Test Bank For Essential Statistics Exploring the world through data 3th Edition by Robert N. Gould,

Gould/Ryan/Wong Essentials Statistics 3e Chapter 1 Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Answer the question.

1) Data can be defined as numbers in context. Suppose you are given the following set of numbers: 1.73, 1.83, 1.57, 1.88, 1.70, 1.65 What additional information would allow you to define these numbers as data?

A) We need to know who collected these numbers.

B) Units of measurement. This could represent the heights of six 20-year-olds, in meters.

C) Units of measurement. This could represent the heights of six 5-year-olds, in meters.

D) We need to know where these numbers were collected.

Objective: (1) Understand Concepts Regarding Data

2) Data can be defined as numbers in context. Suppose you are given the following set of numbers: 18, 22, 22, 20, 19, 21 What additional information would allow you to define these numbers as data?

A) We need to know who collected these numbers.

B) We need to know where these numbers were collected.

C) Units of measurement. This could represent the ages of six high school students.

D) Units of measurement. This could represent the ages of six college students.

Objective: (1) Understand Concepts Regarding Data

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

3) Give an example of how data could be collected about you on a daily basis.

Objective: (1) Understand Concepts Regarding Data

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

4) A statistics student collected data from other students in her class who ride a bike to school. The following table shows data about their bikes: Color Series Number Weight (lbs) Road Bike Average Speed (mph) Black A120 33 0 16 Blue B640 22 1 24 Green C300 26 0 14 Black D90 15 1 23 How many variables are there?

A) 7 B) 20

C) 4

Objective: (1) Understand the Fundamentals of Statistics

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D) 5

5) A statistics student collected data from other students in her class who ride a bike to school. The following table shows data about their bikes: Color Series Number Weight (lbs) Road Bike Average Speed (mph) Black A120 31 0 16 Blue B640 21 1 24 Green C300 27 0 14 Black D90 14 1 23 Observations were made on how many bikes?

A) 20 B) 4

C) 7

D) 5

Objective: (1) Understand the Fundamentals of Statistics

6) In a recent school poll, the administrators asked if students were satisfied with the school's course offerings. What is the population of interest here?

A) All students who are satisfied with the course offerings.

B) All students who participated in the poll.

C) All students who attend the school.

D) All students who are not satisfied with the course offerings.

Objective: (1) Understand the Fundamentals of Statistics

7) In a recent high school poll, the principal asked if students were satisfied with the amount of after-school activities offered. What is the population of interest here?

A) All students who participated in the poll.

B) All students who attend the school.

C) All students who are not satisfied with the amount of after-school activities that are offered.

D) All students who are satisfied with the amount of after-school activities that are offered.

Objective: (1) Understand the Fundamentals of Statistics

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

8) In a recent survey at UCLA, some incoming freshmen students were asked if they planned to take more than one math class before they graduated. What is the population of interest here and what is the sample?

Objective: (1) Understand the Fundamentals of Statistics

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

9) The average gas mileage of the top selling mini-vans for each U. S. car manufacturer is an example of what type of variable?

A) Categorical variable B) Numerical variable C) Neither Objective: (2) Distinguish Between Numerical and Categorical Variables

10) A state senator's comments about the dangers of global warming are an example of what type of variable?

A) Categorical variable B) Numerical variable C) Neither Objective: (2) Distinguish Between Numerical and Categorical Variables

11) Marital status of each member of a randomly selected group of adults is an example of what type of variable?

A) Numerical variable B) Categorical variable C) Neither Objective: (2) Distinguish Between Numerical and Categorical Variables

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12) The ethnicity of the individual respondents in a political poll of a randomly selected group of adults is an example of what type of variable?

A) Numerical variable B) Categorical variable C) Neither Objective: (2) Distinguish Between Numerical and Categorical Variables

13) The average number of hours spent completing statistics homework for a randomly selected group of statistics students is an example of what type of variable?

A) Categorical variable B) Numerical variable C) Neither Objective: (2) Distinguish Between Numerical and Categorical Variables

14) The number of parents who attended parent teacher conferences at a local elementary school is an example of what type of variable?

A) Numerical variable B) Categorical variable C) Neither Objective: (2) Distinguish Between Numerical and Categorical Variables

15) A bicycle manufacturer produces four different bicycle models. Information is summarized in the table below: Model Series Number Weight Style Ascension A120 31 Mountain Road Runner B640 19 Road All Terrain C300 27 Hybrid Class Above D90 15 Racing Identify the variables and determine whether each variable is numerical or categorical.

A) series number: numerical; weight: categorical; style: categorical B) series number: categorical; weight: numerical; style: categorical C) series number: numerical; weight: numerical; style: categorical D) series number: categorical; weight: categorical; style: categorical Objective: (2) Distinguish Between Numerical and Categorical Variables

16) An international relations professor is supervising four master's students. Information about the students is summarized in the table.

Student Name Student Number Area of Interest Anna 914589205 Africa Pierre 981672635 Middle East Juan 906539012 Latin America Yoko 977530271 Asia

GPA 3.40 3.87 3.75 3.13

Identify the variables and determine whether each variable is numerical or categorical.

A) student number: numerical; area of interest: categorical; GPA: categorical B) student number: categorical; area of interest: categorical; GPA: categorical C) student number: numerical; area of interest: categorical; GPA: numerical D) student number: categorical; area of interest: categorical; GPA: numerical Objective: (2) Distinguish Between Numerical and Categorical Variables

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17) Determine which of the following five variables are numerical and which are categorical. age, gender, weight, ethnicity, favorite math class A) All of the variables are categorical.

B) Age, weight, and favorite math class are numerical variables. Gender and ethnicity are categorical variables.

C) All of the variables are numerical.

D) Age and weight are numerical variables. Gender, ethnicity, and favorite math class are categorical variables.

Objective: (2) Distinguish Between Numerical and Categorical Variables

18) Determine which of the following five variables are numerical and which are categorical. age, gender, height, favorite candy, eye color A) All of the variables are categorical.

B) All of the variables are numerical.

C) Age and height are numerical variables. Gender, favorite candy, and eye color are categorical variables.

D) Age, height, and favorite candy are numerical variables. Gender and ethnicity are categorical variables.

Objective: (2) Distinguish Between Numerical and Categorical Variables

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

19) Give an example of one categorical variable and one numerical variable.

Objective: (2) Distinguish Between Numerical and Categorical Variables

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

20) In a survey, married couples were asked, "Do you have children?" The response was electronically recorded as a "1" for yes and a "0" for no. This is an example of .

A) Coded categorical data C) Unstacked numerical data

B) Random sample D) None of these

Objective: (3) Understand Methods for Coding Categorical Variables

21) In a survey, high school graduates were asked "Did you play sports in high school?" The response was electronically recorded as a "1" for yes and a "0" for no. This is an example of .

A) Unstacked numerical data C) Coded categorical data

B) Random sample D) None of these

Objective: (3) Understand Methods for Coding Categorical Variables

22) According to the following data table, which variable(s) is(are) categorical?

Age Gender Weight Ethnicity 23 1 180 1 18 0 126 0 20 0 139 2 19 1 154 1 20 1 202 3 A) Age, gender, and ethnicity B) Gender C) Gender and ethnicity D) None are categorical because there are only numbers in the table Objective: (3) Understand Methods for Coding Categorical Variables

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23) According to the following data table, which variable(s) is(are) categorical?

Age Gender Shoe Size Ethnicity 18 1 10 1 23 0 7 0 21 0 6 2 19 1 11 1 20 1 10 3 A) Gender, shoe size, and ethnicity B) Gender and ethnicity C) None are categorical because there are only numbers in the table D) Gender Objective: (3) Understand Methods for Coding Categorical Variables

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

24) In the following table, gender is a categorical variable. Give one possible way the variable could have been coded.

Objective: (3) Understand Methods for Coding Categorical Variables

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

25) The table gives the GPA and gender of students in a business class.

GPA Female 3.54 1 3.20 0 3.87 0 3.86 1 Is the format of the data set stacked or unstacked?

A) stacked

B) unstacked

Objective: (4) Organize Data in Stacked Format and Unstacked Format

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26) The table gives the GPA of some students in two math classes. One class meets in the morning and one in the afternoon.

Morning Afternoon 3.69 3.40 2.97 3.84 3.12 3.81 3.44 3.63 Is the format of the data set stacked or unstacked?

A) unstacked

B) stacked

Objective: (4) Organize Data in Stacked Format and Unstacked Format

27) The following data table is organized using which method?

Men's Ages Women's Ages 35 42 39 33 41 37 37 35 40 39 A) This is unstacked data because each row represents one person.

B) This is stacked data because each row represents one person.

C) This is stacked data because the ages are separated by groups (in this case, gender).

D) This is unstacked data because the ages are separated by groups (in this case, gender).

Objective: (4) Organize Data in Stacked Format and Unstacked Format

28) The following data table is organized using which method?

Gender Age Male 35 Female 42 Female 33 Male 37 Female 39 A) This is unstacked data because the ages are separated by groups (in this case, gender).

B) This is stacked data because the ages are separated by groups (in this case, gender).

C) This is stacked data because each row represents one person.

D) This is unstacked data because each row represents one person.

Objective: (4) Organize Data in Stacked Format and Unstacked Format

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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

29) Determine whether the following data table is stacked or unstacked and explain your reasoning.

Objective: (4) Organize Data in Stacked Format and Unstacked Format

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the data in Table 1A to answer the question.

Note: 1 is female, 0 is male.

30) Suppose you wanted to know whether the student's commute distance was associated with the student's living situation. Using the data table if possible, which variables would you use?

A) Data on student's living situation are not included in this study.

B) Use Commute Distance (Miles) and College Units Acquired.

C) Use Commute Distance (Miles) and Living Situation.

D) Use College Units Acquired and Living Situation.

Objective: (1) Determine Whether Questions Related to Variables in a Given Table Can be Answered by the Table

31) Suppose you wanted to know whether the men or the women had larger ring sizes. In the Female column of the table, 1 represents Female and 0 stands for Male. Using the data table, if possible, which variables would you use?

A) Use Female and Height.

B) Use Height and Ring Size.

C) Use Female and Ring Size.

D) Data on student's ring size are not included in this study.

Objective: (1) Determine Whether Questions Related to Variables in a Given Table Can be Answered by the Table

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32) Suppose you wanted to know whether the student's height was associated with the student's weight. Using the data table, if possible, which variables would you use?

A) Data on student's weight are not included in this study.

B) Use Height and Weight.

C) Use Weight and Ring Size.

D) Use Female and Height.

Objective: (1) Determine Whether Questions Related to Variables in a Given Table Can be Answered by the Table

33) Suppose you wanted to know whether the student's hair color was associated with the shoe size. Using the data table, if possible, which variables would you use?

A) Data on Shoe Size are not included in this study.

B) Use Hair Color and Living Situation.

C) Use Hair Color and Number of Aunts.

D) Use Hair Color and Ring Size.

Objective: (1) Determine Whether Questions Related to Variables in a Given Table Can be Answered by the Table

A data set on Shark Attacks Worldwide posted on StatCrunch records data on all shark attacks in recorded history including attacks before 1800. Variables contained in the data include time of attack, date, location, activity the victim was engaged in when attacked, type of injuries sustained by the victim, whether or not the injury was fatal, and species of shark. Which of the following questions could not be answered using this data set?

(Source: www.sharkattackfile.net) 34) Using the data described, if possible, which variable(s) would you use to determine in which year the least number of shark attacks occurred?

A) Use Date.

B) Use Location.

C) Use Hair Color and Number of Aunts.

D) Data on the year are not included in the table.

Objective: (1) Determine Whether Questions Related to Variables in a Given Table Can be Answered by the Table

35) Using the data described , if possible, which variable would you use to determine if shark attacks happen more often to men than women?

A) Data on gender of the victim are not included in the table.

B) Use Species of Shark.

C) Use Type of Injury.

D) Use Activity of the Victim Objective: (1) Determine Whether Questions Related to Variables in a Given Table Can be Answered by the Table

In a study of 900 adults, 45 out of the 325 men in the study said that they preferred to rent a movie on DVD rather than going out to a movie theater.

36) What is the approximate percentage of men in this study who prefer to rent a movie on DVD? A) 5% B) 13.8% C) 36% Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

37) What is the approximate percentage of women who participated in this study?

A) Not enough information available B) 7.8% C) 41% D) 63.9% Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

In a study of 1050 adults, 175 out of the 650 women in the study said that they preferred to drive an SUV to driving a compact car.

38) What is the approximate percentage of study participants who are women in this study who said that they prefer to drive an SUV to driving a compact car?

A) 16.7% B) 26.9% C) 61.9% Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

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39) What is the approximate percentage of study participants who are women?

A) 16.7% B) 61.9% C) Not enough information available D) 26.9% Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

Solve the problem.

40) In a sample of 775 senior citizens, approximately 67% said that they had seen a television commercial for life insurance. About how many senior citizens is this?

A) 519 B) Not enough information available.

C) 256 D) 67 Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

41) In a sample of 800 first-year college students, 72% said that they check their Facebook page at least three times a day. How many students is this?

A) 224 B) Not enough information available.

C) 72 D) 576 Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

The two-way table below shows teenage driver gender and whether or not the respondent had texted at least once while driving during the last thirty days.

42) What percentage of the sample had texted at least once while driving in the past thirty days?

A) 62.5% B) 50% C) 43.75% D) 37.5% Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

43) What percentage of the sample were female drivers?

A) 50% B) 62.5%

C) 78%

D) 28.3%

Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

The two-way table below shows the survey results when sixty adults were asked whether they had made a clothing purchase in the last thirty days.

44) What percentage of the sample had not made a clothing purchase in the past thirty days?

A) 35% B) 65% C) 33%

D) 50%

Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

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45) Of the adult males surveyed, what percentage had made a clothing purchase in the last thirty days?

A) 33% B) 35% C) 50% D) 65% Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

In a study of 1350 elementary school children, 118 out of the 615 girls in the study said they want to be a teacher when they grow up.

46) What percent of the study's participants were boys?

A) 54.4% B) 19.2% C) 83.7% D) 45.6% Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

47) What percent of girls want to be a teacher when they grow up?

A) 80.8% B) 19.2% C) 45.6%

D) 8.7%

Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

In a study of 1200 adults, 480 out of the 630 women in the study said they attended a state college or university.

48) What percent of the study's participants were women?

A) 76.2% B) 47.5% C) 52.5% D) 40% Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

49) What percent of women attended a state college or university?

A) 47.5% B) 40% C) 76.2%

D) 52.5%

Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

Solve the problem.

50) According to the following two-way table, what percent of people in the sample prefer dogs?

Male Female Dog 40 25 Cat 25 10 A) 40% B) 65% C) 35% D) 25% Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

51) According to the following two-way table, why are percentages more useful than counts to compare pet preferences between males and females?

Male Female Dog 40 25 Cat 25 10 A) There are more people who prefer dogs than cats in the sample.

B) You should only use counts in a two-way table.

C) You should only use percentages in a two-way table.

D) There are more males than females in the sample.

Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

52) According to the following two-way table, what percent of people in the sample take naps?

A) 55%

B) 60%

C) 35%

D) 25%

Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

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53) According to the following two-way table, why are percentages more useful than counts to compare the amount of males and females who take naps?

A) You should only use counts in a two-way table.

B) There are more people who take naps than people who do not in the sample.

C) There are more males than females in the sample.

D) You should only use percentages in a two-way table.

Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

54) A two-way table is useful for describing which types of variables?

A) One numerical variable.

B) Two categorical variables.

C) Two numerical variables.

D) One numerical variable and one categorical variable.

Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

55) A two-way table could be used for which of the following pairs of variables?

A) Gender and age B) Age and height C) Age and favorite class D) Gender and favorite class Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

56) What types of variables are represented in a two-way table? Give an example.

Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

In a recent study of 1200 adult smokers, 125 out of the 560 males in the study said they were interested in joining a help group to quit smoking.

57) What percent of the study's participants were female?

Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

58) What percent of males are interested in joining this group?

Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

Solve the problem.

59) According to the following two-way table, what percent of people in the sample eat breakfast?

Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

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60) According to the following two-way table, why are percentages more useful than counts to compare the amount of males and females who eat breakfast?

Objective: (1) Find Frequencies, Proportions, and Percentages and Use them to Describe and Compare Data

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Identify the type of sampling used.

61) A recent report showed there were 49 accidents involving pedestrians in City A and 62 accidents involving pedestrians in City B this year. The mayor of City A claims that his city is safer for pedestrians than City B. What information is missing that might contradict this claim?

A) The number of crosswalks in both City A and City B B) The total number of pedestrians in both City A and City B C) The number of accidents involving pedestrians from the previous year D) The number of accidents that do not involve pedestrians in both City A and City B Objective: (2) Identify Missing Information

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Answer the question.

62) Only two cafeterias are available at a large university. The first offers vegetarian food and the second offers only non-vegetarian meals. The vegetarian cafeteria serves 30 students on a given Friday, while the non-vegetarian cafeteria serves 15 lunches on that same Friday. A student claims that this is evidence that students who were on campus on that Friday preferred vegetarian food. What information is missing that might contradict this claim?

Objective: (2) Identify Missing Information

63) In a national safety report, the number of bicyclist fatalities in City X was 108 and the number of bicyclist fatalities in City Y was 59. Can we conclude that bicyclists are less safe in City X than in City Y? If you answered no, what additional data would allow us to make a conclusion about which city is less safe for bicyclists?

Objective: (2) Identify Missing Information

64) The number of clinically obese men in State A is 156,261 and the number of clinically obese men in State B is 294,269. Someone makes the claim that this is evidence that men exercise more in State A. What information is missing that might contradict this claim?

Objective: (2) Identify Missing Information

65) In a study at one university, it has been recorded that Model 1 smart phone screens were brought to a shop to be repaired 5,876 times in one year . Model 2 smart phone screens were brought into the same shop to be repaired only 702 times that year. Can we conclude that Model 1 smart phones screens are more fragile than Model 2 smart phone screens? If you answered no, what additional data would allow us to make a conclusion about which type of smart phone screen is more fragile?

Objective: (2) Identify Missing Information

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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Indicate whether the study described is an observational study or a controlled experiment.

66) The obesity rates of elementary age children living in urban areas are compared to those living in rural areas to see whether children in urban settings have higher obesity rates.

A) Controlled experiment B) Observational study Objective: (1) Distinguish Between Observational Studies and Controlled Experiments

67) "People with diabetes are at higher risk for certain cancers than those without the blood sugar disease, suggests a new study based on a telephone survey of nearly 400,000 adults."

A) Controlled experiment B) Observational study Objective: (1) Distinguish Between Observational Studies and Controlled Experiments

68) A group of students is divided into two groups. One group is a given a new chewable vitamin and the other group is given a placebo. After six months they are asked to fill out a questionnaire and given a health exam to see whether the new vitamin has health benefits that are better than a placebo.

A) Observational study B) Controlled experiment Objective: (1) Distinguish Between Observational Studies and Controlled Experiments

69) The smoking rates of teens in urban areas are compared to those living in rural areas to see whether teens living in rural settings have higher rates of smoking.

A) Controlled experiment B) Observational study Objective: (1) Distinguish Between Observational Studies and Controlled Experiments

70) A group of cancer patients is divided into two groups. One group is given a new drug to fight the side effects of chemotherapy and the other group is given a placebo. After three months they are asked to respond to a questionnaire about the frequency and severity of their side effects to see whether the new drug improved the overall negative side effects of chemotherapy.

A) Observational study B) Controlled experiment Objective: (1) Distinguish Between Observational Studies and Controlled Experiments

71) A group of students is divided into two groups. One group listens to classical music while taking a math test and the other group takes the test in silence. The average test scores of the two groups are compared to see whether listening to music during a math test has an effect on scores.

A) Observational study B) Controlled experiment Objective: (1) Distinguish Between Observational Studies and Controlled Experiments

Determine if the following scenario is an observational study or a controlled experiment.

72) A doctor is interested in determining whether a certain medication increases the risk of high blood pressure. He randomly selects 100 people for his study - 50 who will take the medication, and 50 who will take a placebo. He checks the patients' blood pressures weekly for six months.

A) Neither B) Controlled experiment C) Observational study Objective: (1) Distinguish Between Observational Studies and Controlled Experiments

73) A doctor is interested in determining whether a certain medication increases the risk of high blood pressure. He reviews his patients' medical records and finds that a higher proportion of people who take the medication are suffering from high blood pressure.

A) Neither B) Controlled experiment C) Observational study Objective: (1) Distinguish Between Observational Studies and Controlled Experiments

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74) A doctor is interested in determining whether a certain medication reduces migraines. She randomly selects 100 people for his study - 50 who will take the medication, and 50 who will take a placebo.

The patients are examined once a week for six weeks.

A) Neither B) Controlled experiment C) Observational study Objective: (1) Distinguish Between Observational Studies and Controlled Experiments

75) A doctor is interested in determining whether a certain medication reduces migraines. She reviews her patients' medical records and finds that a higher proportion of people who take the medication have fewer migraines than those who did not take the medication.

A) Neither B) Controlled experiment C) Observational study Objective: (1) Distinguish Between Observational Studies and Controlled Experiments

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Determine if the following scenario is an observational study or a controlled experiment and explain your reasoning.

76) A school teacher is interested in determining whether students who take multiple choice tests do better than students who take true/false tests. She has been giving multiple choice tests since she started teaching and is wondering if she should change her testing method. She randomly assigns half of her students to take a multiple choice test about grammar rules, and the other half to take a true/false test about grammar rules. She compares the test scores of the students in each group.

Objective: (1) Distinguish Between Observational Studies and Controlled Experiments

77) A doctor is interested in determining whether a certain medication is effective at treating abdominal pain. He reviews his patients' medical records and finds that a higher proportion of people who took the medication fewer abdominal pain symptoms than those who did not take the medication.

Objective: (1) Distinguish Between Observational Studies and Controlled Experiments

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

78) Consider the following statement "My child was bullied on the school bus and so was my neighbor's child, so obviously, bullying is a big problem on school buses and something needs to be done about it!" What is wrong with this statement?

A) The statement exhibits bias.

B) The person making the statement confused correlation with causation.

C) The statement is anecdotal.

D) None of these--the statement is valid.

Objective: (2) Identify Potential Problems and/or Improvements for a Research Study

79) Before opening a new dealership, an auto manufacturer wants to gather information about car ownership and driving habits of the local residents. The marketing manager of the company randomly selects 1000 households from all households in the area and mails a questionnaire to them. Of the 1000 surveys mailed, she receives 75 back. What is the problem with how the information is gathered?

A) The only responses were from people who chose to send the survey back.

B) Only residents from the local area were polled.

C) The 1000 surveys were not sent to randomly selected households.

D) To get a random sample, surveys would have to be mailed to every household.

Objective: (2) Identify Potential Problems and/or Improvements for a Research Study

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Solve the problem.

80) Consider the following statement, "Babies who breastfeed are less likely to grow into children with behavioral problems by the time they reach age 5 than those who receive formula milk." Which of the following is a plausible confounding variable in this study?

A) The age at which breastfeeding ends B) The quality of the formula milk C) Mother's social-economic status D) All of these E) None of these Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

81) Consider the following statement: "Researchers conducted a large observational study and determined that children who participated in school music programs scored higher on math exams in later grades than those who did not." Suppose that upon hearing this a politician states that all children should participate in school music programs. What is wrong with the politician's statement?

A) The controlled experiment was not double-blinded.

B) This study exhibits bias.

C) There was a placebo effect.

D) The politician confused correlation with causation.

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

82) Consider the following statement, "In a nationwide study, children on an all-organic diet are more alert in school than those not on an all-organic diet." Which of the following is a plausible confounding variable in this study?

A) School start times B) The quality of the non-organic diet C) Parents' social-economic status D) All of these E) None of these Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

83) Researchers conducted an experiment to determine if riding a bike to school improves attention span. What are the treatment and outcome variables?

A) The treatment variable is riding a bike to school. The outcome variable is whether or not the child rode a bike to school.

B) The treatment variable is attention span. The outcome variable is the child's attention span score.

C) The treatment variable is riding a bike to school. The outcome variable is the child's attention span.

D) The treatment variable is attention span. The outcome variable is whether or not the child rode a bike to school.

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

15

84) Researchers conducted an experiment to determine if children who participate in a new after-school tutoring program do better on state-mandated tests than children who do not attend the program. What are the treatment and outcome variables?

A) The treatment variable is the state-mandated test. The outcome variable is the participation in the after-school program.

B) The treatment variable is participation in the after-school program. The outcome variable is the test score on the state-mandated test.

C) The treatment variable is participation in the after-school program. The outcome variable is whether or not a child attended.

D) The treatment variable is the state-mandated test. The outcome variable is the test score on the state-mandated test.

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

85) Researchers conducted a study and determined that students who carpool have less friends than students who ride the bus to school. Can we conclude that carpooling causes students to have less friends?

A) Yes, this is an observational study and we can conclude causation.

B) No, this is an observational study and we cannot conclude causation.

C) Yes, this is an experiment and we can conclude causation.

D) No, this is an experiment and we cannot conclude causation.

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

86) Researchers conducted a study and determined that students who participate in sports are happier than students who do not. Can we conclude that participating in sports makes students happier?

A) Yes, this is an experiment and we can conclude causation.

B) Yes, this is an observational study and we can conclude causation.

C) No, this is an observational study and we cannot conclude causation.

D) No, this is an experiment and we cannot conclude causation.

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

87) A gym is offering a new 6-week diet plan for its members. Members who sign up for the program are weighed and measured once a week for the duration of the program. The owners of the gym want to know if the diet plan actually helps people lose weight. What variable could be a possible confounding factor in determining the cause of weight loss?

A) The person's marital status.

B) The person's exercise routine.

C) The person's social life.

D) The person's education level.

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

88) A gym is offering a new 6-week weight loss exercise program for its members. Members who sign up for the program are weighed and measured once a week for the duration of the program. The owners of the gym want to know if the weight loss program actually helps people lose weight. What variable could be a possible confounding factor in determining the cause of weight loss?

A) The person's diet.

B) The person's marital status.

C) The person's family structure.

D) The person's commitment to the program.

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

16

89) Coconut oil has become quite popular in recent years. People who use coconut oil claim it helps with hair care, skin care, stress relief, weight loss, and a boosted immune system. Can we conclude that the use of coconut oil causes these health benefits?

A) Yes, the claims are true stories, so we do have evidence of the health benefits.

B) Yes, the claims are anecdotes and give us a good comparison group to find health differences.

C) No, the claims are lies, so we do not have evidence of the health benefits.

D) No, the claims are anecdotes and do not give us a true comparison group to find health differences.

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

90) In Los Angeles, juice cleansing is very popular. Some people have claimed that the cleanses are beneficial for weight loss, body detoxification, and treatment and prevention of illnesses. Can we conclude that juice cleansing causes these health benefits?

A) No, the claims are lies, so we do not have evidence of the health benefits.

B) No, the claims are anecdotes and do not give us a true comparison group to find health differences.

C) Yes, the claims are anecdotes and give us a good comparison group to find health differences.

D) Yes, the claims are true stories, so we do have evidence of the health benefits.

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

91) What does it mean for an experiment to be random?

A) Assignment into the control and treatment groups is determined by the researcher.

B) Assignment into the control and treatment groups is determined by a person who is not involved in the research.

C) Assignment into the control and treatment groups is determined by the participants.

D) Assignment into the control and treatment groups is determined by chance.

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

92) What does it mean for an experiment to be double-blinded?

A) The participants do not know who is in the treatment and control groups.

B) Neither the researcher nor the participants know who is in the treatment and control groups.

C) The researcher and the participants know which group they are in because it is unethical to keep this information from them.

D) The researcher does not know which participants are in the treatment and control groups.

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

A group of 500 patients who suffer from skin cancer were asked to participate in a study to determine the effectiveness of a new medication. The patients were randomly divided into two groups, one that was given the actual medication, and one that received a placebo pill. A good outcome was defined as the cancer being in remission after 6 months of treatment. The results of the study are below.

93) Approximately what percent of patients who took the medication had cancer remission?

A) 48% B) 58% C) 50%

D) 67%

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

17

94) Was the new medication effective for cancer remission?

A) Yes, both groups had more patients with cancer remissions.

B) Yes, a higher percent of patients who took the medication had cancer remissions than the patients who took the placebo.

C) No, the patients who took the placebo also had cancer remissions.

D) No, this was not a controlled experiment.

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

95) Can we conclude that the cancer remissions were caused by the new medication?

A) No, even though this is a controlled experiment, there might be a confounding factor since the placebo group had cancer remissions too.

B) No, even though this is a controlled experiment, there was no difference between the treatment and control groups, so we cannot conclude causation.

C) Yes, this is a controlled experiment. Since a higher percent of patients who took the medication had cancer remissions, we can conclude causation.

D) Yes, this is a controlled experiment. We can always conclude causation with a controlled experiment.

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

A group of 500 patients who suffer from hypothyroidism, a condition in which your thyroid does not produce enough of certain hormones, were asked to participate in a study to determine the effectiveness of a new medication. The patients were randomly divided into two groups, one that was given the actual medication, and one that received a placebo pill.

The results of the study are below.

Medication Placebo Symptoms improved 205 140 Symptoms did not improve 65 90 96) What percent of patients who took the medication had improved symptoms?

A) 65.2% B) 41% C) 54%

D) 75.9%

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

97) Was the new medication effective in treating hypothyroidism?

A) Yes, a higher percent of patients who took the medication had improved symptoms than the patients who took the placebo.

B) No, this was not a controlled experiment.

C) Yes, both groups had more patients with improved symptoms.

D) No, the patients who took the placebo also had improved symptoms.

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

98) Can we conclude that the improved symptoms were caused by the new medication?

A) Yes, this is a controlled experiment. Since a higher percent of patients who took the medication had improved symptoms, we can conclude causation.

B) Yes, this is a controlled experiment. We can always conclude causation with a controlled experiment.

C) No, even though this is a controlled experiment, there might be a confounding factor since the placebo group had improved symptoms too.

D) No, even though this is a controlled experiment, there was no difference between the treatment and control groups, so we cannot conclude causation.

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

18

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Solve the problem.

99) Researchers conducted an experiment to determine if having a dog day on college campuses during final exam week lowers students' stress levels. A dog day is when dogs from a local animal shelter are brought onto campus for students to play and interact with. What are the treatment and outcome variables for this experiment?

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

100) Researchers conducted a study and determined that coworkers who socialize outside of work are more productive than coworkers who do not. Can we conclude that socializing outside of work causes coworkers to be more productive? Explain your reasoning.

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

101) A college is offering a new free tutoring program for students in an introductory statistics class. The school wants to know if this new program improves students' test scores on their midterms and final exams. What variable could be a possible confounding factor in determining why students' scores improved or not?

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

102) Give an example of how anecdotal evidence can be used to persuade consumers to purchase a product.

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

103) What is the difference between a blind and a double blind study? Which is most ideal?

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

A group of 500 patients who suffer from severe migraines were asked to participate in a study to determine the effectiveness of a new medication. The patients were randomly divided into two groups, one that was given the actual medication, and one that received a placebo pill. A good outcome was defined as a reduction in the number of migraines during a month's time. The results of the study are below.

104) Approximately what percent of patients who took the medication had a reduction in the amount of migraines?

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

105) Was the new medication effective for reducing migraines? Explain your reasoning and include any calculations.

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

106) Can we conclude that the reduction of migraines was caused by the new medication? Explain your reasoning.

Objective: (3) Understand When and Why to Infer or not Infer a Cause-and-Effect Relationship from a Research Study

19

Answer Key Testname: GOULDCH1TESTGEN

1) B 2) D 3) Answers will vary.

