two experimental conditions: divided attention and no divided attention. Students in the “divided attention” group were asked to memorize a list of 36 words while simultaneously listening to human speech. Students in the control group were asked to memorize a list of 36 words without listening to human speech. Each student was then asked to classify the 36 words into 6 categories. The distributions of the correct number of recalled words/category were approximately normal in each of the groups, and a summary of the data for the words/category recalled are presented below:

Is there evidence that the memory performance differs in the two groups? Test the hypothesis using a significance level of 0.05.

ANSWER: Hypothesis: μ1 = the mean number of classifications per category for the divided attention group; μ2 = the mean number of classifications per category for the control group.

H0: μ1 μ2 = 0 versus Ha: μ1 μ2 ≠ 0 Participants were randomly divided into the treatment and control group. The distribution responses of both groups were approximately normal, so the test statistic should have approximately a t-distribution.

P-value < 0.001 (via table) Since the P-value is less than 0.005, reject the null hypothesis. There is evidence that the mean number of classifications per category is different in the treatment group that listens to human speech.

50. Suppose a researcher is testing a new diet drug. She would like to determine if the drug helps to significantly increase weight loss versus a placebo. She randomly assigns 40 participants to the treatment group and 35 to the placebo group.

After 4 weeks on identical diets, the mean weight loss (in pounds) for each group is computed. Results of the study are as follows: Treatment Group: n = 40, sample mean = 5.6, sample standard deviation = 2.85 Placebo Group: n = 35, sample mean = 1.6, sample standard deviation = 1.47 Perform a hypothesis test to draw a conclusion from this study.

ANSWER: Step One: express the hypothesis H0: μtreat - μplacebo = 0 versus Ha: μtreat - μplacebo > 0 Assuming that conditions for a t-test are met, the test statistic is:

Calculate the degrees of freedom for the t-distribution:

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means

The P-value for the -statistic and degrees of freedom is less than 0.0001, so we would reject the null hypothesis. There is evidence that the treatment mean weight loss for the treatment group is significantly higher than that of the placebo group.

51. When creating a confidence interval involving treatment proportions in an experiment, the interpretation of the confidence interval estimate should be worded in terms of what quantities?

ANSWER: The interpretation should refer to treatment proportions 52. Suppose a researcher is testing a new diet drug. She would like to determine if the drug helps to significantly increase weight loss versus a placebo. She randomly assigns 40 participants to the treatment group and 35 to the placebo group.

After 4 weeks on identical diets, the mean weight loss (in pounds) for each group is computed. Results of the study are as follows: Treatment Group: n = 40, sample mean = 5.6, sample standard deviation = 2.85 Placebo Group: n = 35, sample mean = 1.6, sample standard deviation = 1.47 Create a 95% confidence interval for the difference in treatment effects.

ANSWER: The degrees of freedom for this confidence interval are given by:

The confidence interval is given by:

Therefore, we are 95% confident that the true value of the difference in treatment means is between 2.97 and 5.03.

53. When estimating the difference between two treatment effects, the format of the confidence interval is different from that used to estimate the difference between two population means.

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means a. True b. False ANSWER: False 54. A recent paper described an experiment in which 72 students at a university were assigned at random to one of two groups. All students took a class from the same instructor in the same semester. Students were required to report to an assigned room at a set time to fill out a course evaluation. One group of students reported to a room where they were offered a small bar of chocolate as they entered. The other group reported to a different room where they were not offered chocolate. Summary statistics for the overall course evaluation scores are given in the table below: Group n s Chocolate 36 3.93 0.78 No Chocolate 36 3.69 0.95 A 95% confidence interval for the mean difference in overall course evaluation score is: a. 0.24 ±0.39 b. 0.24 ±0.34 c. 0.24 ±0.41 d. 0.24 ±0.66 ANSWER: c 55. A study is conducted to determine the effect of different doses of a cold medication on reaction times. In a study of 20 participants between 20 and 25 years of age, half were given a single dose of medication and the other half were given two doses. Thirty minutes after dosing, a simple mechanical experiment measured the subject reaction time in milliseconds. The results are summarized in the table below:

Calculate the 95% confidence interval for the difference in reaction times for these two groups. Assume that the reaction times are normally distributed and that the treatments were randomly assigned. a. (-351, 12) b. (-326, -14) c. (-385, 46) d. (-201, -28) ANSWER: b 56. Which of the following are conditions for use of the bootstrap confidence interval for calculation of differences in treatment or population means?

I. II. III.

Samples are conveniently selected from their respective populations.

Sample sizes are large.

Populations can be considered approximately normal. a. I only b. II only

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means c. III only d. Neither I nor II nor III ANSWER: d 57. Under which of the following conditions would you choose to use the bootstrap confidence interval rather than a tConfidence Interval?

I. II. III.

Large sample size Populations can be considered approximately normal Small sample size

a. I only b. II only c. III only d. Neither I nor II nor III ANSWER: c 58. For which types of samples can a bootstrap confidence interval be used to determine a difference in means? a. Paired samples only b. Independent samples only c. Either paired or independent samples d. Bootstrap confidence intervals can only be used for categorical variables ANSWER: c 59. Suppose that 9 adult smokers were randomly selected. Researchers want to check whether the educational movies about the dangers of smoking affect the number of cigarettes adults smoke. The number of cigarettes per day before and after watching the movie was recorded for each smoker from the sample and resulting data are given in the table below:

Select the most appropriate 95% bootstrap confidence interval for a difference in the mean number of cigarettes per day before and after watching the movie for adult smokers and its correct interpretation. a. The bootstrap confidence interval is (-2.000, 7.000). You can be 95% confident that the actual difference in the mean number of cigarettes per day before and after watching the movie is between -2.000 and 7.000. b. The bootstrap confidence interval is (0.222, 3.000). You can be 95% confident that the actual difference in the mean number of cigarettes per day before and after watching the movie is between -0.222 and 3.000. c. The bootstrap confidence interval is (10.889, 17.333). You can be 95% confident that the actual difference in the mean number of cigarettes per day before and after watching the movie is between -10.889 and 17.33.

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means d. The bootstrap confidence interval is (0.000, 3.333). You can be 95% confident that the actual difference in the mean number of cigarettes per day before and after watching the movie is between 0.000 and 3.333.

ANSWER: d 60. Which of the following are conditions for use of a randomization test to test a hypothesis about a difference in treatment or population means?

I. II. III.

Samples are conveniently selected from their respective populations Sample sizes are large Populations can be considered approximately normal

a. I only b. II only c. III only d. Neither I nor II nor III ANSWER: d 61. Under which of the following conditions would you choose to use a randomization test rather than a paired or twosample t-test?

I. II. III.

Large sample size Populations can be considered approximately normal Small sample size

a. I only b. II only c. III only d. Neither I nor II nor III ANSWER: c 62. For which types of samples can a randomization test be used to test a hypothesis about a difference in means? a. Paired samples only b. Independent samples only c. Either paired or independent samples d. Randomization tests can only be used for categorical variables ANSWER: c 63. Researchers suggest that the time of a second race in karting is less than that of the first race since the person racing a second time remembers the track. Suppose 8 adults were randomly selected. The time spent on the first and second races was recorded for each person from the sample and resulting data are given in the accompanying table.

Name:

Class:

Date:

Chapter 13 - Difference Between Two Means

Do these data support the claim that the mean difference in time spent on the first and second races is greater than zero?

Use a randomization test to select the appropriate output for one set of 1000 simulated sample differences in means in means and carry out a hypothesis test for a difference in means. a.

Name:

Chapter 13 - Difference Between Two Means b.

c.

Class:

Date:

Name:

Chapter 13 - Difference Between Two Means d.

ANSWER: d

Class:

Date:

Name:

Class:

Date:

Chapter 14 - Learning from Categorical Data 1. Which of the following are key aspects of how a chi-square goodness-of-fit test can be used to answer a question of interest about a categorical variable?

I) The categorical variable has more than two categories.

II) The question of interest implies category proportion that can be used to form a null hypothesis.

III) The question of interest includes expected values for all category proportions. a. I and II only b. I and III only c. II and III only d. I, II, and III ANSWER: d 2. Which of the following best describes how the null hypothesis is determined as part of a chi-square goodness-of-fit test?

I. A question of interest is used to identify expected mean values for each category.

II. A question of interest is used to identify expected category proportions. a. I only b. II only c. Both I and II d. Neither I nor II ANSWER: b 3. As part of a chi-square goodness-of-fit test, which of the following comparisons are made?

I. Sample means to population means II. Sample means to sampling distribution means III. Observed category counts to expected category counts a. I only b. II only c. III only d. Neither I nor II nor III ANSWER: c 4. A chi-squared goodness-of-fit can be used to test hypotheses about the proportion of the population falling into each of the possible categories. a. True b. False ANSWER: True 5. Which of the following conditions would suggest that a chi-square goodness-of-fit would be appropriate for a given situation?