Examples might include: Facebook postings, Twitter tweets, Instagram photos, emails sent/received, credit/debit card swipes, GPS, text messaging, etc.

4) D 5) B 6) C 7) B 8) The population is the entire freshman class at UCLA. The sample includes the particular freshmen who participated in the survey.

9) B 10) C 11) B 12) B 13) B 14) A 15) B 16) D 17) D 18) C 19) Answers will vary.

Examples might include: categorical gender, favorite candy, year in school, favorite color, etc.; numerical - age, height, weight, speed, etc.

20) A 21) C 22) C 23) B 24) 2 possible ways to code: 0 - Male, 1 Female; OR 0 Female, 1 - Male

25) A 26) A 27) D 28) C 29) This is stacked data because each row represents one person.

30) C 31) C 32) A 33) A 34) A 35) A 36) B 37) D 38) B 39) B 40) A 41) D 42) D 43) A 44) A 45) C 46) A 47) B 48) C 49) C 50) B 51) D 52) A 53) C 54) B 55) D 56) Two categorical variables. Answers will vary. Examples might include: gender & favorite color, gender & year in school, year in school & favorite animal, etc.

640 = 0.533 = 53.3% 57) 1200 58)

125 = 0.223 = 22.3% 560

59)

75 = 0.75 = 75% 100

60) The group sizes are different. There are 55 males, but only 45 females.

61) B 62) It is not known the percentage of the student body in the two cafeterias on Friday. The larger number of students eating at the first cafeteria on Friday could be because the first cafeteria has a larger capacity than the second cafeteria or that it is closer to campus.

An alternate possibility could be that we don't know the number of students on campus that Friday. Quite possibly the university has more than 45 students, and we don't know what the rest of them ate.

(Presumably they went off campus or brought their own food.)

63) We cannot conclude that bicyclists are less safe in City X than in City Y. The population of each city would be needed to compare the fatality percent or rate with respect to total population.

20

64) We need to know the total number of men in State A and State B so that a comparison can be made of the percentage of the men in each state that are clinically obese.

There could be a much higher male population in State B than State A. Also, assumptions about exercise and obesity are being made.

65) It cannot be conclude that Model 1 smart phones screens are more fragile than Model 2 smart phone screens . We need to know the percentage of each type of smart phone model brought into the store for screen repairs. To find this percentage, the number of each type of smart phone models that are in the population is required. Model 1 smart phones could be a lot more popular than Model 2 smart phones, for instance.

66) B 67) B 68) B 69) B 70) B 71) B 72) B 73) C 74) B 75) C

Answer Key Testname: GOULDCH1TESTGEN

76) This is a controlled experiment because the students are randomly assigned to the treatment group (true/false test) and the control group (multiple choice test).

77) This is an observational study because the doctor did not randomly assign patients into groups. Instead, he simply looked at medical files.

78) C 79) A 80) D 81) D 82) D 83) C 84) B 85) B 86) C 87) B 88) A 89) D 90) B 91) D 92) B 93) D 94) B 95) C 96) D 97) A 98) A 99) Treatment variable whether or not a campus had a dog day. Outcome variable - students' stress levels during final exams.

100) No, this is an observational study and we cannot conclude causation.

101) Answers will vary.

Examples might include: a student's access to other help/tutoring programs, a student's major on campus (e.g. a mathematics major versus a history major), a student's study skills prior to the program, etc.

102) Answers will vary.

Examples might include: (1) a pregnancy blog references a few individual women's experiences with cocoa butter lotion and its reduction of stretch marks, (2) a local health store includes quotes from 5 customers on an advertisement that claims coconut oil consumption can reduce stress and improve health, (3) a commercial for skincare products interviews a small group of people that claim the product has cured their acne, etc.

103) In a blind study, the participants do not know which group they have been assigned to. For example, in a medical experiment, the patients do not know if they are receiving actual medication or just a placebo. In a double blind study, neither the researchers, nor the participants know which group the participants have been assigned to. A double blind study is better than a blind study.

185 185 = = 104) 185 + 90 275 0.6727 = 67.3% 105) Yes, a higher percent of patients who took the medication had fewer migraines 185 = 67.3% than 275 the patients who took the placebo 70 = 31.1% 275

106) Yes, this is a controlled experiment. Since a higher percent of patients who took the medication had fewer migraines, we can conclude causation.

21

Gould/Ryan/Wong Essentials Statistics 3e Chapter 3 Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

1) A city planner says, "The typical commute to work for someone living in the city limits is less than the commute to work for someone living in the suburbs." What does this statement mean?

A) If you live in the city limits you will have a longer commute time.

B) All city dwellers spend less time commuting to work than those living in the suburbs.

C) The center of the distribution of commute times for a city-dweller is less than the center of the distribution for those living in the suburbs.

D) There is less variation in the commute time of those living in the suburbs.

Objective: (1) Find and Interpret the Mean and Standard Deviation of a Data Set

2) A school board member says, "The typical bus ride to school for a student living in the city limits is more than the bus ride to school for a student living in the suburbs." What does this statement mean?

A) If you are a student living in the city limits you will have a shorter commute time.

B) The center of the distribution of bus ride times for a city-dweller is more than the center of the distribution for those living in the suburbs C) All students living in the city spend less time riding the bus to school than those living in the suburbs.

D) There is less variation in the bus ride times of those living in the suburbs.

Objective: (1) Find and Interpret the Mean and Standard Deviation of a Data Set

1

The following list shows the age at appointment of U.S. Supreme Court Chief Justices appointed since 1900. Use the data to answer the question.

3) The U.S. Supreme Court Chief Justice data was used to create the following output in an Excel spreadsheet. Choose the statement that best summarizes the variability of the dataset.

A) The age of most of the U.S. Supreme Court Chief Justice's since 1900 are within 31.3 years of the mean age.

B) The age of most of the U.S. Supreme Court Chief Justice's since 1900 are within 5.6 years of the mean age.

C) The ages of most of the U.S. Supreme Court Chief Justices are between 50 and 68 years.

D) None of these.

Objective: (1) Find and Interpret the Mean and Standard Deviation of a Data Set

Solve the problem.

4) The following nine values represent race finish times in hours for a randomly selected group of participants in an extreme 10 km race (a 10 km race with obstacles). Which of the following is closest to the mean of the data set?

1.0, 1.1, 1.2, 1.2, 1.3, 1.4, 1.4, 1.4, 1.5

A) 1.5 hours

B) 1.3 hours

C) 1.6 hours

Objective: (1) Find and Interpret the Mean and Standard Deviation of a Data Set

2

D) 1.1 hours

5) The following nine values represent race finish times in hours for a randomly selected group of participants in an extreme 10k race (a 10k race with obstacles). Which of the following is closest to the mean of the following data set?

1.0, 1.2, 1.2, 1.3, 1.4, 1.5, 1.5, 1.7, 2.1

A) x is about 1.4 hours

B) x is about 1.6 hours

C) x is about 1.1 hours

D) x is about 1.3 hours

Objective: (1) Find and Interpret the Mean and Standard Deviation of a Data Set

The following list shows the age at appointment of U.S. Supreme Court Chief Justices appointed since 1900. Use the data to answer the question.

6) Find the mean, rounding to the nearest tenth of a year, and interpret the mean in this context.

A) The typical age of a U.S. Supreme Court Chief Justice appointed since 1900 is 63.0.

B) The typical age of a U.S. Supreme Court Chief Justice appointed since 1900 is 61.0.

C) The typical age of a U.S. Supreme Court Chief Justice appointed since 1900 is 64.1.

D) The typical age of a U.S. Supreme Court Chief Justice appointed since 1900 is 61.4.

Objective: (1) Find and Interpret the Mean and Standard Deviation of a Data Set

Find the mean for the given sample data. Unless otherwise specified, round your answer to one more decimal place than that used for the observations.

7) The students in Hugh Logan's math class took the Scholastic Aptitude Test. Their math scores are shown below.

Find the mean score.

593 557 354 351 556 357 340 636 470 482 A) 476

B) 460.4

C) 479.2

D) 469.6

Objective: (1) Find and Interpret the Mean and Standard Deviation of a Data Set

8) Last year, nine employees of an electronics company retired. Their ages at retirement are listed below. Find the mean retirement age.

53 65 64 52 62 58 64 54 52 A) 58.2 yr

B) 58 yr

C) 57.6 yr

D) 57 yr

Objective: (1) Find and Interpret the Mean and Standard Deviation of a Data Set

9) The grocery expenses for six families were $82.53, $56.31, $78.99, $64.64, $70.76, and $85.04. Compute the mean grocery bill. Round your answer to the nearest cent.

A) $87.65 B) $73.05 C) $75.65 D) $109.57 Objective: (1) Find and Interpret the Mean and Standard Deviation of a Data Set

3

Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in the original data.

10) Christine is currently taking college astronomy. The instructor often gives quizzes. On the past seven quizzes, Christine got the following scores: 41 10 33 26 16 46 76 A) 22 B) 8786.3 C) 33 D) 11,694 Objective: (1) Find and Interpret the Mean and Standard Deviation of a Data Set

11) The top nine scores on the organic chemistry midterm are as follows.

42, 23, 65, 86, 60, 43, 58, 23, 59 A) 20.4 B) 6.4 C) 19.2

D) 21.8

Objective: (1) Find and Interpret the Mean and Standard Deviation of a Data Set

12) The numbers listed below represent the amount of precipitation (in inches) last year in six different U.S. cities.

15.9 17.7 47.9 38.8 18.3 24.5 A) 43.4 in.

B) 4433.6 in.

C) 5301.1 in.

D) 13.17 in.

Objective: (1) Find and Interpret the Mean and Standard Deviation of a Data Set

Solve the problem.

13) The mean can be thought of as the balancing point of a distribution. According to this description, at what value is the following distribution balanced?

A) About 95

B) About 115

C) About 105

Objective: (1) Find and Interpret the Mean and Standard Deviation of a Data Set

4

D) About 85

14) The mean can be thought of as the balancing point of a distribution. According to this description, at what value is the following distribution balanced?

A) About 40

B) About 50

C) About 30

D) About 20

Objective: (1) Find and Interpret the Mean and Standard Deviation of a Data Set

15) Two Geometry classes at North Hollywood High School took the same quiz. Mr. Davis had 15 students in his class with a mean score of 70. Mrs. Brown's class of 25 students had a mean score of 80. Overall, what was the mean score for all students on the quiz?

A) 76.25 B) 75.00 C) 75.75 D) 74.50 Objective: (1) Find and Interpret the Mean and Standard Deviation of a Data Set

16) Two Physics classes at Jefferson High School took the same quiz. Mr. Spears had 20 students in his class with a mean score of 80. Mrs. Guyton's class of 30 students had a mean score of 90. Overall, what was the mean score for all students on the quiz?

A) 85 B) 86 C) 87 D) 84 Objective: (1) Find and Interpret the Mean and Standard Deviation of a Data Set

17) The heights (in meters) of five adults are listed below. Calculate the mean height of these adults.

1.57, 1.65, 1.73, 1.75, 1.78

A) 1.71 meters

B) 1.70 meters

C) 1.73 meters

D) 1.72 meters

Objective: (1) Find and Interpret the Mean and Standard Deviation of a Data Set

18) The ages of five adults are listed below. Calculate the mean age of these adults.

26, 38, 45, 50, 61

A) 47

B) 45

C) 46

Objective: (1) Find and Interpret the Mean and Standard Deviation of a Data Set

5

D) 44

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

19) The mean can be thought of as the balancing point of a distribution. According to this description, at approximately what value is the following distribution balanced?

Objective: (1) Find and Interpret the Mean and Standard Deviation of a Data Set

20) Two algebra classes at University High School took the same quiz. Mr. Athens had 25 students in his class with a mean score of 80. Mrs. Sutton's class of 30 students had a mean score of 75. Overall, what was the mean score for all students on the quiz?

Objective: (1) Find and Interpret the Mean and Standard Deviation of a Data Set

21) The ages of five college students are listed below. Calculate the mean age of these students.

18, 18, 19, 20, 21 Objective: (1) Find and Interpret the Mean and Standard Deviation of a Data Set

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

22) Below is the standard deviation for extreme 10k finish times for a randomly selected group of women and men.

Chose the statement that best summarizes the meaning of the standard deviation.

Women: s = 0.16

Men: s = 0.25

A) On average, men's finish times will be 0.25 hours faster than the overall average finish time.

B) On average, women's finish times will be 0.16 hours less than men's finish times.

C) The distribution of men's finish times is less varied than the distribution of women's finish times.

D) The distribution of women's finish times is less varied than the distribution of men's finish times.

Objective: (2) Compare Means and Standard Deviations

6

23) Below is the standard deviation for extreme 10k finish times for a randomly selected group of women and men.

Chose the statement that best summarizes the meaning of the standard deviation.

Women: s = 0.17

Men: s = 0.21

A) The distribution of women's finish times is less varied than the distribution of men's finish times.

B) The distribution of men's finish times is less varied than the distribution of women's finish times.

C) On average, men's finish times will be 0.21 hours faster than the overall average finish time.

D) On average, women's finish times will be 0.17 hours less than men's finish times.

Objective: (2) Compare Means and Standard Deviations

24) Which of the following measurements is likely to have the least variation?

A) The individual mass measured in grams of quarters in a randomly selected ten dollar roll of quarters.

B) The individual heights of children, measured in inches, in a randomly selected class of sixth grade students.

C) The individual weights in ounces of oranges in a randomly selected five-pound bag of oranges at the market.

Objective: (2) Compare Means and Standard Deviations

25) Which of the following measurements is likely to have the most variation?

A) The volume of individual pop cans measured in fluid ounces from a randomly selected twenty-four pack.

B) The individual weights in ounces of tennis balls in a randomly selected can of tennis balls.

C) The individual weights in ounces of potatoes in a randomly selected crate of potatoes.

Objective: (2) Compare Means and Standard Deviations

26) For the pair of histograms below, determine which distribution has the larger standard deviation.

A) (ii) has a larger standard deviation than (i).

B) There is no way to determine which one is larger.

C) Both histograms have the same standard deviation.

D) (i) has a larger standard deviation than (ii).

Objective: (2) Compare Means and Standard Deviations

7

27) For the pair of histograms below, determine which distribution has the smaller standard deviation.

A) There is no way to determine which one is smaller.

B) (ii) has a smaller standard deviation than (i).

C) Both histograms have the same standard deviation.

D) (i) has a smaller standard deviation than (ii).

Objective: (2) Compare Means and Standard Deviations

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

28) For the pair of histograms below, determine which distribution has the smaller standard deviation. Why?

Objective: (2) Compare Means and Standard Deviations

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the empirical rule to solve the problem.

29) At one college, GPA's have a distribution that is unimodal and symmetric with a mean of 2.6 and a standard deviation of 0.5. What is the range of GPA's from one standard deviation below the mean to one standard deviation above the mean?

A) 2.6 to 3.1 B) 2.1 to 3.1 C) 0.5 to 3.1 D) 2.1 to 2.6 Objective: (3) Use Means and Standard Deviations

8

30) At one college, GPA's have a distribution that is unimodal and symmetric with a mean of 2.6 and a standard deviation of 0.5. Is a GPA of 3.8 more than one standard deviation above the mean?

A) Yes B) No Objective: (3) Use Means and Standard Deviations

Use the following information to answer the question. The mean age of lead actresses from the top ten grossing movies of 2010 was 29.6 years with a standard deviation of 6.35 years. Assume the distribution of the actresses' ages is approximately unimodal and symmetric.

31) Between what two values would you expect to find about 95% of the lead actresses ages?

A) 16.9 and 42.3 years B) 10.55 and 48.65 years C) 23.25 and 35.95 years D) None of these Objective: (1) Use the Empirical Rule

32) Between what two values would you expect to find about 68% of the lead actresses ages?