I) You need to test a hypothesis II) You have experimental data III) You have a single, numerical variable IV) You have a single, categorical variable a. I and II only b. I and IV only c. II, III, and IV only

Name:

Class:

Date:

Chapter 14 - Learning from Categorical Data d. III and IV only ANSWER: b 6. Which of the following conditions would suggest that a chi-square goodness-of-fit would NOT be appropriate for a given situation?

I) You need to perform an estimation II) You have experimental data III) You have a single, numerical variable IV) You have a single, categorical variable a. IV only b. I only c. II only d. I and IV only ANSWER: a 7. Which of the following conditions would suggest that a chi-square goodness-of-fit would be appropriate for a given situation?

I) You need to test a hypothesis II) You have sampling data III) You have a single, categorical variable IV) You have one sample a. I and II only b. II and III only c. I, II, and IV only d. I, II, III, and IV ANSWER: d 8. The chi-square goodness-of-fit test is used to test hypotheses regarding single categorical variables with multiple categories. Which of the following is true regarding the null hypothesis in these hypothesis tests?

I. It specifies a value for the proportion of the population falling into one of the categories for the categorical variable.

II. It specifies a value for the proportion of the population falling into one of the categories for the categorical variable.

III. It specifies the proportions of the population falling into each of the categories of interest associated with the categorical variable. a. I only b. II only c. III only d. Neither I nor II nor III ANSWER: c 9. Suppose a categorical variable had three categories. How many proportion values would the null hypothesis use in a chi-square goodness-of-fit test specify? a. One b. Three c. Four

Name:

Class:

Date:

Chapter 14 - Learning from Categorical Data d. Ten ANSWER: b 10. In order to decide whether the observed data is compatible with the null hypothesis, the observed cell counts are compared to the cell counts to the expected counts. a. True b. False ANSWER: False 11. The chi-square test statistic, X2, measures the extent to which the observed cell counts differ from those expected when H0 is true. a. True b. False ANSWER: True 12. For the chi-square, goodness-of-fit squared test, the associated P-value is the area under the appropriate chi-square curve to the left of the calculated value of X2. a. True b. False ANSWER: False 13. Which of the following are conditions for use of the chi-square goodness-of-fit test?

I) Observed counts must be based on a conveniently collected sample from the population of interest II) The sample size is sufficiently large that all expected counts are greater than 5 III) Observed counts must be taken from a sample that is representative of the population a. I only b. III only c. II only d. II and III only ANSWER: b, d 14. Which of the following are conditions for use of the chi-square goodness-of-fit test?

I) Observed counts must be based on a random sample from the population of interest II) The sample size is sufficiently large that all expected counts are greater than or equal to 5 III) Observed counts must be taken from a sample that is representative of the population a. II only b. I only c. II and III only d. Either I and II or II and III ANSWER: d 15. Suppose you have gathered a random sample of observed counts for a categorical variable with six categories. Which of the following are requirements for use of the chi-square goodness-of-fit for a hypothesis test involving this sample?

I. The expected counts for three or more of the categories are greater than 5 II. The expected counts for at least one category are less than or equal to 5 III. The expected counts for all categories are equal to or greater than 5

Name:

Class:

Date:

Chapter 14 - Learning from Categorical Data a. I only b. II only c. III only d. Neither I nor II nor III ANSWER: c 16. The observed and expected counts for customers who ordered each of three different types of ground beef sandwiches from a particular sandwich shop are shown below: • • •

Cheddar cheeseburger: Bacon lettuce burger: Salsa pepper burger

observed = 178 observed = 133 observed = 139

expected = 121 expected = 158 expected = 171

Calculate the test statistic and P-value for the chi-square test for the expected and observed counts of ground beef sandwiches. a. Test statistic = 26.8, P value < 0.001 b. Test statistic = 3.96, P value > 0.10 c. Test statistic = 5.98, P value = 0.053 d. Test statistic = 36.8, P value < 0.001 ANSWER: d 17. The observed and expected counts for customers who ordered each of four different types of hot beverages from a particular cafe are shown below: • • • •

expressor: green tear: mocha: late:

observed = 50 observed = 110 observed = 80 observed = 105

expected = 56 expected = 85 expected = 92 expected = 112

Calculate the test statistic and P-value for the chi-square test for the expected and observed counts of café beverages. a. Test statistic = 8.01, P value 0.045 b. Test statistic = 10.0, P value = 0.019 c. Test statistic = 5.88, P value >0.100 d. Test statistic = 16.67, P value <0.001 ANSWER: b 18. For a sample size n, there are n - 1 degrees of freedom associated with the goodness-of-fit test statistic, X2. a. True b. False ANSWER: False 19. What is the approximate P – value for X2 = 11.64 and df = 5? a. 0.095 b. 0.040 c. 0.020 d. 0.088

Name:

Class:

Date:

Chapter 14 - Learning from Categorical Data ANSWER: b 20. A random sample of 120 sixth-graders were asked to pick their preference from five different flavors of ice cream with results shown below:

A hypothesis test will be carried out to determine if there is evidence that the five flavors are not equally preferred. The test statistic will have a chi-square distribution with how many degrees of freedom? a. df = 3 b. df = 5 c. df = 4 d. df = 8 ANSWER: c 21. Each person in a random sample of 105 ice cream eaters was asked to “vote for” a preferred flavor from the flavors listed in the table below:

What is the value of the test statistic, and P-value for the hypothesis that, given these flavor choices, ice cream eaters have no flavor preference? For a significance of α = 0.05, what can we conclude regarding the flavor preferences of ice cream eaters? a. Test statistic = 4.67, P-value >0.100, fail to reject the null hypothesis, so conclude that ice cream eaters have no flavor preference b. Test statistic = 10.01, P-value 0.040, reject the null hypothesis, conclude that ice cream eaters have flavor preferences c. Test statistic = 8.02, P-value =0.090, fail to reject the null hypothesis, so conclude that ice cream eaters have no flavor preference d. Test statistic = 21.4, P-value <0.001, reject the null hypothesis, so conclude that ice cream eaters have flavor preferences ANSWER: a 22. Each person in a random sample of 54 students living in the dorms at a large university was asked whether they preferred to study in the dorm room, in the dorm’s study lounge, or at the university library. The resulting data is summarized in the table below:

Determine if there is evidence that the three locations are not equally preferred by students at the university who live in the dorm.

Assume α = 0.100 a. P-value > 0.100, fail to reject the null hypothesis, students do not have an equal preference regarding study locations b. P-value =0.080, reject the null hypothesis, students have an equal preference regarding study locations c. P-value = 0.045, fail to reject the null hypothesis, students do not have an equal preference regarding study locations d. P-value > 0.100, reject the null hypothesis, students have an equal preference regarding study locations

Name:

Class:

Date:

Chapter 14 - Learning from Categorical Data ANSWER: a 23. Each person in a random sample of university students was asked which of the five flavors of ice cream they preferred. The resulting data was used to test the null hypothesis H0: p1= 0.2, p2 = 0.2, p3 = 0.2, p4 = 0.2, p5 = 0.2 versus Ha: Ho is not true The P-value associated with this test was 0.067. If a significance level of 0.05 is used for the test, which of the following is an appropriate conclusion? a. Fail to reject H0, there is convincing evidence that there is no preference for one flavor of ice cream over another. b. Fail to reject H0, there is no convincing evidence that there is a preference for one flavor of ice cream over another. c. Reject H0, there is convincing evidence that there is no preference for one flavor of ice cream over another. d. Reject H0, there is convincing evidence that there is a preference for one flavor of ice cream over another.

ANSWER: b 24. Suppose that we are studying the purchasing behavior of individuals buying dog food. We hypothesize that half of the dog food purchases will be brand A, and the remaining purchases will be divided equally between two other brands B and C. a) Define appropriate statistical variables and use them to state the null and alternative hypothesis that would be used to decide if there was convincing evidence against the hypothesized distribution of purchases across the three brands. b) Suppose that each individual in a random sample of 200 purchasers provides information about his or her choice of brand. For each category, what are the expected values? c) How many degrees of freedom are associated with the chi-square goodness-of-fit statistic? d) Suppose that X2 = 6.10. What can be said about the P-value for this hypothesis test?

ANSWER: (a) p1 = population proportion of dog food purchasers who choose brand A P2 = population proportion of dog food purchasers who choose brand B P3 = population proportion of dog food purchasers who choose brand C (b) If 200 purchasers provide information, then the number of brand A purchasers = 100, number of brand B purchasers = 50, brand C purchasers = 50. (c) 2 degrees of freedom associated with the chi-square goodness-of-fit statistic (d) 0.045 < P < 0.050 25. In baseball, hits can be one of four types: singles, doubles, triples, or home runs. In the last baseball season, 64% of the hits were singles, 20% were doubles, 2% were triples, and 14% were home runs. Spring training games are played in March before the regular season to help the players get in shape. A sports writer thinks that perhaps the distribution of types of hits is different in these games. The sportswriter gathers a random sample of 251 hits from spring training games.

Here is the distribution of types of hits for these games: Singles = 153, Doubles = 59, Triples = 5, Home Runs = 34 At the 0.05 significance, test the hypothesis that the proportions of the different types of hits in the springs is the same as for the last baseball season.

ANSWER: First, define variables: P1 = population proportion of singles spring training hits P2 = population proportion of doubles spring training hits P3 = population proportion of triples spring training hits

Name:

Class:

Date:

Chapter 14 - Learning from Categorical Data P4 = population proportion of home run training hits Hypothesis: Second, check that conditions of chi-square goodness-of-fit are met: the sample is large (expected values for all categories >5), and a sample was randomly gathered (given in the problem statement).

Third, calculate the X2 test statistic:

The P-value for df =3 is > 0.10, so fail to reject the null hypothesis. We cannot conclude that the proportions of different types of hits in spring training are not the same as those from last year.

26. In a recent study of hot beverage preferences of faculty and staff at a university, 100 randomly selected individuals were each given a voucher to purchase the hot beverage of their choice from the university café. The number of individuals who chose each drink is summarized below: cream tea = 31, caffe latte = 22, cocoa = 42, expresso = 5 At the 0.05 significance, test the hypothesis that the proportions of faculty and staff preferring each of the four hot beverages is the same.

ANSWER: First, define variables: P1 = population proportion of individuals preferring cream tea P2 = population proportion of individuals preferring caffe latte P3 = population proportion of individuals preferring cocoa P4 = population proportion of individuals preferring expresso Hypothesis: Second, check that conditions of chi-square goodness-of-fit are met: the sample is large (expected values for all categories >5), and a sample was randomly gathered (given in the problem statement).

Third, calculate the X2 test statistic:

The P - value for df = 3 is < 0.001, so reject the null hypothesis. We conclude that the proportions of faculty and staff preferring each drink are not the same.

27. A local newspaper asked each person in a random sample of 44 subscribers which section of the paper he or she read first. The resulting data are shown in the table below.

A chi-square test is to be performed to determine if the data provide evidence that the proportions choosing each of the sections are not the same. If the null hypothesis is that there is no difference in the proportions, what is the expected frequency of those who read the Business section first?

Name:

Class:

Date:

Chapter 14 - Learning from Categorical Data a. 8 b. 44 c. 11 d. 4 ANSWER: c 28. A question of interest to game managers is the hunting strategy of predators. Do they just take the first prey that comes along, or are they selective? In a study of winter prey selection in a National Park, radio-tagged cougars were observed to have killed prey according to the table below. At the most recent census in the National Park, there were about 3,500 white-tailed deer, 1,000 elk, and 500 moose.

Do these data provide sufficient evidence at the 0.05 level that the cougars are not selecting their prey at random? That is, is there evidence that the proportion of deer, elk, and moose killed by cougars is not in the same proportions as in the park population?

ANSWER: P1 = the population proportion of white-tailed deer selected P2 = the population proportion of elk selected P3 = the population proportion of moose selected Check the appropriateness of the chi-square test: sample is random (stated in the problem); sample size is large (yes, all expected counts are greater than or equal to 5) Two-way table:

X2 = 30.21, df = 2 which is approximately 0 Since the P-value is prey at random.

, we reject the null hypothesis and conclude that the cougars are not selecting their

29. The row and column marginal totals provide information on the distribution of observed values for each of the two variables defining the two-way frequency table. a. True b. False ANSWER: True 30. The expected cell count for the row a column b entry in a bivariate two-way frequency table is equal to the product of the row a and column b marginal totals. a. True b. False ANSWER: False

Name:

Class:

Date:

Chapter 14 - Learning from Categorical Data 31. In a two-way frequency table, the chi-squared test statistic for testing homogeneity has degrees of freedom equal to (#rows – 1) (#columns – 1). a. True b. False ANSWER: True 32. Which of the following are ways in which data can be summarized in a two-way table?

I) Rows represent different populations and columns represent categorical variable categories II) Rows represent categories of one categorical variable and columns represent categories of another categorical variable III) Rows represent groups from one population and columns represent groups from another population a. I only b. II only c. I and II only d. II and III only ANSWER: c 33. A two-way table can display which of the following?

I) Values for one categorical variable using samples from multiple populations II) Values for two categorical variables using samples from a single population III) Values for multiple categorical variables using samples from multiple populations a. I and II only b. II and III only c. I, II, and III only d. II only ANSWER: a 34. When data on multiple categorical variables taken from a single sample are summarized in a two-way table, which of the following tests can be performed?

I. Large-sample t-test II. Chi-square test for homogeneity III. Chi-square test for independence a. I only b. II only c. III only d. Neither I nor II nor III ANSWER: c 35. When data from two independent samples on one categorical variable are summarized in a two-way table, which of the following tests can be performed?

I. Large-sample t-test II. Chi-square test for homogeneity III. Chi-square test for independence a. I only b. II only

Name:

Class:

Date:

Chapter 14 - Learning from Categorical Data c. III only d. Neither I nor II nor III ANSWER: b 36. State air quality managers are concerned about the number of unregulated particulate pollution sources in one county.

They conduct a survey of 500 randomly selected homeowners to determine the number of smoke-emission sources, including fireplaces, wood stoves, and campfire sites in two towns. Which of the following tests would be appropriate if the regulators wanted to determine if the distribution of smoke emission sources was the same for the two towns?

I. Chi-square goodness-of-fit test II. Chi-square test for homogeneity III. Chi-square test for independence a. I only b. II only c. III only d. Neither I nor II nor III ANSWER: b 37. Suppose you are a chef planning the dessert for a large dinner party. You know that most of the dinner guests come from an area where most people prefer tea as an after-dinner beverage rather than coffee. You could serve a chocolatebased dessert or fruit-based dessert and would like to know if there is a relationship between after-dinner beverage preference and dessert preference for people from your guests’ area. You consult published banquet food preference studies for your guests’ area and find one which queried after-dinner dessert and beverage preference for included 200 randomly selected adults. Which of the following tests would be appropriate ways to use the published study data to determine whether or not there is an association between dessert and after-dinner beverage preferences?

I. Chi-square goodness-of-fit test II. Chi-square test for homogeneity III. Chi-square test for independence a. I only b. II only c. III only d. Neither I nor II nor III ANSWER: c 38. Wildlife biologists are monitoring bird nesting in two study areas. Each year, the biologists randomly select 50 nests from each study area and determine what materials birds use to make their nests. Over the past fifteen years, biologists have discovered that the prevalent nesting materials have changed from twigs to grasses in both study areas. Biologists know that a five-consecutive-year drought can lead to nesting material changes in certain bird species and would like to know if there is an association between the occurrence of a five-year drought and the observed nesting material change.

Drought occurrence data is available for both study areas. Which of the following tests would be appropriate for answering the biologists’ question?

I. Chi-square goodness-of-fit test II. Chi-square test for homogeneity III. Chi-square test for independence a. I only b. II only c. III only d. Neither I nor II nor III

Name:

Class:

Date:

Chapter 14 - Learning from Categorical Data ANSWER: c 39. Educators at one college are interested in determining if students’ confidence in their own learning capability increased with the duration of academic or professional training. In order to investigate, the educators surveyed randomly selected students and trainees from two groups. The first group included college freshmen and new trades apprentices.

The second group included college juniors and tradespeople nearing the end of their apprenticeships. All participants answered “yes” or “no” to questions related to the speed and effectiveness of learning new skills. Which of the following tests would be appropriate for determining if learning capability increased with training duration?

I. Chi-square goodness-of-fit test II. Chi-square test for homogeneity III. Chi-square test for independence a. I only b. II only c. III only d. Neither I nor II nor III ANSWER: b 40. A group of sustainable landscapers is assessing two different soil contouring methods based on sustainability performance benchmarks including water retention, erosion control, and native plant growth. The landscapers sample ten sites for each of the two soil contouring methods and determine the proportion of each method that shows acceptable water retention, erosion control, and native plant growth. Which of the following tests would be appropriate for determining if there were differences in the sustainability performance of the two soil contouring methods?