A) 23.25 and 35.95 years B) 16.9 and 42.3 years C) 10.55 and 48.65 years D) None of these Objective: (1) Use the Empirical Rule

33) In 1993, actress Anna Paquin won an academy award in for the movie "The Piano." She was 11-years-old. Finish the statement: "According to the Empirical Rule, the ages of nearly all lead actresses will be between and

years. Anna Paquin was

this range when she won the academy award."

A) 23.3; 36.0; within C) 10.6; 48.7; not within

B) 10.6; 48.7; within D) 16.9; 42.3; not within

Objective: (1) Use the Empirical Rule

Use the following information to answer the question. The mean age of lead actors from the top ten grossing movies of 2007 was 36.4 years with a standard deviation of 9.87 years. Assume the distribution of the actors ages is approximately unimodal and symmetric.

34) Between what two values would you expect to find about 68% of the lead actors ages?

A) 16.66 and 56.14 years B) 26.53 and 46.27 years C) 6.87 and 66.01 years D) None of these Objective: (1) Use the Empirical Rule

35) Between what two values would you expect to find about 95% of the lead actors ages?

A) 6.87 and 66.01 years B) 16.66 and 56.14 years C) 26.53 and 46.27 years D) None of these Objective: (1) Use the Empirical Rule

36) In 2002, actor Adrian Brody won an academy award in for the movie "The Pianist." He was 29-years-old. Finish the statement: "According to the Empirical Rule, the ages of nearly all lead actors will be between and years. Adrien Brody was

this range when she won the academy award."

A) 26.5; 46.3; not within C) 6.8; 66.0; within

B) 16.7; 56.1; within D) 6.8; 66.0; not within

Objective: (1) Use the Empirical Rule

9

Use the following information to answer the question. The economic impact of an industry, such as sport fishing, can be measured by the retail sales it generates. In 2006, the economic impact of great lakes fishing in states bordering the great lakes had a mean of $318 and a standard deviation of $83.5. Note that all dollar amounts are in millions of dollars.

Assume the distribution of retail sales is unimodal and symmetric. (Source: National Oceanic and Atmospheric Administration).

37) For what percentage of great lakes states would you expect the economic impact from fishing to be between $234.5 and $401.5 (in millions of dollars)?

A) Nearly all B) 95% C) 68% D) None of these Objective: (1) Use the Empirical Rule

38) The economic impact of fishing for nearly all great lakes states should fall within what range (in millions of dollars)?

A) $234.5 to $401.5 B) $151 to $485 C) $83.5 to $318 D) $67.5 to $568.5 Objective: (1) Use the Empirical Rule

39) For what percentage of great lakes states would you expect the economic impact from fishing to be between $151.00 and $485.00 (in millions of dollars)?

A) 95% B) Nearly all C) 68% D) None of these Objective: (1) Use the Empirical Rule

Provide an appropriate response.

40) The amount of television viewed by today's youth is of primary concern to Parents Against Watching Television (PAWT). 300 parents of elementary school-aged children were asked to estimate the number of hours per week that their child watched television. The mean and the standard deviation for their responses were 12 and 2, respectively. PAWT constructed a stem-and-leaf display for the data that showed that the distribution of times was a bell-shaped distribution. Give an interval around the mean where you believe most (approximately 95%) of the television viewing times fell in the distribution.

A) less than 10 and more than 14 hours per week B) between 6 and 18 hours per week C) between 10 and 14 hours per week D) between 8 and 16 hours per week Objective: (1) Use the Empirical Rule

41) A small computing center has found that the number of jobs submitted per day to its computers has a distribution that is approximately bell shaped, with a mean of 60 jobs and a standard deviation of 6. Where do we expect most (approximately 95%) of the distribution to fall?

A) between 48 and 78 jobs per day B) between 42 and 78 jobs per day C) between 48 and 72 jobs per day D) between 54 and 66 jobs per day Objective: (1) Use the Empirical Rule

Solve the problem.

42) A class of 30 introductory statistics students took a quiz worth 100 points. The standard deviation of the scores was 0. What must be true about the students' scores?

A) Every student received the same score.

B) Every student scored 100 on the quiz.

C) The mean, median, and mode must all be 0.

D) There was an error in the calculation for standard deviation.

Objective: (1) Use the Empirical Rule

10

43) A class of 30 French students took a quiz worth 50 points. The standard deviation of the scores was 0. What must be true about the students' scores?

A) There was an error in the calculation for standard deviation.

B) Every student scored 50 on the quiz.

C) The mean, median, and mode must all be 0.

D) Every student received the same score.

Objective: (1) Use the Empirical Rule

Use the following information to answer the question. The distribution of the number of hours of sleep people get per night is unimodal and symmetric with a mean of 6 hours and a standard deviation of 1.5 hours.

44) Approximately what percent of people sleep between 6 and 7.5 hours per night?

A) 16% B) 68% C) 34% D) 24% Objective: (1) Use the Empirical Rule

Use the following information to answer the question. The distribution of the number of hours people spend at work per day is unimodal and symmetric with a mean of 8 hours and a standard deviation of 0.5 hours.

45) 95% of all people work between ______ and ______ hours per day?

A) 7.5 and 8.5 hours B) 7 and 8.5 hours C) 7 and 9 hours D) 7.5 and 9 hours Objective: (1) Use the Empirical Rule

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Use the following information to answer the question. A math professor has two routes he can take to campus. The length of time it takes to drive each of these routes depends on traffic. Route A has a mean travel time of 20 minutes, with a standard deviation of 4 minutes. Route B has a mean travel time of 16 minutes, with a standard deviation of 3 minutes.

Assume that both distributions are unimodal and roughly symmetric.

46) If the professor takes Route A, how often will he be able to drive to campus between 16 and 24 minutes?

Objective: (1) Use the Empirical Rule

Solve the problem.

47) A class of 20 history students took a quiz worth 100 points. The standard deviation of the scores was 0.

What can you say about the scores of the students on this quiz?

Objective: (1) Use the Empirical Rule

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the following information to answer the question. The mean age of lead actresses from the top ten grossing movies of 2010 was 29.6 years with a standard deviation of 6.35 years. Assume the distribution of the actresses' ages is approximately unimodal and symmetric.

48) In 2010, popular actress Jennifer Aniston was 41-years-old. What is Jennifer Aniston's age if it is standardized?

Would it be unusual for a 41-year-old actress to be in a top-grossing film of 2010? Assume the Empirical Rule applies and round to the nearest hundredth.

A) z = 1.80; It would not be unusual.

B) z = -1.80; It would not be unusual.

C) z = -1.80; It would be unusual.

D) z = 1.80; It would be unusual.

Objective: (2) Solve Problems Using z-Scores

11

Use the following information to answer the question. The mean age of lead actors from the top ten grossing movies of 2007 was 36.4 years with a standard deviation of 9.87 years. Assume the distribution of the actors ages is approximately unimodal and symmetric.

49) In 2007, popular actor and singer Justin Timberlake was 26-years-old. What is Justin Timberlake's age in 2007 if it is standardized? Would it be unusual for a 26-year-old actor to be in a top-grossing film of 2007? Assume the Empirical Rule applies and round to the nearest hundredth.

A) z = -1.05; It would not be unusual.

B) z = 1.05; It would not be unusual.

C) z = 1.05; It would be unusual.

D) z = -1.05; It would be unusual.

Objective: (2) Solve Problems Using z-Scores

Use the following information to answer the question. The economic impact of an industry, such as sport fishing, can be measured by the retail sales it generates. In 2006, the economic impact of great lakes fishing in states bordering the great lakes had a mean of $318 and a standard deviation of $83.5. Note that all dollar amounts are in millions of dollars.

Assume the distribution of retail sales is unimodal and symmetric. (Source: National Oceanic and Atmospheric Administration).

50) If a new report came out saying that the economic impact of great lakes sport fishing on the economy of Illinois was $93,588,546, would you say this was unusual? Note that this dollar amount must be converted before calculating a standard score.

A) No, it is in the range of typical values.

B) Yes, it is unusually high.

C) Not enough information available D) Yes, it is unusually low.

Objective: (2) Solve Problems Using z-Scores

Solve the problem.

51) The mean price of a pound of ground beef in 75 cities in the Midwest is $2.11 and the standard deviation is $0.56.

A histogram of the data shows that the distribution is symmetrical. A local Midwest grocer is selling a pound of ground beef for $3.25. What is this price in standard units? Assuming the Empirical Rule applies, would this price be unusual or not? Round to the nearest hundredth.

A) z = -2.04; This is unusually inexpensive ground beef.

B) z = 2.04; This is unusually expensive ground beef.

C) z = 2.04; This price would not be unusual.

D) z = -2.04; This price would not be unusual.

Objective: (2) Solve Problems Using z-Scores

52) In 2007, the mean price per pound of lobster in New England was $11.48 and the standard deviation was $2.12. A histogram of the data shows that the distribution is symmetrical. A local New England grocer is selling lobster for $8.99 per pound. What is this price in standard units? Assuming the Empirical Rule applies, would this price be considered unusual or not? Round to the nearest hundredth.

A) z = 1.17; This is unusually expensive lobster.

B) z = 1.17; This price would not be unusual.

C) z = -1.17; This is unusually inexpensive lobster.

D) z = -1.17; This price would not be unusual.

Objective: (2) Solve Problems Using z-Scores

Provide an appropriate response.

53) Many firms use on-the-job training to teach their employees new software. Suppose you work in the personnel department of a firm that just finished training a group of its employees in new software, and you have been requested to review the performance of one of the trainees on the final test that was given to all trainees. The mean and standard deviation of the test scores are 76 and 4, respectively, and the distribution of scores is mound-shaped and symmetric. Suppose the trainee in question received a score of 67. Compute the trainee's z-score.

A) z = 2.25 B) z = -2.25 C) z = 0.83 D) z = -0.83 Objective: (2) Solve Problems Using z-Scores

12

54) A television station claims that the amount of advertising per hour of broadcast time has an average of 12 minutes and a standard deviation equal to 1.7 minutes. You watch the station for 1 hour, at a randomly selected time, and carefully observe that the amount of advertising time is equal to 19 minutes. Calculate the z-score for this amount of advertising time.

A) z = 1.44 B) z = 4.12 C) z = -4.12 D) z = -1.44 Objective: (2) Solve Problems Using z-Scores

Use the following information to answer the question. The distribution of the number of hours people spend at work per day is unimodal and symmetric with a mean of 8 hours and a standard deviation of 0.5 hours.

55) If Anthony's z-score for his work hours was -1.3, how many hours did he work?

A) 7.50 hours B) 8.65 hours C) 7.35 hours D) 7.20 hours Objective: (2) Solve Problems Using z-Scores

56) If Anthony's z-score for his work hours was -1.3, explain what this value means in terms of the number of hours he works.

A) Anthony works 1.3 hours less than the average person.

B) The number of hours Anthony works is 1.3 standard deviations above the mean.

C) Anthony works 1.3 hours more than the average person.

D) The number of hours Anthony works is 1.3 standard deviations below the mean.

Objective: (2) Solve Problems Using z-Scores

57) If Stacy worked 8.7 hours yesterday, would you consider this unusual?

A) Yes, 8.7 hours is more than 2 standard deviations above the mean.

B) No, 8.7 hours is less than 1 standard deviations above the mean.

C) Yes, 8.7 hours is more than 1 standard deviations above the mean.

D) No, 8.7 hours is less than 2 standard deviations above the mean.

Objective: (2) Solve Problems Using z-Scores

Use the following information to answer the question. The distribution of the number of hours of sleep people get per night is unimodal and symmetric with a mean of 6 hours and a standard deviation of 1.5 hours.

58) If James had a z-score of 1.2, how many hours did he sleep?

A) 8.0 hours B) 7.8 hours C) 8.2 hours D) 7.5 hours Objective: (2) Solve Problems Using z-Scores

59) If James had a z-score of 1.2, explain what this value means in terms of the number of hours of sleep he gets.

A) The number of hours James sleeps is 1.2 standard deviations above the mean.

B) The number of hours James sleeps is 1.2 standard deviations below the mean.

C) James sleeps 1.2 hours more than the average person.

D) James sleeps 1.2 hours less than the average person.

Objective: (2) Solve Problems Using z-Scores

60) If Amanda slept 9.2 hours last night, would you consider this unusual?

A) No, 9.2 hours is less than 3 standard deviations above the mean.

B) Yes, 9.2 hours is more than 3 standard deviations above the mean.

C) No, 9.2 hours is less than 2 standard deviations above the mean.

D) Yes, 9.2 hours is more than 2 standard deviations above the mean.

Objective: (2) Solve Problems Using z-Scores

13

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Use the following information to answer the question. A math professor has two routes he can take to campus. The length of time it takes to drive each of these routes depends on traffic. Route A has a mean travel time of 20 minutes, with a standard deviation of 4 minutes. Route B has a mean travel time of 16 minutes, with a standard deviation of 3 minutes.

Assume that both distributions are unimodal and roughly symmetric.

61) Today, the z-score for the professor's travel time was -2.1. How many minutes did it take him to drive to campus if he took Route B? Objective: (2) Solve Problems Using z-Scores

62) Explain what a z-score of 1.3 would mean if the professor took Route A. Objective: (2) Solve Problems Using z-Scores

63) If it took the professor 24 minutes to drive to campus using Route B one day, would you consider this an unusual drive time? Why? Objective: (2) Solve Problems Using z-Scores

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

64) Suppose we have a distribution of the number of "friends" all users of a popular social media site have.

What measure of spread would be best to describe this data?

A) spread should be described with the IQR because the distribution will be symmetric.

B) The spread should be described with the IQR because the distribution will be skewed to the right.

C) The spread should be described with the standard deviation because the distribution will be symmetric.

D) The spread should be described with the standard deviation because the distribution will be skewed to the right.

Objective: (1) Understand Concepts Related to Measures of Center and Spread

65) Suppose we have a distribution of student exam scores on an easy test. What measure of spread would be best to describe this data?

A) The spread should be described with the IQR because the distribution will be skewed to the left.

B) spread should be described with the IQR because the distribution will be symmetric.

C) The spread should be described with the standard deviation because the distribution will be skewed to the left.

D) The spread should be described with the standard deviation because the distribution will be symmetric.

Objective: (1) Understand Concepts Related to Measures of Center and Spread

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

66) Suppose we have the distribution of household income in the United States. What measures of center and spread would be best to describe this data?

Objective: (1) Understand Concepts Related to Measures of Center and Spread

14

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the following information to answer the question. Here is a table recording the number of deaths for the top thirteen worst U.S. tornados since 1925. A histogram showing the distribution is also included.

67) Estimate the most appropriate measure of variability.

A) IQR; 156 C) Standard Deviation; 169.4

B) IQR; 574 D) Standard Deviation; 178.5

Objective: (2) Find the Median and Interquartile Range of a Data Set

Find the median for the given sample data.

68) The salaries of ten randomly selected doctors are shown below. $123,000 $112,000 $187,000 $205,000 $218,000 $119,000 $119,000 $842,000 $235,000 $186,000

A) $235,000

B) $261,000

C) $187,000

D) $186,500

Objective: (2) Find the Median and Interquartile Range of a Data Set

69) A new business had the following monthly net gains: $6992 $3051 $1040 $8048 $6496 $2296 $2375 $7300 $4597 $4615

A) $4597.00

B) $4606.00

C) $5201.11

Objective: (2) Find the Median and Interquartile Range of a Data Set

15

D) $4681.00

70) In ten trips to Las Vegas, a person had the following net gains: $2001 $2597 $4870 $6672 $2581 $3149 $6155 $7775 $6033 $4694

A) $4653.20

B) $4870

C) $4782.00

D) $5170.72

Objective: (2) Find the Median and Interquartile Range of a Data Set

71) A store manager kept track of the number of newspapers sold each week over a seven-week period. The results are shown below.