I. Chi-square goodness-of-fit test II. Chi-square test for homogeneity III. Chi-square test for independence a. I only b. II only c. III only d. Neither I nor II nor III ANSWER: b 41. You’re evaluating the effect of daytime exercise on sleep quality. You take a representative sample of 100 adults from your community and ask them questions regarding their exercise level (none, light, medium, and vigorous) as well as their perceived sleep quality (poor vs. good). Which of the following null hypotheses would you use to test whether the proportion of individuals reporting good sleep was the same regardless of daily exercise level? For this question, variables P1, P2, P3, and P4 refer to the proportions of individuals with none, light, medium, and vigorous exercise levels who report good quality sleep. a. b. c. d.

ANSWER: c 42. You’re evaluating the effect of daytime exercise on sleep quality. You take a representative sample of 100 adults from your community and ask them questions regarding their exercise level (none, light, medium, and vigorous) as well as their perceived sleep quality (poor vs. good). Which of the following null hypotheses would you use to test whether or not daily exercise level affected sleep quality? For this question, variables P1, P2, P3, and P4 refer to the proportions of individuals

Name:

Class:

Date:

Chapter 14 - Learning from Categorical Data with none, light, medium, and vigorous exercise levels who report good quality sleep. a. b. c. d.

ANSWER: c 43. You’re evaluating the effect of home exercise on the outcomes of surgical knee repair. You take a random sample of 200 adults who received a surgical knee repair procedure and ask them questions regarding their post-procedure program (no exercise, therapeutic exercise, general fitness exercise) as well as their procedure outcome (successful vs. unsuccessful). Which of the following null hypotheses would you use to test whether the proportion of individuals reporting a successful procedure outcome was the same regardless of the home exercise program they followed? For this question, variables p1, p2, and p3 refer to the proportions of individuals with no exercise, therapeutic exercise, and general fitness exercise who report a successful surgical outcome. a. b. c. d.

ANSWER: c 44. You’re evaluating the effect of home exercise on the outcomes of surgical knee repair. You take a random sample of 200 adults who received a surgical knee repair procedure and ask them questions regarding their post-procedure program (no exercise, therapeutic exercise, general fitness exercise) as well as their procedure outcome (successful vs. unsuccessful). Which of the following null hypotheses would you use to test whether or not home exercise level affected surgical repair success? For this question, variables p1, p2, and p3 refer to the proportions of individuals with no exercise, therapeutic exercise, and general fitness exercise who report a successful surgical outcome. a. b. c. d.

ANSWER: c 45. The arithmetical and statistical procedures for the test of homogeneity and the test of independence are the same.

Explain in a few sentences what distinguishes these two hypothesis tests.

ANSWER: A test of homogeneity compares the distribution of one variable in two or more populations and requires two or more independent random samples. A test of independence tests if there is an association between two variables in one population and requires one random sample.

46. The authorship of ancient writings is frequently in dispute. One method for judging authorship of writings from the Classical Greek period is to analyze the proportion of sentences containing the word (an article something like “a”, “an”, or “the” in English). If a particular collection of works has markedly different frequencies of the use of

, this

would be considered evidence against the same author having written all the works.

In the table below, data from random samples of 200 sentences from each of the 4 works are presented. The alleged author is one Philo Judaeus, a philosopher writing in ancient Alexandria, Egypt.

Name:

Class:

Date:

Chapter 14 - Learning from Categorical Data

Test the hypothesis that the use of

is the same in these 4 works. Assume significance level α = 0.05.

ANSWER: Check the appropriateness of the chi-square test: sample is random (stated in the problem); sample size is large (yes, all expected counts are greater than or equal to 5) Two-way table:

Since the P-value is , we fail to reject the null hypothesis and cannot conclude that the frequencies of the use of are different in the 4 works.

47. Juvenile free-living ground squirrels utilize responses known as “alarm calls”, that is, vocalizations elicited by a predator. These calls can alert others to danger from a predator. Newly weaned squirrels emerge from the nest at about 25 days of age and enter a noisier world than they are used to. Do the squirrels emerge with automatic responses to alarm signals, or are the responses learned? To answer this question, a biologist played recordings of alarm calls for three populations (by age) of squirrels and observed the squirrels’ responses. The biologist reasoned that if the responses were not different for the different age groups, the squirrels must be responding by instinct. On the other hand, if the responses differ with the age of the squirrels the young squirrels must be learning to respond to the alarm calls. The data for the responses to a whistle chorus, categorized by age, is presented in the table below:

Is there convincing evidence that the responses to a chorus of whistles are different for the different age groups? Test the relevant hypothesis at the 0.05 level.

ANSWER: Check the appropriateness of the chi-square test: sample is random (stated in the problem); sample size is large (yes, all expected counts are greater than or equal to 5) Two-way table:

Name:

Class:

Date:

Chapter 14 - Learning from Categorical Data

Since the P-value is squirrels get older

, we fail to reject the null hypothesis and cannot conclude that responses change as the

48. The authorship of ancient writings is frequently in dispute. One method for judging authorship of writings from the Classical Greek period is to analyze the proportion of sentences containing the word (an article something like “a”, “an”, or “the” in English). If a particular collection of works has markedly different frequencies of the use of

, this

would be considered evidence against the same author having written all the works.

In the table below, data from random samples of 200 sentences from each of the 4 works are presented. The alleged author is Xenophon (c. 428 – c.45 BCE), a Greek soldier.

Test the hypothesis that the use of

is the same in these 4 works. Assume significance level α = 0.05.

ANSWER: Check the appropriateness of the chi-square test: sample is random (stated in the problem); sample size is large (yes, all expected counts are greater than or equal to 5) Two-way table:

Since the P-value is

, we reject the null hypothesis and conclude the alternative hypothesis.

49. Over the course of 20 flights occurring over a variety of weekdays, nights, and weekends, researchers selected a random sample of passengers that had been seated next to individuals with a different level of dress formality. The

Name:

Class:

Date:

Chapter 14 - Learning from Categorical Data passengers were surveyed as they left the boarding area. The researchers were interested in the level of agitation felt when passengers’ “seatmates” used the common armrest. Only one person was randomly selected to be interviewed from a seatmate pair. The question of interest was whether formally or casually dressed passengers are equally bothered by the use of the common armrest by someone oppositely dressed. The data from passenger interviews is summarized below: • •

Casually dressed: Formally dressed:

19 bothered 38 bothered

26 not bothered 18 not bothered

What is the appropriate null hypothesis for this investigation? What can be concluded about the hypothesis by applying the appropriate chi-square test? Assume significance level α = 0.05.

ANSWER: Check the appropriateness of the chi-square test: sample is random (stated in the problem); sample size is large (yes, all expected counts are greater than or equal to 5) Two-way table:

Since the P-value is , we reject the null hypothesis and conclude that a passenger’s dress formality and being bothered by a seatmate’s use of the common armrest are not independent.

50. Scandinavian researchers investigate the effects of hunting male bears on succeeding generations. They hypothesized that, when a male is killed, a new male moves in and maximizes its reproductive success by killing existing cubs. A random sample of radio-tagged females was monitored and data on the number of bear cubs surviving 1.5 years were gathered. In the southern area, hunters killed bears legally; in the northern area, no hunting took place. The data on cub survival in this sample are summarized below. The researcher suspects an association between the location of the females and cub survival.

Write an appropriate null hypothesis for this investigation and use an appropriate chi-square procedure to evaluate it.

Assume significance level α = 0.05.

ANSWER: Check the appropriateness of the chi-square test: sample is random (stated in the problem); sample size is large (yes, all expected counts are greater than or equal to 5) Two-way table:

Name:

Class:

Date:

Chapter 14 - Learning from Categorical Data

Since the P-value is are not independent.

, we reject the null hypothesis and conclude that cub survival and adult males killed

51. Black bears and their dwelling in National Parks can be a problem for humans. Bear travels are governed by the need for food, as well as a high degree of natural curiosity. Some humans inadvertently or purposefully feed the bears, leading them to harass the human population. When bears become troublesome, one strategy is to transplant them. In a study of the success of transplantation strategy, researchers kept track of the troublesome bears’ fate over the course of 10 years of transplantations. One question of interest was whether the strategy worked equally well for “experienced” and “inexperienced” bears. “Experienced” bears are bears being transplanted a second time after wandering back and being troublesome again. The relevant data are presented in the table below.

Test the hypothesis that the transplant outcome and the “experience level” of the population of troublesome bears are independent. For purposes of this question, you may assume that the captured bears are a random sample of the troublesome bear population.

ANSWER: Check the appropriateness of the chi-square test: sample is random (stated in the problem); sample size is large (yes, all expected counts are greater than or equal to 5) Two-way table:

Since the P-value is , we fail to reject the null hypothesis and cannot conclude that experience and transplant outcome are not independent.

Name:

Class:

Date:

Chapter 15 - Understanding Relationships-Numerical Data 1. The general form of a probabilistic model is y = (deterministic function) + (random deviation) a. True b. False ANSWER: True 2. The simple linear regression model is a deterministic model. a. True b. False ANSWER: False 3. Which of the following describes essential features of a deterministic model?

I) One of the terms must include a random deviation II) The value of the dependent variable is completely determined by a mathematical function of the independent variable III) The dependent variable includes a mathematical function of the independent variable plus a random deviation. a. I only b. II only c. III only d. I and III only ANSWER: b 4. Which of the following describes essential features of a probabilistic model?

I) One of the terms includes a random deviation II) The value of the dependent variable is completely determined by a mathematical function of the independent variable III) The dependent variable includes a mathematical function of the independent variable plus a random deviation. a. I only b. II only c. III only d. I and III only ANSWER: d 5. In the simple linear regression model, the randomness of e implies that y itself is subject to uncertainty. a. True b. False ANSWER: True 6. In the simple linear regression model, α and β are fixed numbers that are usually unknown. a. True b. False ANSWER: True 7. In the simple linear regression mode, σe depends on the value of x. a. True b. False

Name:

Class:

Date:

Chapter 15 - Understanding Relationships-Numerical Data ANSWER: False 8. The number of degrees of freedom associated with estimating σe with se in the simple linear regression model is n-2. a. True b. False ANSWER: True 9. Use the scatterplot below to answer the following questions:

When a linear model is fit to the data, which of the following can be stated with the greatest confidence? a. The residual for point B is greater than the residual for point D. b. The residual for point A is greater than the residual for point C. c. The residual for point C is greater than the residual for point B. d. The residual for point B is greater than the residual for point A. ANSWER: c 10. In a study of the surface temperature of vital (living) and non-vital (endodontically treated) teeth in a random sample of 32 adults seeking dental care at a university clinic, temperatures of vital and non-vital teeth were measured for each individual. The computer output shown below was generated.

(a) What proportion of observed variation in the surface temperature of vital teeth can be explained by the surface temperature of non-vital teeth? (b) Does the simple linear regression model appear to be useful? Justify your response with specific references to the computer output.

Name:

Class:

Date:

Chapter 15 - Understanding Relationships-Numerical Data ANSWER:

(a) (b) Yes, since and the corresponding P-value is < 0.0001, there appears to be a useful linear relationship between vital and non-vital tooth temperatures

11. If there is a negative linear relationship between two variables x and y, which of the following must be true of β, the slope of the population regression line? a. b. c. d.

ANSWER: a 12. The expected change in the value of y for one unit change in x is α. a. True b. False ANSWER: False 13. As part of a study of the swimming speed of sharks, a random sample of 18 lemon sharks was observed in a laboratory sea tunnel. Body lengths and maximum sustainable swimming speeds (“MSSS”, reported in body lengths per second) were measured for each shark. The computer output from a regression with y = MSSS and x = body length is given below:

According to the above computer output, if body length increases by one unit, by how much will the swimming speed, in body lengths per second, change? a. 1.893 b. -0.0104 c. -1.893 d. 1.184 ANSWER: b

Name:

Class:

Date:

Chapter 15 - Understanding Relationships-Numerical Data 14. A study was carried out to investigate the relationship between x = the number of components needing repair and y = the time of the service call (in minutes) for a computer repair company. The number of components and the service times for a random sample of 20 service calls was used to fit a simple regression model. Partial computer output is shown below:

S = 19.058, R-Sq=91.3%, R-Sq(adj) = 90.0% One of the numbers in the above computer output indicates the number of additional minutes required per additional component serviced. What is the value of this number? a. 32.441 b. 11.6205 c. 8.121 d. 19.058 ANSWER: b 15. The residual plot below indicates that one or more of the assumptions of the linear regression model may not be met.

Which of the following is a reasonable conclusion based on this residual plot?

a. The residual plot clearly indicates a non-linear model would be more appropriate. b. There is evidence that the residuals are not normally distributed. c. The slope of the regression line is non-zero. d. There is evidence that the residuals do not have the same variance for all x values.

ANSWER: a 16. What are the four “Basic Assumptions: of the simple linear regression model”?

ANSWER: The 4 basic assumptions are: • • • •

The distribution of deviations, e, at any particular x value has a mean value of 0.

The standard deviation of e is the same for any particular x value.

The distribution of e at any particular x value is normal.

The deviations associated with different observations are independent of one another.

Name:

Class:

Date:

Chapter 15 - Understanding Relationships-Numerical Data 17. In the simple linear regression model, the point estimate and the point prediction are identical for a particular value of x. a. True b. False ANSWER: True 18. A standardized residual plot with spread increasing from left to right suggests that the variance of y is not the same at each x value. This appearance of the standardized residual suggests that one of the basic assumptions for a simple linear regression model is not being met. a. True b. False ANSWER: True 19. When the four basic assumptions for a simple linear regression model are satisfied, (a) What is equal to? (b) What is equal to? (c) What is the shape of the sampling distribution of b? (d) What is the probability distribution of the standardized variable, ANSWER:

?

(a) (b) (c) The shape is a normal distribution (d) This is a t distribution with df = n – 2

20. The computer output given below shows a regression of data on the Body Mass (g) vs. Wing Length (mm) for sphinx moths.

Name:

Class:

Date:

Chapter 15 - Understanding Relationships-Numerical Data

What is the estimated regression line?

What is the calculated value of sb?

What is the calculated value of se? In a few sentences, interpret se in the context of this problem.

Construct a 95% Confidence Interval for β.

ANSWER: Regression line: Body Mass = – 1.211 + 0.057 (WingLength) sb = 0.0072, se = 0.513, the value of se estimates the typical variation of points around the regression line. The typical variation of weights is about 0.513 g for any given wing length.

The 95% confidence interval for β is given by:

21. The computer output given below shows a regression of data on the Wing Length (mm) vs. Body Mass (g) for sphinx moths.

Name:

Class:

Date:

Chapter 15 - Understanding Relationships-Numerical Data

What is the estimated regression line?

What is the calculated value of sb?

What is the calculated value of se? In a few sentences, interpret se in the context of this problem.

Construct a 95% Confidence Interval for β.

ANSWER: Regression line: Winglength = 28.142 + 12.132 (BodyMass) sb = 1.579, se = 7.471, the value of se estimates the typical variation of points around the regression line. The typical variation of wing lengths is about 7.471 mm for any given body mass.

The 95% confidence interval for β is given by:

22. The computer output given below shows a regression of Social Studies Concepts vs. Reading Comprehension scores for a random sample of sophomores.

What is the estimated regression line?

What is the calculated value of sb?

What is the calculated value of se? Briefly interpret se in the context of the problem.

Construct a 95% Confidence Interval for β.

Name:

Class:

Date:

Chapter 15 - Understanding Relationships-Numerical Data ANSWER: Regression line: Social Studies = 76.56 + 0.731 (Reading) sb = 0.0351, se = 25.83, t = 20.84 The value of se estimates the typical variation of points around the regression line.

Assuming the basic assumptions for the simple linear regression model have been met, a 95% confidence interval for β is given by:

23. The computer output given below shows a regression of Science Knowledge vs. Reading Comprehension scores for a random sample of sophomores.

What is the estimated regression line?

What is the calculated value of sb?

What is the calculated value of se. Briefly interpret se in the context of the problem.

Construct a 95% Confidence Interval for β.

ANSWER: Regression line: Science = 44.794 + 0.844 (Reading) sb = 0.0309, se = 22.27, t = 27.33 The value of se estimates the typical variation of points around the regression line.

Assuming the basic assumptions for the simple linear regression model have been met, a 95% confidence interval for β is given by:

24. The computer output given below shows a regression of data on the Body Mass (g) vs. Wing Length (mm) for sphinx moths.

Name:

Class:

Date:

Chapter 15 - Understanding Relationships-Numerical Data

What is the estimated regression line?

What is the calculated value of sb?

What is the calculated value of se? In a few sentences, interpret se in the context of this problem.

Using the computer output above, perform the Model Utility Test at a 0.05 level of significance.

ANSWER: Regression line: Body Mass = –1.211 + 0.057 (WingLength) sb = 0.0072, se = 0.513, the value of se estimates the typical variation of points around the regression line. The typical variation of weights is about 0.513 g for any given wing length.

The points appear to fall in a linear pattern, with a consistent variation. Assuming that the distribution of errors at a particular x value is approximately normal and that errors are independent of one another, the assumptions of the simple linear regression model are appropriate

Since P<α, reject the null hypothesis. There is a meaningful linear relationship between weight and wing length.

25. The computer output given below shows a regression of data on the Wing Length (mm) vs. Body Mass (g) for sphinx moths.

Name:

Class:

Date:

Chapter 15 - Understanding Relationships-Numerical Data

What is the estimated regression line?

What is the calculated value of sb?