58, 48, 223, 156, 289, 248, 238

A) 156 newspapers

B) 180 newspapers

C) 223 newspapers

D) 238 newspapers

Objective: (2) Find the Median and Interquartile Range of a Data Set

72) The number of vehicles passing through a bank drive-up line during each 15-minute period was recorded. The results are shown below.

22 24 22 25 25 22 27 24 32 28 28 26 21 28 22 17 12 24 24 24 A) 28 vehicles

B) 25 vehicles

C) 23.85 vehicles

D) 24 vehicles

Objective: (2) Find the Median and Interquartile Range of a Data Set

Determine the interquartile range.

73) Determine the interquartile range.

2, 3, 6, 8, 10, 12, 2, 3, 6, 8, 10, 12 A) 7

B) 6.5

C) 3

D) 7.5

Objective: (2) Find the Median and Interquartile Range of a Data Set

74) The test scores of 19 students are listed below. Find the interquartile range.

91 46 86 62 97 57 82 83 54 41 92 94 A) 32.5

71 58 90 77 88 74 67

B) 32

C) 77

Objective: (3.3) Find the Median and Interquartile Range of a Data Set

16

D) 31.5

75) The weekly salaries (in dollars) of sixteen government workers are listed below. Find the interquartile range.

787 641 820 475 609 535 584 699 875 591 460 546 A) $297

677 655 501 490

B) $170.00

C) $184.00

D) $176

Objective: (2) Find the Median and Interquartile Range of a Data Set

Solve the problem.

76) The number of students enrolled in a college algebra class for the last seven semesters are listed below. Find the median.

71 68 68 76 72 73 68

A) 76

B) 71

C) 70

D) 68

Objective: (2) Find the Median and Interquartile Range of a Data Set

77) The number of students enrolled in a college algebra class for the last seven semesters are listed below. Find the median.

60 61 55 57 64 58 58

A) 60

B) 59

C) 58

D) 57

Objective: (2) Find the Median and Interquartile Range of a Data Set

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

78) The number of dogs available at a local animal shelter was recorded for the past 8 days. Find the median.

53 27 45 43 46 67 50 32 Objective: (2) Find the Median and Interquartile Range of a Data Set

17

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

79) Here are the ages of the male and female employees at First River Bank. Compare the interquartile ranges of the ages of male and female employees.

Male Female 18 21 19 21 21 23 21 26 24 26 26 28 27 29 28 35 29 37 A) Male: 7.5 Female: 9

B) Male: 7.5 Female: 10

C) Male: 7 Female: 10

D) Male: 7 Female: 10.5

Objective: (3) Compare Medians and Interquartile Ranges

80) Here are the heights in inches of the male and female employees at First City Bank. Compare the interquartile ranges of the heights of male and female employees.

Male Female 62 56 64 59 66 60 66 62 68 66 70 66 73 68 75 71 78 73 A) Male: 9 Female: 10

B) Male: 9 Female: 9

C) Male: 9.5 Female: 10

Objective: (3) Compare Medians and Interquartile Ranges

18

D) Male: 8 Female: 10.5

Use the following information to answer the question. Here is a table recording the number of deaths for the top thirteen worst U.S. tornados since 1925. A histogram showing the distribution is also included.

81) The worst tornado on record since 1925 is a tornado that went through Missouri, Illinois, and Indiana on March 18, 1925. It killed 689 people. Suppose that when this value was entered into a calculator or other software a mistake was made and it was entered as 1,689. Choose the statement that describes what affect this mistake will have on the mean and median.

A) The median and the mean will not be affected by the error. Both measures of center are resistant to extreme values.

B) The median will not be affected by the error, but the mean will be higher than it should be.

C) The median will be higher than it should be, but the mean will not be affected by the error.

D) Both the median and the mean will be higher than they should be.

Objective: (1) Understand Concepts Related to Outliers, Including How they Influence Measures of Center

Solve the problem. Round monetary amounts to the nearest dollar.

82) Packages of a certain candy vary slightly in weight. Here are the measured weights of nine packages, in ounces: 1.8223 1.8244 1.8251 1.8266 1.7962 1.8248 1.8229 1.8235 1.8258 a. Find the mean and the median of these weights. b. Which, if any, of these weights would you consider to be an outlier? c. What are the mean and median weights if the outlier is excluded?

A) a. Mean: 1.8213; median: 1.8244 B) a. Mean: 1.8213; median: 1.8244 b. 1.7962 is an outlier. b. 1.7962 is an outlier. c. Mean: 1.8244; median: 1.8244 c. Mean: 1.8244; median: 1.8256 C) a. Mean: 1.8213; median: 1.8244 D) a. Mean: 1.8213; median: 1.8244 b. There is no outlier. b. 1.7962 is an outlier. c. No change. Mean: 1.8213; median: 1.8244 c. Mean: 1.8244; median: 1.8246 Objective: (1) Understand Concepts Related to Outliers, Including How they Influence Measures of Center

19

Solve the problem.

83) The distributions of income in the United States is strongly skewed to the right. Which of the following is true?

A) There is not enough information to compare the median and mean values.

B) The median income is smaller than the mean income.

C) The median income is equal to the mean income.

D) The median income is larger than the mean income.

Objective: (1) Understand Concepts Related to Outliers, Including How they Influence Measures of Center

84) The distribution of the number of "friends" all users of a popular social media site have is strongly skewed to the right. Which of the following is true?

A) The median number of friends is smaller than the mean.

B) The median number of friends is larger than the mean.

C) There is not enough information to compare the median and mean values.

D) The median number of friends is equal to the mean.

Objective: (1) Understand Concepts Related to Outliers, Including How they Influence Measures of Center

85) Suppose we have a data set of the number of car accidents per day in Los Angeles during the year 2013.

The data was input into a spreadsheet manually by an assistant at the Department of Transportation. For one day in June 2013, he input that there were 1230 car accidents; but there were actually only 123 that day. How will this error affect the measures of center for this data?

A) The median will be higher than it should be, but the mean will not be affected.

B) The mean and the median will be higher than they should be.

C) The mean will be higher than it should be, but the median will not be affected.

D) The mean and the median will not be affected by this error.

Objective: (1) Understand Concepts Related to Outliers, Including How they Influence Measures of Center

86) Suppose we have a data set of the number of car accidents per day in Los Angeles during the year 2013.

The data was input into a spreadsheet manually by an assistant at the Department of Transportation. For one day in July 2013, he input that there were 14 car accidents; but there were actually only 140 that day.

How will this error affect the measures of center for this data?

A) The median will be lower than it should be, but the mean will not be affected.

B) The mean and the median will not be affected by this error.

C) The mean will be lower than it should be, but the median will not be affected.

D) The mean and the median will be lower than they should be.

Objective: (1) Understand Concepts Related to Outliers, Including How they Influence Measures of Center

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

87) For a left-skewed distribution, how will the median value compare to the mean value?

Objective: (1) Understand Concepts Related to Outliers, Including How they Influence Measures of Center

88) Suppose we have a data set of the number of car accidents per day in Los Angeles during the year 2013.

The data was input into a spreadsheet manually by an assistant at the Department of Transportation. For one day in July 2013, he input that there were 1500 car accidents; but there were actually only 150 that day. How will this error affect the measures of center for this data?

Objective: (1) Understand Concepts Related to Outliers, Including How they Influence Measures of Center

20

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the following information to answer the question. Here is a table recording the number of deaths for the top thirteen worst U.S. tornados since 1925. A histogram showing the distribution is also included.

89) Choose the most appropriate measure of center then calculate the typical value rounded to the nearest tenth.

A) Mean; 239.9 B) Mean; 181.0 C) Median; 181.0 D) Median; 239.9 Objective: (2) Determine an Appropriate Measure of Center

Provide an appropriate response.

90) The annual profits of five large corporations in a certain area are given below. Which measure of central tendency should be used? $139,000 $147,000 $167,000 $137,000 $1,217,000 A) standard deviation B) median C) mode D) mean Objective: (2) Determine an Appropriate Measure of Center

21

Use the side-by-side boxplots below to answer the question. The boxplots summarize the number of sentenced prisoners by state in the Midwest and West.

91) Pick the statement that best describes the shape of the distribution for the states in the West.

A) The data appears to be left-skewed with large variability.

B) The data appears to be right-skewed with a possible outlier.

C) The data appears to be roughly symmetrical with a possible outlier.

Objective: (1) Interpret Boxplots

92) Based on the boxplot for the Midwest, which of the following is true?

A) 50% of the states sentenced less than 4,322 prisoners.

B) 50% of the states sentenced more than 29,928 prisoners.

C) 25% of the states sentenced more than 29,928 prisoners.

D) 25% of the states sentenced less than 1,435 prisoners.

Objective: (1) Interpret Boxplots

93) Using the boxplot for the Midwest, determine which of the following statements about the distribution cannot be justified.

A) The distribution is skewed to the right.

B) The range is 32,467.

C) About 75% of the West states had 3,887 or more prisoners.

D) There are fewer states with 3887.5 to 6887 prisoners than states with 6887 to 15,706 prisoners.

Objective: (1) Interpret Boxplots

94) Pick the statement that best describes the shape of the distribution for the states in the Midwest.

A) The data appears to be roughly symmetrical with a possible outlier.

B) The data appears to be right-skewed with large variability.

C) The data appears to be right-skewed with a possible outlier.

D) The data appears to be left-skewed with large variability.

Objective: (1) Interpret Boxplots

95) Based on the boxplot for the West, which of the following is true?

A) 25% of the states sentenced less than 3,888 prisoners.

B) 50% of the states sentenced less than 15,706 prisoners.

C) 25% of the states sentenced more than 15,706 prisoners.

D) 50% of the states sentenced less than 22,662 prisoners.

Objective: (1) Interpret Boxplots

22

96) Using the boxplot for the West, determine which of the following statements about the distribution cannot be justified.

A) The interquartile range is about 11,819.

B) There are fewer states with 3887.5 to 6887 prisoners than states with 6887 to 15,706 prisoners.

C) The distribution is skewed to the right.

D) The range is 32,467.

E) About 75% of the West states had 3,887 or more prisoners.

Objective: (1) Interpret Boxplots

The following boxplot contains information about the length of time (in minutes) it took women participants to finish the marathon race at the 2012 London Olympics.

97) What can be said about the shape of the distribution of women's running times for the marathon?

A) The distribution is right-skewed.

B) The distribution is symmetric.

C) The distribution is unimodal.

D) The distribution is left-skewed.

Objective: (1) Interpret Boxplots

98) The fastest 25% of women participants ran the marathon how quickly?

A) More than 155 minutes.

B) Less than 155 minutes.

C) More than 160 minutes.

D) Less than 150 minutes.

Objective: (1) Interpret Boxplots

23

The following boxplot contains information about the length of time (in minutes) it took men participants to finish the marathon race at the 2012 London Olympics.

99) What can be said about the shape of the distribution of men's running times for the marathon?

A) The distribution is left-skewed.

B) The distribution is right-skewed.

C) The distribution is unimodal.

D) The distribution is symmetric.

Objective: (1) Interpret Boxplots

100) The slowest 25% of men participants ran the marathon how quickly?

A) Less than 136 minutes.

B) More than 143 minutes.

C) Less than 139 minutes.

D) More than 139 minutes.

Objective: (1) Interpret Boxplots

24

Solve the problem.

101) The boxplots below represent movie runtimes (length of a movie in minutes) for movies that have been rated by the Motion Picture Association of America as R, PG-13, PG, and G. List ratings according to their median runtimes, from shortest to longest.

A) G, PG, R, PG-13

B) G, PG, PG-13, R

C) PG-13, R, PG, G

D) R, PG-13, PG, G

Objective: (1) Interpret Boxplots

102) The boxplots below represent movie runtimes (length of a movie in minutes) for movies that have been rated by the Motion Picture Association of America as R, PG-13, PG, and G. List ratings according to their median runtimes, from longest to shortest.

A) R, PG-13, PG, G

B) G, PG, R, PG-13

Objective: (1) Interpret Boxplots

25

C) PG-13, R, PG, G

D) G, PG, PG-13, R

103) What feature of a distribution can NOT be determined from a boxplot?

A) Center B) Skewness C) Modality

D) Spread

Objective: (1) Interpret Boxplots

104) What feature of a distribution can NOT be determined from a boxplot?

A) Skewness B) Number of observations C) Spread D) Center Objective: (1) Interpret Boxplots

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

105) The boxplots below represent critics' movie ratings (from 0 to 100) for movies that have been rated by the Motion Picture Association of America as R, PG-13, PG, and G. List the movie ratings according to their median critics' rating, from worst to best.

Objective: (1) Interpret Boxplots

26

106) Approximately what value corresponds to the first quartile of the following boxplot?

Objective: (1) Interpret Boxplots

107) What is one feature of a distribution that can NOT be determined from a boxplot?

Objective: (1) Interpret Boxplots

The following boxplot contains information about the length of time (in minutes) it took men participants to finish the marathon race at the 2012 London Olympics.

108) What do the dots on the right side of the boxplot represent? What does this mean in terms of marathon times?

Objective: (1) Interpret Boxplots

109) The fastest 25% of men participants ran the marathon how quickly?

Objective: (1) Interpret Boxplots

27

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

110) Calculate the five-number summary for the following dataset.

51 53 62 34 36 39 43 63 73 79 A) 34, 37.5, 51, 62.5, 73 B) 34, 39, 52, 63, 79 C) 34, 37.5, 53, 68, 79

D) 32, 39, 52, 63, 79

Objective: (2) Construct Boxplots

111) Calculate the five-number summary for the following dataset.

41.19, 83.51, 19.98, 114.60, 63.08, 83.88 A) 19.98, 41.19, 73.295, 83.88, 114.6 B) 19.98, 41.19, 75, 115, 83.88 C) 19, 41, 63, 84, 115 D) 41.19, 73.295, 83.88, 114.6 Objective: (2) Construct Boxplots

Obtain the five-number summary for the given data.

112) 2, 4, 6, 8, 9, 11, 13 A) 2, 6, 8, 9, 13 B) 2, 4, 8, 11, 13

C) 2, 5.5, 6, 4.5, 13

Objective: (2) Construct Boxplots

Solve the problem.

113) Which boxplot represents the same data as the histogram shown below?

A)

B)

28

D) 2, 5, 8, 10, 13

C)

D)

Objective: (2) Construct Boxplots

114) Which boxplot represents the same data as the histogram shown below?

A)

B)

29

C)

D)

Objective: (2) Construct Boxplots

115) Calculate the five-number summary for the following dataset.

51 53 62 34 36 39 43 63 73 79 A) 34, 39, 52, 63, 79 B) 34, 37.5, 53, 68, 79 C) 32, 39, 52, 63, 79

D) 34, 37.5, 51, 62.5, 73

Objective: (2) Construct Boxplots

116) Calculate the five-number summary for the following dataset.

41.19, 83.51, 19.98, 114.60, 63.08, 83.88 A) 41.19, 73.295, 83.88, 114.6 B) 19.98, 41.19, 73.295, 83.88, 114.6 C) 19, 41, 63, 84, 115 D) 19.98, 41.19, 75, 115, 83.88 Objective: (2) Construct Boxplots

117) The five-number summary of the ages of passengers on a cruise ship is listed below.

Consider the following two statements regarding outliers for this data and determine which, if any, are correct. (i) There is at least one passenger whose age is a low outlier. (ii) There is at least one passenger whose age is a high outlier.

A) Neither statement (i) or (ii) is correct.

B) Only statement (ii) is correct.

C) Only statement (i) is correct.

D) Both statements (i) and (ii) are correct.

Objective: (2) Construct Boxplots

30

118) The five-number summary of the ages of a group of 100 adults is listed below.

Consider the following two statements regarding outliers for this data and determine which, if any, are correct. (i) There is at least one adult whose age is a low outlier. (ii) There is at least one adult whose age is a high outlier.

A) Only statement (i) is correct.

B) Both statements (i) and (ii) are correct.

C) Only statement (ii) is correct.

D) Neither statement (i) or (ii) is correct.