What is the calculated value of se? In a few sentences, interpret se in the context of this problem.

Using the computer output above, perform the Model Utility Test at a 0.05 level of significance.

ANSWER: Regression line: WingLength = 28.142 + 12.132 (BodyMass) sb = 1.579, se = 7.471, the value of se estimates the typical variation of points around the regression line. The typical variation of wing lengths is about 7.471 mm for any given body mass.

The points appear to fall in a linear pattern, with a consistent variation. Assuming that the distribution of errors at a particular x value is approximately normal and that errors are independent of one another, the assumptions of the simple linear regression model are appropriate

Since P<α, reject the null hypothesis. There is a meaningful linear relationship between weight and wing length.

26. As part of a study of the swimming speed of sharks, a random sample of 18 lemon sharks was observed in a laboratory sea tunnel. Body lengths and maximum sustainable swimming speeds (“MSSS”, reported in body lengths per second) were measured for each shark. The computer output from a regression with y = MSSS and x = body length is given below: Linear Fit

Name:

Class:

Date:

Chapter 15 - Understanding Relationships-Numerical Data MSSS = 1.8928955 – 0.0104278 × Length Summary of Fit RSquare 0.526395 RSquare Adj 0.496794 S 0.272031 Mean of Response 1.24 N Observations 18 Analysis of Variance Source DF Sum of Squares Mean Square F Ratio Model 1 1.3159870 1.31599 17.7834 Error 16 1.1840130 0.07400 Prob > F Total 17 2.5000000 0.0007* Parameter Estimates Term Estimate Std Error t Ratio Prob > |t| Intercept 1.8928955 0.167575 11.30 < 0.0001* Length(cm) –0.010428 0.002473 –4.22 0.0007* The null hypothesis is that there is no linear relationship between body length and maximum sustainable swimming rate.

At the 0.05 level of significance, should the null hypothesis be rejected? Assume all the proper conditions are met for applying linear regression analysis. a. Yes b. No c. There is not enough information to tell ANSWER: a 27. If there is no evidence of a linear relationship between x and y, what decision will b made in a test of ? a. Reject H0 and conclude that there is no evidence that the linear model is useful b. Reject H0 and conclude that there is evidence that the linear model is useful c. Fail to reject H0 and conclude that there is no evidence that the linear model is useful d. Fail to reject H0 and conclude that there is evidence that the linear model is useful ANSWER: c 28. In a study of toy safety, parents over age 35 and parents under age 35 were asked to rate the safety of toys on a scale of 1 (very safe) to 5 (very unsafe). The investigators did a regression analysis of the over-age-35 parents’ ratings vs. the under-age-35 parents’ ratings for each toy. A computer-generated normal probability plot of the residuals is shown below:

Name:

Class:

Date:

Chapter 15 - Understanding Relationships-Numerical Data

Write a brief description of the plot and, based on your description, recommend to the investigators whether or not the appropriate assumption is met for simple linear regression.

ANSWER: There appears to be a reasonably linear pattern in the normal probability plot. This means that the assumption of a normal distribution of errors appears to be met.

29. The scatter plot and residual plot shown below are from a regression analysis of Prehistoric Native American projectile points. The lengths of the projectiles were regressed on the width of the projectile points

Using these plots, categorize each of the Basic Assumptions of the simple linear regression model as one of the following: not checkable, checked and met, checked and not met For all assumptions checked, explain what aspect of the graphs led you to your conclusion that the assumption was met or not met.

ANSWER: • The distribution of deviations, e, at any particular x value has a mean value of 0 (checked and met).

The residual plot is reasonably symmetric over the line defined by residual = 0.

• The standard deviation of e is the same for any particular x value (checked and not met). There seems to be more variation in the values for higher values of width. The residual plot fans out somewhat.

• The distribution of e at any particular x value is normal (not checkable). While the residual plot is symmetric, it is hard to tell if the distribution of residuals is close to a normal distribution.

• The deviation associated with different observations are independent of one another (not checkable).

There is no information provided about how this sample was obtained. If some of the points were found together, perhaps made by the same individual with a unique style, the deviations might not be

Name:

Class:

Date:

Chapter 15 - Understanding Relationships-Numerical Data independent.

30. In a study of toy safety, parents over age 35 and parents under age 35 were asked to rate the safety of toys on a scale of 1 (very safe) to 5 (very unsafe). The investigators did a regression analysis of the over-age-35 parents’ ratings vs. the under-age-35 parents’ ratings for each toy. A computer-generated normal probability plot of the residuals is shown below:

Write a brief description of the plot and, based on your description, recommend to the investigators whether or not the appropriate assumption is met for simple linear regression.

ANSWER: There appears to be some degree of systematic nonlinear behavior in the pattern of the normal probability plot, particularly at the low end. This means that the assumption of a normal distribution of errors may not be met.

31. The scatter plot and residual plot shown below are from a regression analysis of Prehistoric Native American projectile points. The lengths of the projectiles were regressed on the width of the projectile points

Name:

Class:

Date:

Chapter 15 - Understanding Relationships-Numerical Data

Using these plots, categorize each of the Basic Assumptions of the simple linear regression model as one of the following: not checkable, checked and met, checked and not met For all assumptions checked, explain what aspect of the graphs led you to your conclusion that the assumption was met or not met.

ANSWER: • The distribution of deviations, e, at any particular x value has a mean value of 0 (checked and met).

There are only a couple of points, at either end, for which this is in doubt.

• The standard deviation of e is the same for any particular x value (checked and not met). There seems to be more variation in the middle of the range, and less on either end.

• The distribution of e at any particular x value is normal (checked and not met). This appears to be skewed toward the higher values, with the tails of the residuals extending to +15 on the positive side, but only about -5 on the negative side.

• The deviation associated with different observations are independent of one another (not checkable).

There is no information provided about how this sample was obtained. If some of the points were found together, perhaps made by the same individual with a unique style, the deviations might not be independent.

32. Which of the following best describes an outlier?

I. An observation with a high y-value II. An observation with either a high or low x-value III. An observation with a large residual a. I only b. II only

Name:

Class:

Chapter 15 - Understanding Relationships-Numerical Data c. III only d. Neither I nor II nor III ANSWER: c 33. Which of the following describes the location of an outlier on an xy plot?

I. Far removed from the rest of the data in the x-direction II. Far removed from the rest of the data in the y-direction III. Far away from the estimated regression line in the y-direction a. I only b. II only c. III only d. Neither I nor II nor III ANSWER: c 34. Which of the following describes the location of an influential observation on an xy plot?

I. Far removed from the rest of the data in the x-direction II. Far removed from the rest of the data in the y-direction III. Far away from the estimated regression line in the y-direction a. I only b. II only c. III only d. Neither I nor II nor III ANSWER: a

Date:

Name:

Class:

Date:

Chapter 16 - More Than Two Means 1. You’re a traffic engineer planning new transportation infrastructure between two cities. There are three

existing routes: A, B, and C. Travel time on route A varies with traffic, while routes B and C vary with road and weather conditions. You would like to know if the mean travel times for the three routes are significantly different. If the mean travel times on routes A, B, and C are and alternative hypotheses would accurately express your question?

, then which of the following null

a. b. c. d.

ANSWER: d 2. You’re an engineer testing the bonding strength of three different adhesives A, B, and C. You measure

average bonding strengths of 100 psi for adhesive A, 110 psi for adhesive B, and 130 psi for adhesive C in a standard test of five samples per adhesive. The adhesive application and curing processes used cannot be performed exactly the same for each sample, so you expect variability in bonding strengths. If the mean bonding strengths for adhesives A, B, and C are , then which of the following null and alternative hypotheses would accurately express your question? a. b. c. d.

ANSWER: c 3. The owner of a downtown coffee shop is estimating the sales performance of three different hot beverages

sold in the shop: expresso, green tea, and latte. They sample sales for ten business days and record the number of sales for each of the three different beverages each day. The sample averages and standard deviations are shown below: Expresso: sample mean = 48 sales/day, sample standard deviation = 6 sales/day Green tea: sample mean = 58 sales/day, sample standard deviation = 12 sales/day Latte: sample mean = 56 sales/day, sample standard deviation = 16 sales/day If the mean daily sales for each beverage are expresso = μA, green tea = μB, and latte =μC, then which of the following null and alternative hypotheses would accurately express your question? a. b. c. d.

ANSWER: c 4. A researcher wants to find out if the best sprinters on the planet improve the racing time at world

championships in the 100 meters running discipline among men. They consider the results of the final races of the last three world championships and compare the average time in each final racing. The collected data are shown in the table below:

Name:

Class:

Date:

Chapter 16 - More Than Two Means

Choose the correct null and alternative hypothesis which addresses the researcher’s question: a. b. c. d.

ANSWER: d 5. The two main human blood group systems are the ABO and Resus (Rh) systems. According to the

information from the American Red Cross (http://www.redcrossblood.org), Rhesus Negative blood type is rarer than Rhesus Positive. A researcher wants to know if the proportion of people with Rh(-) is equal for each ABO human blood type. To exclude the spread of people through the different ABO types, the researcher generates 10 random samples of equal size (100 people) for each of the ABO types and draws attention to the number of people with Rh(-). The summary results of the blood test are represented in the table below.

Choose the correct null and alternative hypotheses statements for the F test. a. b. c. d.

ANSWER: d 6. A professor wants to know whether their students have equally absorbed the learning objectives for the

course. During the term, the professor conducts three in-class tests. The average scores of students were 71.8, 81.5, and 75.8 (out of a maximum of 100 points). Using the information above, answer the question of how the professor should define the difference between the three average in-class test scores. a. The professor should set the null hypothesis Ho: μ1 ≠ μ2 ≠ μ3 and conduct an F test.

Name:

Class:

Date:

Chapter 16 - More Than Two Means b. The professor should set the null hypothesis Ho: μ1 = μ2 = μ3 and conduct an F test. c. The professor should set the null hypothesis Ho: μ1 = 71.8; μ2 = 81.5, μ3 = 75.8 and conduct an F test. d. The professor should set the null hypothesis Ho: μ1 ≠ 71.8; μ2 ≠ 81.5, μ3 ≠ 75.8 and conduct an F test.

ANSWER: b 7. A graduate student of the college conducted the following research. They considered four consulting

companies and selected 13-15 approximately similar vacancies in each of these companies, which were posted on the official websites during the last year. The student was interested in the information about the wages indicated in the vacancies.

Assume that you know that the student decided to conduct an F test to compare the interested values, and draw the null hypothesis for this test in plain English. a. The null hypothesis is that the average wages in all consulting companies for a position of interest are equal. b. The null hypothesis is that the average wages in the four companies considered are equal. c. The null hypothesis is that the average wages in the four samples of vacancies for a position of interest are equal. d. The null hypothesis is that the average wages in the four companies considered for a position of interest are equal.

ANSWER: d 8. You’re evaluating the outcomes of the three different treatments in an experiment. You have sample means

and standard deviations for each treatment and would like to use the ANOVA F test to determine whether or not there are significant differences between the means. Which of the following must be true for you to use the ANOVA F test in this situation?

I) Each of the three treatment response distributions is normal II) The standard deviations for the normal distributions for all three treatments are the same III) The observations in any particular treatment are independent of one another IV) The random samples from each of the treatments are selected independently of the other treatments. a. I and II only b. II and III only c. I, II, and III only d. I, II, III, and IV only ANSWER: d 9. You’re evaluating the responses to a survey sent to students from four different universities. You’re interested in whether the survey responses indicate differences in the population means of students at each university. Which of the following conditions must be true for you to use the ANOVA F test in this situation?

I) Each of the three treatment response distributions is normal II) The standard deviations for the normal distributions for all three treatments are the same III) The observations in any particular treatment are independent of one another IV) The random samples from each of the treatments are selected independently of the other treatments. a. I and II only b. II and III only c. I, II, and III only

Name:

Class:

Date:

Chapter 16 - More Than Two Means d. I, II, III, and IV only ANSWER: d 10. The manager of a campus café is estimating sales of three pastries based on random samples of sales over the past month. The sample means and standard deviations are shown below: Caramel Custard: sample mean = 48 sales/day, sample standard deviation = 6 sales/day Oatmeal Brownie: sample mean = 58 sales/day, sample standard deviation = 12 sales/day Fudge Cake: sample mean = 56 sales/day, sample standard deviation = 16 sales/day Would the conditions for equality of population standard deviations for an ANOVA F test be considered to be reasonably met for these three samples? a. Yes, because the largest standard deviation is over twice that of the smallest. b. Yes, because the largest standard deviation is less than twice the value of the next largest standard deviation. c. No, because the largest standard deviation is more than twice the value of the smallest standard deviation. d. None of these.

ANSWER: c 11. A recruitment agency provides a study of the average amount of time people work in information technology companies. Four companies were considered for the study: company A, company B, company C, and company D. In this study, a company is considered new if it has been in existence for less than 20 years ago and considered as old if it has been in existence for more than 50 years ago. A small company has about 200 employees and a big company has more than 1,000 employees.

Is it correct to conduct an F test for these four companies? a. For new companies, the distribution of the amount of time people work at the company is not normal because the population is very small. We cannot use the F test. b. If you generate a random sample of equal size for each company, then all conditions for applying the F test will be met. We can use the F test. c. For new companies, distribution of the amount of time people work there is limited by the age of the company and therefore certainly has a smaller standard deviation. We cannot use the F test. d. Big companies will have large samples and therefore the samples will be dependent. We cannot use the F test.

ANSWER: c 12. A researcher wants to find out if the best sprinters on the planet improve the racing time at world championships in the 100 meters running discipline among men. They consider the results of the final races of the last three world championships and compare the average time in each final racing. The collected data are shown in the table below:

Carry out an ANOVA f test, find the F and P-values, and interpret the results for a significance level α = 0.10. a. F = 3.41; df1 = 2, df2 = 22; P-value slightly greater than 0.05; reject the null hypothesis and conclude that the means of the final racing times were different.

Name:

Class:

Date:

Chapter 16 - More Than Two Means b. F = 1.70; df1 = 2, df2 = 22; P-value greater than 0.10; fail to reject the null hypothesis and conclude that the means of the final racing times were not different. c. F = 3.41; df1 = 3, df2 = 22; P-value slightly smaller 0.05; reject the null hypothesis and conclude that the means of the final racing times were different. d. F = 1.70; df1 = 3, df2 = 22; P-value greater than 0.10; fail to reject the null hypothesis and conclude that the means of the final racing times were not different.

ANSWER: a 13. Before releasing a new product, a small company wants to compare the prices in the market for similar products from other brands presented in the same field. To do this, research has been conducted, and information has been collected for three similar brands. The information is presented in the table below:

Carry out an ANOVA f test, find the F and P-values, and interpret the results for a significance level α = 0.05. a. F = 4.57; df1 = 3, df2 = 123; P-value is less than 0.01, reject the null hypothesis and conclude that the mean prices for the three brands are not all the same. b. F = 1.80; df1 = 2, df2 = 123; P-value greater than 0.10; fail to reject the null hypothesis and conclude that the mean prices for the three brands are the same c. F = 4.57; df1 = 2, df2 = 22; P-value slightly greater than 0.01; reject the null hypothesis and conclude that the mean prices for the three brands are not all the same. d. F = 1.80; df1 = 3, df2 = 22; P-value greater than 0.10; fail to reject the null hypothesis and conclude that the mean prices for the three brands are the same.

ANSWER: c 14. A student is investigating the effect of sleep on the average rate of home and workplace accidents in adults. The first part of the investigation is to establish whether there is a difference in the average duration of sleep for people of different age groups. For this purpose, the student considers several random samples to study four age groups where the values are hours of sleep per night:

Carry out an ANOVA F test, find the F and P-values, and interpret the results for a significance level α = 0.05. a. F = 2.68; df1 = 3, df2 = 60; P-value is between 0.05 and 0.10. Fail to reject the null hypothesis and conclude that the mean nightly hours of sleep for the four age groups are the same. b. F = 2.68; df1 = 4, df2 = 60; P-value is between 0.025 and 0.05. Reject the null hypothesis and conclude that the mean nightly hours of sleep for the four age groups are not the same. c. F = 4.25; df1 = 3, df2 = 60; P-value is less than 0.01. Reject the null hypothesis and conclude that the mean

Name:

Class:

Date:

Chapter 16 - More Than Two Means nightly hours of sleep for the four age groups are not the same. d. F = 4.25; df1 = 4, df2 = 60; P-value is less than 0.01. Reject the null hypothesis and conclude that the mean nightly hours of sleep for the four age groups are not the same.