Objective: (2) Construct Boxplots

119) Ten households were asked how many pets they currently own. The results are shown below.

1

0

2

4

3

2

1

1

6

4

What is the IQR for this set of data?

A) 4 B) 2

C) 3

D) 1

Objective: (2) Construct Boxplots

120) Ten parents were asked the ages of their oldest child. The results are shown below.

29 12 10 6

22 19 16 14 2

28

What is the IQR for this set of data?

A) 12 B) 15

C) 27

D) 10

Objective: (2) Construct Boxplots

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

121) The five-number summary of the length of phone calls of 100 people is listed below.

Consider the following two statements regarding outliers for this data and determine which, if any, are correct. Explain your reasoning. (i) There is at least one person made a phone call that is a low outlier. (ii) There is at least one person made a phone call that is a high outlier.

Objective: (2) Construct Boxplots

122) Ten parents were asked the ages of their youngest child. The results are shown below.

6

25 12 20 6

2

17 22 23 10

What is the IQR for this set of data?

Objective: (2) Construct Boxplots

31

Answer Key Testname: GOULDCH3TESTGEN

1) C 2) B 3) B 4) B 5) A 6) D 7) D 8) A 9) B 10) A 11) A 12) D 13) C 14) C 15) D 16) B 17) B 18) D 19) The mean is approximately 27.

20) Mean Score = (25 · 80) + (30 · 75) = 25 + 30 4250 = 77.27.

55

21) Mean Age = 18 + 18 + 19 + 20 +21 5 =

96 = 19.2 years old.

5

22) D 23) A 24) A 25) C 26) D 27) B 28) Histogram (ii) has the smaller standard deviation because more observations are closer to the mean.

29) B 30) A 31) A 32) A 33) B 34) B 35) B

36) C 37) C 38) B 39) A 40) D 41) C 42) A 43) D 44) C 45) C 46) According to the Empirical Rule, the professor will be able to drive to campus between 16 and 24 minutes 68% of the time. This is because we move one standard deviation above and below the mean (20 - 4 = 16 and 20 + 4 = 24).

47) Every student received the same score on the quiz.

48) A 49) A 50) D 51) B 52) D 53) B 54) B 55) C 56) D 57) D 58) B 59) A 60) D 61) Using the z-score formula, -2.1 = x - 16 . If we solve for 3

62) The number of minutes it took the professor to get to campus is 1.3 standard deviations above the mean. It took him longer than average to get to campus.

63) Yes, 24 minutes is more than 2 standard deviations above the mean (16 + 3 + 3 = 22). Since 24 > 22, it took the professor an unusually long amount of time to get to campus.

64) B 65) A 66) The median should be used to describe the center, and the IQR should be used to describe the spread because the distribution will be skewed to the right.

67) A 68) D 69) B 70) C 71) C 72) D 73) A 74) B 75) B 76) B 77) C

x, we get x = 9.7. So, it took the professor 9.7 minutes to drive to campus.

32

78) The median number of dogs at the animal shelter is 45.5. When the numbers are ordered (27, 32, 43, 45, 46, 50, 53, 67), we see that the median is between 45 and 46.

So, taking the average of those two numbers yields a median of 45.5 dogs.

79) B 80) A 81) B 82) D 83) B 84) A 85) C 86) C 87) For a left-skewed distribution, the median value will be larger than the mean.

88) The mean will be higher than it should be, but the median will not be affected.

This is because the median is resistant to outliers, but the mean is not.

89) C 90) B 91) B 92) C 93) D 94) B 95) C 96) B 97) A 98) D 99) B 100) B 101) A 102) C 103) C 104) B 105) Worst to best: PG, PG-13, R, G.

Answer Key Testname: GOULDCH3TESTGEN

106) Quartile 1 (Q1) is represented by the line that creates the left edge of the box.

The value is greater than 20, but less than 30, so an appropriate estimate for Q1 would be 25.

107) There are 2 answers here: modality and the number of observations in the original data.

108) The dots on the right side of the boxplot represent high outliers. This means that the men whose times are represented by the dots ran the marathon much slower than the rest of the participants.

109) Faster than 136 minutes. (Note: Values may vary based on approximations, but should be between 135 and 137 minutes.)

110) B 111) A 112) D 113) B 114) D 115) A 116) B 117) B 118) C 119) C 120) A

121) Only statement (ii) is correct - there is at least one cell phone which has a battery life that is a high outlier. In order to determine which values may be outliers, use the 1.5IQR Rule as follows:

122) When the values are arranged in order (2, 6, 6, 10, 12, 17, 20, 22, 23, 25), we find that Q3 = 22 and Q1 = 6.

Therefore, IQR = Q3 - Q1 = 22 - 6 = 16.

33

Gould/Ryan/Wong Essentials Statistics 3e Chapter 4 Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

1) Which scatterplot shows a greater strength of association between the variables?

(a)

(b)

A) a

B) b

Objective: (1) Compare Scatterplots to Determine Which One Shows a Greater Strength of Association

Solve the problem.

2) Suppose temperatures and monthly ice cream sales were measured for 100 randomly selected cities. Which variable is the explanatory variable and which one is the response?

A) Temperature is the explanatory variable and ice cream sales is the response because a city's temperature could explain the amount of ice cream sales.

B) Ice cream sales is the explanatory variable and temperature is the response because the ice cream sales could explain the city's temperature.

C) Ice cream sales is the explanatory variable and temperature is the response because a city's temperature could explain the amount of ice cream sales.

D) Temperature is the explanatory variable and ice cream sales is the response because the ice cream sales could explain the city's temperature.

Objective: (1) Compare Scatterplots to Determine Which One Shows a Greater Strength of Association

3) Suppose the ages and heights of 100 randomly selected people were recorded. Which variable is the explanatory variable and which one is the response?

A) Age is the explanatory variable and height is the response because a person's height could explain his/her age.

B) Height is the explanatory variable and age is the response because a person's height could explain his/her age.

C) Height is the explanatory variable and age is the response because a person's age could explain his/her height.

D) Age is the explanatory variable and height is the response because a person's age could explain his/her height.

Objective: (1) Compare Scatterplots to Determine Which One Shows a Greater Strength of Association

1

4) Which scatterplot below depicts a stronger linear relationship? Why?

A) Scatterplot (i) shows a stronger linear relationship because it has less vertical variation between points.

B) Scatterplot (ii) shows a stronger linear relationship because it has more vertical variation between points.

C) Scatterplot (i) shows a stronger linear relationship because it has more vertical variation between points.

D) Scatterplot (ii) shows a stronger linear relationship because it has less vertical variation between points.

Objective: (1) Compare Scatterplots to Determine Which One Shows a Greater Strength of Association

5) Which scatterplot below depicts a stronger linear relationship? Why?

A) Scatterplot (ii) shows a stronger linear relationship because it has more vertical variation between points.

B) Scatterplot (ii) shows a stronger linear relationship because it has less vertical variation between points.

C) Scatterplot (i) shows a stronger linear relationship because it has more vertical variation between points.

D) Scatterplot (i) shows a stronger linear relationship because it has less vertical variation between points.

Objective: (1) Compare Scatterplots to Determine Which One Shows a Greater Strength of Association

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

6) Suppose data were collected on neighborhoods about the number of crimes committed and the number of police who patrol the area. Which variable is the explanatory variable and which one is the response? Explain your reasoning.

Objective: (1) Compare Scatterplots to Determine Which One Shows a Greater Strength of Association

2

7) Which scatterplot below depicts a stronger linear relationship? Why? Explain what the scatterplot shows regarding a tree's volume.

Objective: (1) Compare Scatterplots to Determine Which One Shows a Greater Strength of Association

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

8) The scatterplot below shows the hat size and IQ of some adults. Is the trend positive, negative, or near zero?

A) Negative

B) Near Zero

C) Positive

Objective: (2) Describe and Interpret Increasing Trends, Decreasing Trends, or no Trends from Scatterplots

9) Choose the best statement to summarize the association shown between hat size and IQ in the scatterplot below.

A) As hat size increases, IQ scores tend to decrease.

B) Hat size causes IQ to increase.

C) As hat size increases, IQ scores tend to increase.

D) The scatterplot does not show a trend that would indicate an association between hat size and IQ scores.

Objective: (2) Describe and Interpret Increasing Trends, Decreasing Trends, or no Trends from Scatterplots

3

10) Doctors hypothesize that smoking cigarettes inflames the bronchial tubes and so makes it harder to breathe. They measured the lung capacity (in liters) and the number of cigarettes smoked in a typical day for a sample of adults.

Is the scatterplot below consistent with the researcher's hypothesis?

A) There is no evidence in support or contradiction of the hypothesis.

B) Yes, it is consistent.

C) No, it contradicts this hypothesis.

Objective: (2) Describe and Interpret Increasing Trends, Decreasing Trends, or no Trends from Scatterplots

11) The scatterplot below shows the number of tackles received and the number of concussions received for a team of football players for the most recent season. Choose the statement that best describes the trend.

A) Teams that receive a greater number of tackles tend to receive a lower number of concussions.

B) There is no association between the number of tackles a team receives and the number of concussions.

C) Teams that receive a greater number of tackles tend to have a higher number of concussions.

Objective: (2) Describe and Interpret Increasing Trends, Decreasing Trends, or no Trends from Scatterplots

12) What key things should you look for when examining the potential linear association between two variables?

A) A noticeable overall linear shape on the scatterplot.

B) A noticeable positive or negative trend on the scatterplot.

C) The vertical spread of the points on the scatterplot which indicate the strength of an association.

D) All of these.

Objective: (2) Describe and Interpret Increasing Trends, Decreasing Trends, or no Trends from Scatterplots

4

The scatterplot shows the relationship between average number of years of education and births per woman of child bearing age in selected countries. Use the scatterplot to determine whether the statement is true or false.

13) The graph shows a strong increasing trend.

Births per Woman

A) False

Average number of years of education of Married Women of Child-Bearing Age

B) True

Objective: (2) Describe and Interpret Increasing Trends, Decreasing Trends, or no Trends from Scatterplots

14) The graph shows very little or no trend.

Births per Woman

A) True

Average number of years of education of Married Women of Child-Bearing Age

B) False

Objective: (2) Describe and Interpret Increasing Trends, Decreasing Trends, or no Trends from Scatterplots

5

15) The graph shows a strong decreasing trend.

Births per Woman

A) True

Average number of years of education of Married Women of Child-Bearing Age

B) False

Objective: (2) Describe and Interpret Increasing Trends, Decreasing Trends, or no Trends from Scatterplots

Solve the problem.

16) A study in the Los Angeles Times reported that the number of liquor stores in a neighborhood has a strong positive linear association with the amount of crime in that neighborhood. What can you determine about the relationship between the number of liquor stores and the amount of crime?

A) Neighborhoods with a higher number of liquor stores tend to have a higher amount of crimes.

B) People who live in neighborhoods with more liquor stores commit more crimes.

C) If we decrease the number of liquor stores in a neighborhood, the amount of crimes will decrease.

D) No conclusions can be drawn without seeing a scatterplot of the data.

Objective: (2) Describe and Interpret Increasing Trends, Decreasing Trends, or no Trends from Scatterplots

17) A study about high school student SAT scores reported that a student's SAT Math score has a strong positive linear association with his/her SAT Verbal score. What can you determine about the relationship between SAT Math scores and SAT Verbal scores?

A) If a student’’s SAT Math score decreases, his SAT Verbal score will also decrease.

B) Students who like Math also like Verbal.

C) Students with higher SAT Math scores tend to have higher SAT Verbal scores.

D) No conclusions can be drawn without seeing a scatterplot of the data.

Objective: (2) Describe and Interpret Increasing Trends, Decreasing Trends, or no Trends from Scatterplots

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

18) A study about exercise routines reported that the amount of time a person spends working out has a strong positive linear association with the amount of weight he/she loses. What can you determine about the relationship between amount of time spent at the gym and the amount of weight a person loses?

Objective: (2) Describe and Interpret Increasing Trends, Decreasing Trends, or no Trends from Scatterplots

6

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

19) The following calculator screenshots show the scatterplot and the correlation coefficient between car weight and car length for a sample of 2009 model year cars.

The relationship between "car length" and "car weight" can be described as A) A strong negative linear relationship B) A strong positive linear relationship C) A moderate positive linear relationship D) A weak negative relationship Objective: (1) Identify and Interpret Correlation in a Scatterplot

20) The following calculator screenshots show the scatterplot and the correlation coefficient between the number of days absent and the final grade for a sample of college students in a general education statistics course at a large community college.

The relationship between "days absent" and "final grade" can be described as A) A strong negative linear relationship B) A moderate positive linear relationship C) A weak negative relationship D) A strong positive linear relationship Objective: (1) Identify and Interpret Correlation in a Scatterplot

7

21) The table shows the number of minutes ridden on a stationary bike and the approximate number of calories burned. Plot the points on the grid provided then choose the most likely correlation coefficient from the answer choices below.

A) -0.99

B) -0.20

C) 0.99

D) 0.20

Objective: (1) Identify and Interpret Correlation in a Scatterplot

22) The table shows the number of minutes ridden on a stationary bike and the approximate number of calories burned. Plot the points on the grid provided then choose the most likely correlation coefficient from the answer choices below.

A) 0.99

B) 0.30

C) -0.30

Objective: (1) Identify and Interpret Correlation in a Scatterplot

8

D) -0.99

Choose the scatterplot that matches the given correlation coefficient.

23) r = 0.8787 A)

B)

C)

Objective: (1) Identify and Interpret Correlation in a Scatterplot

9

24) r = -0.6542 A)

B)

C)

Objective: (1) Identify and Interpret Correlation in a Scatterplot

10

25) r = -0.3120 A)

B)

C)

Objective: (1) Identify and Interpret Correlation in a Scatterplot

11

26) r = -0.3526 A)

B)

C)

Objective: (1) Identify and Interpret Correlation in a Scatterplot

12

27) r = 0.8670 A)

B)

C)

Objective: (1) Identify and Interpret Correlation in a Scatterplot

Solve the problem.

28) Which of the following statements regarding the correlation coefficient is not true?

A) The correlation coefficient has values that range from -1.0 to 1.0 inclusive.

B) The correlation coefficient measures the strength of the linear relationship between two numerical variables.

C) A correlation coefficient value of 0.00 indicates that two variables have no linear correlation at all.

D) All of these are true statements.

Objective: (1) Identify and Interpret Correlation in a Scatterplot

29) Which of the following statements regarding the correlation coefficient is not true?

A) A value of 0.00 indicates that two variables are perfectly linearly correlated.

B) The correlation coefficient measures the strength of the linear relationship between two numerical variables.

C) The correlation coefficient has values that range from -1.0 to 1.0 inclusive.

D) All of these are true statements.

Objective: (1) Identify and Interpret Correlation in a Scatterplot

13

30) Which of the following scatterplots shows data with the highest correlation between the explanatory and response variables?

A) B)

C)

D)

Objective: (1) Identify and Interpret Correlation in a Scatterplot

31) Which of the following scatterplots shows data with the highest correlation between the explanatory and response variables?

A) B)

C)

D)

Objective: (1) Identify and Interpret Correlation in a Scatterplot

14

32) Given the following scatterplot, if the point in the upper right corner were removed, what will happen to the value of the correlation coefficient, r?

A) r will get closer to 1.

C) r will get closer to 0.

B) r will not change.

D) r will get closer to -1.

Objective: (1) Identify and Interpret Correlation in a Scatterplot

33) Given the following scatterplot, if a point was added in the upper left corner with an x-value of 10 and a y-value of 20, what would happen to the value of the correlation coefficient, r?

A) r will get closer to -1.

C) r will get closer to 0.

B) r will not change.

D) r will get closer to 1.

Objective: (1) Identify and Interpret Correlation in a Scatterplot

34) Which of the following statements regarding the correlation coefficient is true?

A) A correlation coefficient of -1 means that as one variable increases, the other decreases.