ANSWER: a 15. A student is investigating the effect of sleep on the average rate of home and workplace accidents in adults. The first part of the investigation is to establish whether there is a difference in the average duration of sleep for people of different age groups. For this purpose, the student considers several random samples to study four age groups where the values are hours of sleep per night:

Using a multiple comparison procedure, identify differences between mean durations of sleep for the considered age groups. Use a 95% Tukey-Kramer confidence interval. a. Using the 95% Studentized range critical value q = 3.74, we can calculate the CI: Population Mean Difference 95% T-K CI Comments μ18–24 – μ25–44

(-0.04, 1.04) Includes 0, means are not significantly different

μ18–24 – μ45–64

(-1.03, 0.03) Includes 0, means are not significantly different

μ18–24 – μ65+

(0.43, 1.57)

μ25–44 – μ45–64

(-1.52, -0.48) Does not include 0, means are significantly different

μ25–44 – μ65+

(-0.05, 1.05) Includes 0, means are not significantly different

μ45–64 – μ65+

(0.96, 2.04)

Does not include 0, means are significantly different

Does not include 0, means are significantly different

b. Using the 95% Studentized range critical value q = 4.05, we can calculate the CI: Population Mean Difference 95% T-K CI Comments μ18–24 – μ25–44

(-1.10, 2.10)

Includes 0, means are not significantly different

μ18–24 – μ45–64

(-2.08, 1.08)

Includes 0, means are not significantly different

μ18–24 – μ65+

(-0.68, 2.68)

Includes 0, means are not significantly different

μ25–44 – μ45–64

(-2.53, 0.53)

Includes 0, means are not significantly different

μ25–44 – μ65+

(-1.13, 2.13)

Includes 0, means are not significantly different

μ45–64 – μ65+

(-0.11, 3.11)

Includes 0, means are not significantly different

c. Using the 95% Studentized range critical value q = 3.74, we can calculate the CI: Population Mean Difference 95% T-K CI Comments μ18–24 – μ25–44

(-0.98, 1.98) Includes 0, means are not significantly different

μ18–24 – μ45–64

(-1.96, 0.96) Includes 0, means are not significantly different

μ18–24 – μ65+

(-0.55, 2.55) Includes 0, means are not significantly different

μ25–44 – μ45–64

(-2.41, 0.41) Includes 0, means are not significantly different

Name:

Class:

Date:

Chapter 16 - More Than Two Means μ25–44 – μ65+

(-1.00, 2.00) Includes 0, means are not significantly different

μ45–64 – μ65+

(0.02, 2.98)

Does not include 0, means are significantly different

d. Using the 95% Studentized range critical value q = 4.05, we can calculate the CI: Population Mean Difference 95% T-K CI Comments μ18–24 – μ25–44

(-0.08, 1.08) Includes 0, means are not significantly different

μ18–24 – μ45–64

(-1.08, 0.08) Includes 0, means are not significantly different

μ18–24 – μ65+

(0.39, 1.61)

μ25–44 – μ45–64

(-1.56, -0.44) Does not include 0, means are significantly different

μ25–44 – μ65+

(-0.10, 1.110) Includes 0, means are not significantly different

μ45–64 – μ65+

(0.91, 2.09)

Does not include 0, means are significantly different

Does not include 0, means are significantly different

ANSWER: c 16. Meteorologists studying climate in the state of Texas use data from the website (www.climatedata.com) to estimate average precipitation for three Texas cities: Austin, Dallas, and San Antonio. The precipitation for the three cities is summarized in the table below: Using a multiple comparison procedure, identify differences between average precipitation for the three cities. Use a 95% Tukey-Kramer confidence interval. a. Using q = 3.74, we can calculate the CIs: Population Mean Difference 95% T-K CI Comments μA – μD

(-1.03, -0.09) Does not include 0, means are significantly different

μA – μSA

(-0.36, 0.58) Includes 0, means are not significantly different

μD – μSA

(0.20, 1.14)

Does not include 0, means are significantly different

b. Using q = 3.74, we can calculate the CIs: Population Mean Difference 95% T-K CI

Comments

μA – μD

(-1.15, -0.39) Does not include 0, means are significantly different

μA – μSA

(-0.83, 1.06) Includes 0, means are not significantly different

μD – μSA

(0.27, 1.62)

Does not include 0, means are significantly different

c. Using q -= 3.47 we can calculate the CI: Population Mean Difference 95% T-K CI

Comments

μA – μD

(-1.23, 0.11) Includes 0, means are not significantly different

μA – μSA

(-0.56, 0.78) Includes 0, means are not significantly different

μD – μSA

(0.00, 1.34)

Does not include 0, means are significantly different

d. Using q -= 3.83 we can calculate the CIs: Population Mean Difference 95% T-K CI

ANSWER: b

Comments

μA – μD

(-1.30, 0.18)

Includes 0, means are not significantly different

μA – μSA

(-0.63, 0.85)

Includes 0, means are not significantly different

μD – μSA

(-0.07, 1.41)

Includes 0, means are not significantly different

Name:

Class:

Date:

Chapter 16 - More Than Two Means 17. Researchers investigate the average life expectancy (months) of domestic cats by breed. They generate four random samples for each of the most popular worldwide domestic cat breeds. These breeds include American Shorthair, Persian, Siamese, and Maine Coon. The table below summarizes the study data.

American Shorthair Persian Siamese Sample size n 19 19 19 19 Sample mean 78.28 74.89 82.17 86.

Sample standard deviation s 8.46 7.84 7.56 7.8 An ANOVA F test with a significance level of 0.05 rejected the null hypothesis, indicating that the difference between mean life expectancy for at least one pair of breeds was statistically significant. Use a multiple comparison procedure to identify the pair (or pairs) of breeds for which life expectancies are different. Use a 95% Tukey-Kramer confidence interval. a. Mean life expectancies for American Shorthairs and Persians are significantly different. There are no significant differences in life expectancies in other pairs of breeds. b. Mean life expectancies for American Shorthairs and Maine Coons are significantly different. Mean life expectancies for Persians and Siamese are significantly different. Mean life expectancies for Persians and Maine Coons are significantly different. There are no significant differences in life expectancies in other pairs of breeds. c. Mean life expectancies for Persians and Siamese are significantly different. Mean life expectancies for Persians and Maine Coons are significantly different. There are no significant differences in life expectancies in other pairs of breeds. d. Mean life expectancies for Persians and Maine Coons are significantly different. There are no significant differences in life expectancies in other pairs of breeds.

ANSWER: b 18. When issuing a textbook, there are always several defective copies. The publishing house conducts a study to determine whether the number of defective copies depends on the format of the textbook. For the study, three random samples of the textbook editions for the different book sizes were generated: a large portrait (LP), a portrait (P), and a US letter (let), each of the editions has an approximately equal number of copies. Twenty-one textbooks of each format were used for the study. The table below summarizes the data: Difference -3.06 -3.22 -0.17 MSTr 69.11 MSE 12.35 F 5.60 P-value 0.0059 An ANOVA F test with a significance level α = 0.05 rejected the null hypothesis, indicating that the mean number of defective copies between at least one pair of textbook sizes was significantly different.

Use a multiple comparison procedure to identify which pairs of textbook sizes have significantly different mean numbers of defects. Use a 95% Tukey-Kramer confidence interval. a. The mean number of defective copies for portrait-size textbooks and letter-size textbooks is significantly different. There are no significant differences in a mean number of defective copies for other pairs of textbook sizes. b. The mean number of defective copies for portrait-size textbooks and letter-size textbooks is significantly different. The mean number of defective copies for large portrait-size textbooks and letter-size textbooks is significantly different. There are no significant differences in the mean number of defective copies for other pairs of textbook sizes.

Name:

Class:

Date:

Chapter 16 - More Than Two Means c. The mean number of defective copies for large-portrait-size textbooks and letter-size textbooks is significantly different. The mean number of defective copies for large portrait-size textbooks and portrait-size textbooks is significantly different. There are no significant differences in the mean number of defective copies for other pairs of textbook sizes. d. The mean number of defective copies for large-portrait-size textbooks and letter-size textbooks is significantly different. There are no significant differences in the mean number of defective copies for other pairs of textbook sizes.

ANSWER: c 19. Meteorologists studying climate in the state of Texas use data from the website (www.climatedata.com) to estimate average precipitation for three Texas cities: Austin, Dallas, and San Antonio. Using a multiple comparison procedure the meteorologists identify the differences between the average precipitation level, in inches per month, for the considered three cities, and construct the Tukey-Kramer confidence interval for 95% Studentized range critical value.

Population Difference μA – μH μA – μSA μH – μSA 95% T-K CI (-1.80, -0.04) (-0.77, 0.99) (0.15, 1.91) Help the meteorologists to draw a correct conclusion about the differences between the average precipitation levels in these cities. a. b. c. d.

ANSWER: a 20. A market researcher wants to compare market prices for the same product made by several popular manufacturers. A random sample has been generated for the product of each manufactory. The information is presented in the table below:

Carry out multiple comparison procedures and interpret the results using a 95% Tukey-Kramer confidence interval. a. The mean price for manufactories A and B differs from the prices for manufactories C and D. b. The mean prices for manufactory B differ from the mean prices for manufactories C and D, and the mean price for manufactory A differs from the mean price for manufactory D. c. The mean price for manufactory B differs from the mean prices for manufactories C and D. d. The mean price for manufactory B differs from the mean price for manufactory D. ANSWER: b