B) A high correlation coefficient tells us the data are linear.

C) A correlation coefficient of 0 means that two variables are perfectly linearly related.

D) The correlation coefficient is a value between 0 and 1.

Objective: (1) Identify and Interpret Correlation in a Scatterplot

15

35) Which of the following statements regarding the correlation coefficient is false?

A) The correlation coefficient is a value between -1 and 1.

B) A correlation coefficient of -1 means that as one variable increases, the other decreases.

C) A high correlation coefficient tells us the data are linear.

D) A correlation coefficient of 1 means that two variables are perfectly linearly related.

Objective: (1) Identify and Interpret Correlation in a Scatterplot

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

36) When will a correlation coefficient be negative?

Objective: (1) Identify and Interpret Correlation in a Scatterplot

37) Which of the following scatterplots shows data with the highest correlation between the explanatory and response variables? Explain your reasoning.

Objective: (1) Identify and Interpret Correlation in a Scatterplot

38) Given the following scatterplot, if the point in the upper left corner were removed, what would happen to the value of the correlation coefficient, r?

Objective: (1) Identify and Interpret Correlation in a Scatterplot

16

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

39) Calculate the linear correlation coefficient for the data below. x -12 -10 -3 -6 -8 -9 -7 -5 -4 -11 -7 -5 12 -3 2 -5 y 4 1 6 9 A) 0.990 B) 0.792 C) 0.819

D) 0.881

Objective: (2) Calculate the Correlation Coefficient of Data

40) Calculate the linear correlation coefficient for the data below. x 3 5 12 9 7 6 8 10 11 4 -1 12 y 15 10 -2 3 7 8 5 0 A) -0.671 B) -0.995 C) -0.778

D) -0.885

Objective: (2) Calculate the Correlation Coefficient of Data

41) Calculate the linear correlation coefficient for the data below. x 0 -2 -3 -1 1 2 -6 -4 3 -5 -1 10 11 y 15 -2 12 1 2 5 9 A) -0.549 B) -0.132 C) -0.104

D) -0.581

Objective: (2) Calculate the Correlation Coefficient of Data

42) The data below are the final exam scores of 10 randomly selected calculus students and the number of hours they slept the night before the exam. Calculate the linear correlation coefficient.

Hours, x 2 4 1 7 1 3 3 4 5 2 Scores, y 62 77 57 85 63 75 82 87 87 68 A) 0.991 B) 0.847 C) 0.761 D) 0.654 Objective: (2) Calculate the Correlation Coefficient of Data

43) The data below are the average one-way commute times (in minutes) of selected students during a summer literature class and the number of absences for those students for the term. Calculate the linear correlation coefficient.

Commute time (min), x 77 90 96 95 93 103 80 105 85 Number of absences, y 1 5 8 8 6 13 2 13 3 A) 0.819 B) 0.881 C) 0.980 D) 0.890 Objective: (2) Calculate the Correlation Coefficient of Data

44) The data below are the ages and annual pharmacy b ills (in dollars) of 9 randomly selected employees. Calculate the linear correlation coefficient.

Age, x 35 38 42 45 48 50 54 58 62 Pharmacy bill ($), y 113 117 120 128 139 142 145 147 149 A) 0.960 B) 0.908 C) 0.890 D) 0.998 Objective: (2) Calculate the Correlation Coefficient of Data

45) The data below are the number of hours worked (per week) and the final grades of 9 randomly selected students from a drama class. Calculate the linear correlation coefficient.

Hours worked, x 1 4 7 5 10 3 16 9 6 Final Grade, y 88 76 70 72 61 82 45 66 72 A) -0.899 B) -0.918 C) -0.991 D) -0.888 Objective: (2) Calculate the Correlation Coefficient of Data

17

46) A manager wishes to determine the relationship between the number of years the manager's sales representatives have been with the company and their average monthly sales (in thousands of dollars). Calculate the linear correlation coefficient.

Years with company, x 2 3 10 7 8 15 3 1 11 Sales, y 24 26 71 55 58 54 41 48 113 A) 0.717 B) 0.561 C) 0.632 D) 0.791 Objective: (2) Calculate the Correlation Coefficient of Data

47) In order for a company's employees to work in a foreign office, they must take a test in the language of the country where they plan to work. The data below shows the relationship between the number of years that employees have studied a particular language and the grades they received on the proficiency exam. Calculate the linear correlation coefficient.

Number of years, x 6 7 7 8 6 9 5 10 6 Grades on test, y 57 64 71 78 69 86 54 89 68 A) 0.891 B) 0.902 C) 0.911 D) 0.934 Objective: (2) Calculate the Correlation Coefficient of Data

48) In an area of the Great Plains, records were kept on the relationship between the rainfall (in inches) and the yield of wheat (bushels per acre). Calculate the linear correlation coefficient.

Rainfall (in inches), x 11 9.3 13.9 13 19.3 10.8 7.5 16.1 16.5 Yield (bushels per acre), y 45.5 41.2 53.8 54 77.4 44.2 26.9 71 73.8 A) 0.900 B) 0.899 C) 0.981 D) 0.998 Objective: (2) Calculate the Correlation Coefficient of Data

49) Calculate the coefficient of correlation, r, letting Row 1 represent the x-values and Row 2 represent the y-values.

Now calculate the coefficient of correlation, r, letting Row 2 represent the x-values and Row 1 represent the y-values. What effect does switching the explanatory and response variables have on the linear correlation coefficient?

Row 1 1 8 5 3 2 4 6 7 0 -1 Row 2 -19 -1 0 -8 -11 -15 -10 -6 -3 -1 A) 0.440; -0.440; The new correlation coefficients is the opposite B) 0.440; 2.273; The new correlation coefficients is the reciprocal C) -0.440; 0.440; The new correlation coefficients is the opposite D) 0.440; 0.440; The correlation coefficient remains unchanged.

Objective: (2) Calculate the Correlation Coefficient of Data

Solve the problem.

50) Suppose 50 married couples are asked to provide their ages. For all couples, the husband is exactly 2 years older than his wife. For example, a 50-year-old husband has a wife who is 48 years old. What is the best estimate of the correlation coefficient between the ages of husbands and their wives?

A) The correlation coefficient between the ages of husbands and wives is equal to 1.

B) The correlation coefficient between the ages of husbands and wives is equal to -1.

C) The correlation coefficient between the ages of husbands and wives is equal to 0.

D) No conclusions can be drawn without seeing a scatterplot of the data.

Objective: (2) Calculate the Correlation Coefficient of Data

18

51) Suppose daily high and low temperature measures were taken for 50 days. For each day, the daily high temperature was exactly 10 degrees higher than the daily low temperature. For example, on a day with a high temperature of 80°, the low temperature was 70°. What is the best estimate of the correlation coefficient between the daily high and daily low temperatures?

A) The correlation coefficient between the daily high and low temperatures is equal to 1.

B) The correlation coefficient between the daily high and low temperatures is equal to 0.

C) No conclusions can be drawn without seeing a scatterplot of the data.

D) The correlation coefficient between the daily high and low temperatures is equal to -1.

Objective: (2) Calculate the Correlation Coefficient of Data

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

52) Suppose the heights of teenagers were recorded in 2003 and then recorded again 5 years later, in 2008. For each person, the height in 2008 was 6 inches (15.24 centimeters) taller than the height in 2003. For example, a teenager who was 53 inches (134.62 cm) tall in 2003 measured at a height of 59 inches (149.86 cm) in 2008. What would be the correlation coefficient between the 2003 heights and the 2008 heights? Explain your reasoning.

Objective: (2) Calculate the Correlation Coefficient of Data

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the following information to answer the question. The following linear regression model can be used to predict ticket sales at a popular water park.

Ticket sales per hour = -631.25 + 11.25(current temperature in °F)

53) What is the predicted number of tickets sold per hour if the temperature is 86°F? Round to the nearest whole ticket.

A) About 301 tickets B) About 336 tickets C) About 252 tickets D) About 276 tickets Objective: (1) Predict Values From a Regression Equation

54) What is the predicted number of tickets sold per hour if the temperature is 79°F? Round to the nearest whole ticket.

A) About 250 tickets B) About 257 tickets C) About 310 tickets D) About 258 tickets Objective: (1) Predict Values From a Regression Equation

Use the following regression equation regarding professor salaries to answer the question. ^

Salary = 95000 + 1280 · (Years) Note that Years is the number of years a professor has worked at a college, and Salary is the annual salary (in dollars) the professor earns.

55) What is the expected salary of a professor who has worked at a college for 15 years?

A) $114,200 B) $95,000 C) $106,700 D) $96,280 Objective: (1) Predict Values From a Regression Equation

19

Use the following regression equation regarding car mileage to answer the question. ^

Highway = 0.892 + 1.337 · (City) Note that City is the estimated miles per gallon (mpg) a car gets while driving on city streets, and Highway is the estimated miles per gallon (mpg) a car gets while driving on highways.

56) What is the expected salary of a professor who has worked at a college for 15 years?

A) 30.8 mpg B) 31.6 mpg C) 21.9 mpg D) 16.5 mpg Objective: (1) Predict Values From a Regression Equation

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Use the following regression equation regarding airline tickets to answer the question. ^

Price = 49 + 0.22 · (Distance) Note that Distance is the amount of miles between the departure and arrival cities, and Price is the cost of an airline ticket.

57) What is the expected ticket price for a flight between Los Angeles and New York City, which are 2448.3 miles apart?

Objective: (1) Predict Values From a Regression Equation

Suppose data were recorded for 100 employees of a large company that included annual salaries and the number of years the employee has been in their current position. The mean annual salary was $58,000 with a standard deviation of 12,500. The mean number of years in the current position is 10 with a standard deviation of 3. The correlation coefficient between the two variables is approximately 0.93.

58) If an employee earns an annual salary of $85,000, approximately how long has she held her current position at the company? Round your answer to the nearest year.

Objective: (1) Predict Values From a Regression Equation

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

59) Suppose it has been established that "annual income" and "Years of college" are linearly related, and that the relationship can be modeled using the following equation: Annual Income = $23,400+$7200(Years of College). In this model, "Annual Income" is the ? variable, and "Years of College" is the ? variable.

The two variables have a

?

linear relationship.

A) Dependent; Independent; Positive C) Independent; Dependent; Negative

B) Independent; Dependent; Positive D) Dependent; Independent; Negative

Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

60) Suppose it has been established that "home value" and "Years of college" are linearly related, and that the relationship can be modeled using the following equation: Home value = $75,000+$12,500(Years of College). In this model, "years of college" is the ? variable, and "home value" is the ? variable. The two variables have a

?

.

A) Independent; Dependent; Negative C) Dependent; Independent; Positive

B) Independent; Dependent; Positive D) Dependent; Independent; Negative

Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

20

61) A veterinarian is going to investigate whether homes with more pets tend to have more fleas. In this scenario, the explanatory variable is and the response variable is .

A) Number of fleas spotted in a period of time; number of pets B) Slope; intercept C) Number of pets; number of fleas spotted in a period of time D) None of these Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

62) A concert ticket agent is going to investigate whether an increase in money spent on radio advertisements for a particular venue tends to lead to more concert ticket sales. In this scenario, the response variable is and the explanatory variable is .

A) Amount of radio advertisement money spent; concert ticket sales B) Slope; intercept C) Concert ticket sales; amount of radio advertisement money spent D) None of these Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

Use the following information to answer the question. The following linear regression model can be used to predict ticket sales at a popular water park.

Ticket sales per hour = -631.25 + 11.25(current temperature in °F)

63) Choose the statement that best states the meaning of the slope in this context.

A) The slope tells us that a one degree increase in temperature is associated with an average increase in ticket sales of 11.25 tickets.

B) The slope tells us that high temperatures are causing more people to buy tickets to the water park.

C) The slope tells us that if ticket sales are decreasing there must have been a drop in temperature.

D) None of these Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

64) In this context, does the intercept have a reasonable interpretation?

A) Not enough information available B) Yes, it is reasonable for people to go to a water park when it is 0°F, so park managers might want to know how many tickets they would sell on average on a 0°F day.

C) No, at a temperature of 0°F, ticket sales would be -631.25 and it is not reasonable (or possible) to have negative ticket sales.

Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

21

Use the following information to answer the question. A random sample of 30 married couples were asked to report the height of their spouse and the height of their biological parent of the same gender as their spouse. The output of a regression analysis for predicting spouse height from parent height is shown. Assume that the conditions of the linear regression model are satisfied.

65) What is the slope of the regression line? Choose the statement that is the correct interpretation of the slope in context.

A) The slope is 0.25. On average, for each 0.25 inches taller a parent is, the spouse is about 1 inch taller, in the sample.

B) The slope is 0.25. On average, for each inch taller a parent is, the spouse is about 0.25 inches taller, in the sample.

C) The slope is 48.40. On average, for each inch taller a parent is, the spouse is about 48.40 inches taller, in the sample.

D) The slope is 48.40. On average, for each inch taller a parent is, the spouse is about 0.25 inches taller, in the sample.

Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

66) If the intercept was 0 and the slope was 1, what would that say about the association?

A) It would mean that the spouse height should not be predicting using parent height.

B) It would mean that on average, the spouse and the parent are the same height.

C) It would mean that on average, the spouse is 1 inch taller than the parent.

D) None of these.

Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

22

Use the following information to answer the question. A random sample of 30 couples who were also new home owners were asked to report the cost of their first house and their combined age when they married. The output of a regression analysis for predicting home cost from combined age is shown. Assume that the conditions of the linear regression model are satisfied.

67) What is the slope of the regression line? Choose the statement that is the correct interpretation of the slope in context.

A) The slope is 73.74. On average, for each additional year in combined age, the home cost is about $2,122.75 higher, in the sample.

B) The slope is 73.74. On average, for couples with a combined age over 73.74, the home cost is an additional $2,122.75 per year over 73.74.

C) The slope is 2122.75. On average, for each additional year in combined age, home cost is about $2,122.75 higher, in the sample.

D) The slope is 2122.75. On average, for each additional $2,122.75 in home cost, the combined age is about 1 year higher, in the sample.

Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

68) If the slope were 1, what would that say about the association?

A) If the slope were 1, it would mean that on average, for every additional year in combined age, the home cost would be $2,122.75 higher.

B) If the slope were 1, it would mean that on average, for every additional year in combined age, the home cost would be 1 dollar more.

C) If the slope were 1, it would mean that on average, for every additional year in combined age, the home cost would be $2,122.75 lower.

D) None of these.

Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

Solve the problem.

69) A horticulturist conducted an experiment on 110 thirty-six inch plant boxes to see if the amount of plant food given to the plant boxes was associated with the number of tomatoes harvested from the plants. The average amount of plant food given was 27.8 milliliters with a standard deviation of 2.1 milliliters. The average number of tomatoes harvested was 7.5 with a standard deviation of 1.5. The correlation coefficient was 0.7691. Use the information to calculate the slope of the linear model that predicts the number of tomatoes harvested from the amount of plant food given. Show your work and round to the nearest hundredth.

A) 0.55 B) -7.50 C) The slope cannot be determined without the actual data.

D) 1.08 Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

23

70) A horticulturist conducted an experiment on 140 thirty-six inch plant boxes to see if the amount of plant food given to the plant boxes was associated with the number of habanera peppers harvested from the plants. The average amount of plant food given was 17.8 milliliters with a standard deviation of 0.7 milliliters. The average number of habanera peppers harvested was 6.5 with a standard deviation of 1.5. The correlation coefficient was 0.8123. Use the information to calculate the slope of the linear model that predicts the number of habanera peppers harvested from the amount of plant food given. Show your work and round to the nearest hundredth.

A) 0.38 B) -1.50 C) 1.74 D) The slope cannot be determined without the actual data.

Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

A random sample of 100 cars was taken and data were recorded on the miles per gallon (mpg) in the city and on the highway. The mean city mpg was 28 with a standard deviation of 9.2. The mean highway mpg was 35 with a standard deviation of 8.6. The correlation coefficient between city mpg and highway mpg is 0.95.

71) Determine the correct value of the slope for the linear model that predicts highway mpg from city mpg and interpret it in context.

A) The slope is 0.888. For every one mpg increase in city mpg, the highway mpg is predicted to increase by 0.888.

B) The slope is 1.016. For every one mpg increase in city mpg, the highway mpg is predicted to increase by 1.016.

C) The slope is 0.888. For every one mpg increase in highway mpg, the city mpg is predicted to increase by 0.888.

D) The slope is 1.016. For every one mpg increase in highway mpg, the city mpg is predicted to increase by 1.016.

Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

72) Determine which is the correct calculation of the intercept for the linear model that predicts highway mpg from city mpg.

A) a = 35 - 1.016(28) = 6.552 B) a = 35 - 0.888(28) = 10.136 C) a = 28 - 0.888(35) = -3.08 D) a = 28 - 1.016(35) = -7.56 Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

Data were recorded for 117 months on a household's gas bill (in dollars) and the average monthly temperatures for its neighborhood. The mean monthly temperature was 48.7°F with a standard deviation of 20.6. The mean gas bill price was $81.20 with a standard deviation of 66.5. The correlation coefficient between monthly temperature and gas bill price is -0.92.

73) Determine the correct value of the slope for the linear model that predicts gas bill price from monthly temperature and interpret it in context.

A) The slope is -2.97. For every one degree increase in monthly temperature, the gas bill price is predicted to decrease by $2.97.

B) The slope is -0.28. For every one degree increase in monthly temperature, the gas bill price is predicted to decrease by $0.28.

C) The slope is -2.97. For every one dollar increase in gas bill price, the monthly temperature is predicted to decrease by 2.97°.

D) The slope is -0.28. For every one dollar increase in gas bill price, the monthly temperature is predicted to decrease by 0.28°.

Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

24

74) Determine which is the correct calculation of the intercept for the linear model that predicts gas bill price from monthly temperature.

A) a = 81.20 + 0.28(48.7) = 94.84 B) a = 81.20 + 2.97(48.7) = 225.84 C) a = 48.7 + 2.97(81.20) = 289.86 D) a = 48.7 + 0.28(81.20) = 71.44 Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

Use the following regression equation regarding professor salaries to answer the question. ^

Salary = 95000 + 1280 · (Years) Note that Years is the number of years a professor has worked at a college, and Salary is the annual salary (in dollars) the professor earns.

75) Interpret the slope in the context of the data.

A) The slope is 95000. For every additional year a professor works at a college, his/her salary is predicted to increase by $95,000.

B) The slope is 1280. For every additional year a professor works at a college, his/her salary is predicted to increase by $1,280.

C) The slope is 95000. If a professor has never worked at a college, his/her salary is expected to be $95,000.

D) The slope is 1280. If a professor has never worked at a college, his/her salary is expected to be $1,280.

Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

76) Interpret the intercept in the context of the data. State whether the value is meaningful.

A) The intercept is 95000. If a professor has completed 0 years of work at a college, his/her salary is expected to be $95,000. The value is meaningful because it represents the starting salary of a professor.

B) The intercept is 95000. For every additional year a professor works at a college, his/her salary is predicted to increase by $95,000. The value is meaningful because the more a person works, the more money he/she typically makes.

C) The intercept is 1280. If a professor has completed 0 years of work at a college, his/her salary is expected to be $1,280. The value is meaningful because it represents the starting salary of a professor.

D) The intercept is 1280. For every additional year a professor works at a college, his/her salary is predicted to increase by $1,280. The value is meaningful because the more a person works, the more money he/she typically makes.

Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

Use the following regression equation regarding car mileage to answer the question. ^

Highway = 0.892 + 1.337 · (City) Note that City is the estimated miles per gallon (mpg) a car gets while driving on city streets, and Highway is the estimated miles per gallon (mpg) a car gets while driving on highways.

77) Interpret the slope in the context of the data.

A) The slope is 1.337. If a car gets 0 mpg in the city, it will get 1.337 mpg on the highway.

B) The slope is 1.337. For every additional mpg a car gets in the city, its highway mpg is predicted to increase by 1.337.

C) The slope is 0.892. For every additional mpg a car gets in the city, its highway mpg is predicted to increase by 0.892.

D) The slope is 0.892. If a car gets 0 mpg in the city, it will get 0.892 mpg on the highway.

Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

25

78) Interpret the intercept in the context of the data. State whether the value is meaningful.

A) The intercept is 0.892. If a car gets 0 mpg in the city, it will get 0.892 mpg on the highway. The value is not meaningful because if a car is not moving, it cannot have a mpg value.

B) The intercept is 1.337. For every additional mpg a car gets in the city, its highway mpg is predicted to increase by 1.337. The value is meaningful.

C) The intercept is 0.892. For every additional mpg a car gets in the city, its highway mpg is predicted to increase by 0.892. The value is meaningful.

D) The intercept is 1.337. If a car gets 0 mpg in the city, it will get 1.337 mpg on the highway. The value is not meaningful because if a car is not moving, it cannot have a mpg value.

Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Use the following regression equation regarding airline tickets to answer the question. ^

Price = 49 + 0.22 · (Distance) Note that Distance is the amount of miles between the departure and arrival cities, and Price is the cost of an airline ticket.

79) Interpret the slope of the regression equation in the context of the data.

Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

80) Interpret the intercept of the regression equation in the context of the data. Explain why the value is or is not meaningful.

Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

Suppose data were recorded for 100 employees of a large company that included annual salaries and the number of years the employee has been in their current position. The mean annual salary was $58,000 with a standard deviation of 12,500. The mean number of years in the current position is 10 with a standard deviation of 3. The correlation coefficient between the two variables is approximately 0.93.

81) Determine the correct value of the slope for the linear model that predicts annual salary from the number of years in current position and interpret it in context.

Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

82) Calculate the value of the intercept for the linear model that predicts annual salary from the number of years in current position and interpret it in context, if appropriate.

Objective: (2) Interpret or Set Up a Regression Equation and/or Scatterplot

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

83) In the NHL, the correlation between "Goals scored per game" and "minutes on the ice" for a team of players is found to be 0.8178. Choose the statement that is true about the coefficient of determination.

A) The coefficient of determination states that about 66.88% of the variation in goals scored per game is explained by minutes on the ice.

B) The coefficient of determination, r2 , is equal to approximately 0.6688.

C) When given as a percent, the coefficient of determination is always between 0 and 100%.

D) All of these are true statements.

Objective: (1) Apply Concepts for Linear Models

26

84) In the NBA, the correlation between "steals per game" and "blocked shots per game" is found to be 0.8045. Choose the statement that is true about the coefficient of determination.

A) The coefficient of determination states that about 64.72% of the variation in blocked shots per game is explained by steals per game.

B) The coefficient of determination, r2 , is equal to approximately 0.6472.

C) When given as a percent, the coefficient of determination is always between 0 and 100%.

D) All of these are true statements.

Objective: (1) Apply Concepts for Linear Models

85) Which of the following is not true about the coefficient of determination, r2 ?

A) In order to interpret r2 the linearity condition of the linear regression model must be satisfied.

B) A hypothesis test should be conducted verify that r2 is large enough to conclude a linear relationship exists.

C) The coefficient of determination, r2 , is a statistic that will give some information about how well the data fits

the model, but it should not be the only piece of information taken into consideration when determining how useful a linear model might be.

D) The coefficient of determination, r2 , ranges from 0% to 100% and represents the amount of variability in the

response variable (y) explained by the regression line.

Objective: (1) Apply Concepts for Linear Models

86) The following model was created to show the association between the number of massages received per month and self-predicted stress level: Stress level = 10 - 0.02(number of massages per month). The coefficient of determination for the model is 0.066 or 6.6%. Choose the true statement regarding this model.

A) The model shows that getting even one massage a month will decrease your stress level.

B) The model shows that there is a negative association between stress level and number of monthly massages, but the relatively small coefficient of determination suggests that very little of the variation is explained by the model, so the model is probably not very good at predicting stress level.

C) The model shows that on average a person getting no massages will always have a stress level of 10.

D) None of these.

Objective: (1) Apply Concepts for Linear Models

27

87) It is determined that a positive linear association exists between age (for children between the ages of 3 and 9 years) and attention span (measured in minutes). The scatterplot below shows the association. The prediction equation is also given. A college instructor uses the model to predict the attention span of the students in her class who have an average age of 29. Choose the best statement to summarize why this is not an appropriate use for the model. attention span = 4.68 + 3.40(age)

A) This is an inappropriate use of the model because a 29-year-old person would be an outlier in this context.

B) This is an inappropriate use of the model because age does not cause attention span to increase. Correlation does not mean causation.

C) This is an inappropriate use of the model because the model was used to make predictions beyond the scope of the data. The college instructor is extrapolating.

Objective: (1) Apply Concepts for Linear Models

88) It is determined that a positive linear association exists between amount of a new smoking cessation drug taken (in milliliters) and weight gain in women (in pounds). The scatterplot below shows the association. The prediction equation is also given. A pharmacy technician uses the model to predict the potential weight gain for a man who takes the recommended dosage. Choose the best statement to summarize why this is not an appropriate use for the model.

A) This is an inappropriate use of the model because taking the smoking cessation drug does not cause weight gain. Correlation does not mean causation.

B) This is an inappropriate use of the model because the model was used to make predictions beyond the scope of the data. The Pharmacy Technician is extrapolating.

C) This is an inappropriate use of the model because a man would be an outlier in this context.

Objective: (1) Apply Concepts for Linear Models

89) For any set of data, the regression equation will always pass through A) Every point in the data set.

B) The point that represents the mean value of x and the mean value of y.

C) The intercept and the slope.

D) At least two points in the data set.

Objective: (1) Apply Concepts for Linear Models

28

90) For any set of data, the regression equation will always pass through A) The point with the smallest value of x and the largest value of x.

B) The point that represents the mean value of x and the mean value of y.

C) Every point in the data set.

D) At least two points in the data set.

Objective: (1) Apply Concepts for Linear Models

91) What effects might an outlier have on a regression equation?

A) An outlier has no effect on a regression equation.

B) An outlier may affect only the correlation coefficient of a regression equation.

C) An outlier may affect both the slope and the correlation coefficient of a regression equation.

D) An outlier may affect only the slope of a regression equation.

Objective: (1) Apply Concepts for Linear Models

92) What effects might an outlier have on the slope of a regression equation?

A) An outlier could either increase or decrease the slope, depending on its location.

B) An outlier always decreases the slope.

C) An outlier always increases the slope.

D) An outlier has no effect on the slope of a regression equation.

Objective: (1) Apply Concepts for Linear Models

93) Which of the following sets of numbers would result in a negative correlation of -1?

A) The correlation coefficient would be unchanged because it is not affected by changes in units.

B) The correlation coefficient would increase because we are adding 12 additional values (one for each month) on the x-axis.

C) The correlation coefficient would decrease because we have less data points per month as opposed to per year.

D) We cannot make any conclusions about the correlation coefficient because we would need to use the new data values to calculate it.

Objective: (1) Apply Concepts for Linear Models

94) Which of the following sets of numbers would result in a positive correlation of 1?

A) B) C)

Objective: (1) Apply Concepts for Linear Models

29

D)

The scatterplot below shows the relationship between the ages of women when they first married and the ages when they had their first child. The correlation coefficient between the values is 0.9315.

The regression equation for the data is ^

Age-first child = 6.404 + 0.955 · (Age-married)

95) Would it be appropriate to say that the age at which a woman first marries causes her to have her first child after that age?

A) Yes, since the correlation coefficient is close to 1, we can conclude causation.

B) No, correlation never implies causation.

C) Yes, the scatterplot shows a strong linear association, so the older a woman is when she first marries, the older she will be when she has her first child.

D) No, since the correlation coefficient does not equal 1, we cannot conclude causation.

Objective: (1) Apply Concepts for Linear Models

96) Can we use the regression equation to predict the age at which a woman has her first child for a woman who first married at the age of 50?

A) Yes, we can always make predictions once we have a regression equation.

B) No, we cannot make a prediction because a woman who marries at age 50 is outside the range of our data.

We would be extrapolating.

C) No, we cannot make a prediction because the correlation coefficient does not equal 1.

D) Yes, we can make a prediction because the scatterplot shows a strong positive linear relationship.

Objective: (1) Apply Concepts for Linear Models

97) Suppose the correlation coefficient describing how the heights of teenage boys predicts their weights is 0.85. What is the coefficient of determination (r2 ) and what does it mean in context?

A) r2 is 0.85. 85% of the variation in weights of teenage boys can be explained by their height.

B) r2 is 0.7225. 72.25% of the variation in heights of teenage boys can be explained by their weight.

C) r2 is 0.85. 85% of the variation in heights of teenage boys can be explained by their weight.

D) r2 is 0.7225. 72.25% of the variation in weights of teenage boys can be explained by their height.

Objective: (1) Apply Concepts for Linear Models

30

The scatterplot below shows the relationship between a car's speed and the distance it traveled to come to a complete stop when hitting the brakes. The correlation coefficient between the values is 0.81.

The regression equation for the data is ^

Distance = -17.579 + 3.932 · (Speed)

98) Would it be appropriate to say that a car's speed causes its stopping distance?

A) No, correlation never implies causation.

B) Yes, the scatterplot shows a strong linear association, so the faster a car is going, the longer it takes to stop it.

C) Yes, since the correlation coefficient is close to 1, we can conclude causation.

D) No, since the correlation coefficient does not equal 1, we cannot conclude causation.

Objective: (1) Apply Concepts for Linear Models

99) Can we use the regression equation to predict the stopping distance of a car that is traveling at 40 mph?

A) Yes, we can make a prediction because the scatterplot shows a strong positive linear relationship.

B) No, we cannot make a prediction because a car that is traveling at 40 mph is outside the range of our data.

We would be extrapolating.

C) Yes, we can always make predictions once we have a regression equation.

D) No, we cannot make a prediction because the correlation coefficient does not equal 1.

Objective: (1) Apply Concepts for Linear Models

100) What is the value of the coefficient of determination (r2 ) and what does it mean in context?

A) r2 is 0.81. 81% of the variation in a car's stopping distance can be explained by its speed.

B) r2 is 0.6561. 65.61% of the variation in a car's speed can be explained by its stopping distance.

C) r2 is 0.81. 81% of the variation in a car's speed can be explained by its stopping distance.

D) r2 is 0.6561. 65.61% of the variation in a car's stopping distance can be explained by its speed.

Objective: (1) Apply Concepts for Linear Models

31

The scatterplot shows the relationship between a vehicle's age (in years) and its current value (in dollars).

The coefficient of determination was found to be 98.74%.

101) Calculate the value of the correlation coefficient between a car's age and its current value.

A) r = -0.9937 B) r = 0.9937 C) r = 0.9874

D) r = -0.9874

Objective: (1) Apply Concepts for Linear Models

102) If we converted the x-axis to months, instead of years, what would happen to the value of the correlation coefficient?

A) The correlation coefficient would be unchanged because it is not affected by changes in units.

B) The correlation coefficient would decrease because we have less data points per month as opposed to per year.

C) We cannot make any conclusions about the correlation coefficient because we would need to use the new data values to calculate it.

D) The correlation coefficient would increase because we are adding 12 additional values (one for each month) on the x-axis.

Objective: (1) Apply Concepts for Linear Models

32

The scatterplot shows the relationship between the foot lengths and foot widths of children. The coefficient of determination was found to be 41.09%.

103) Calculate the value of the correlation coefficient between a car's age and its current value.

A) r = 0.4109 B) r = 0.6410 C) r = -0.6410

D) r = -0.4109

Objective: (1) Apply Concepts for Linear Models

104) If we converted the x-axis to inches, instead of centimeters, what would happen to the value of the correlation coefficient?

A) The correlation coefficient would decrease because we there are 2.54 centimeters in 1 inch.

B) We cannot make any conclusions about the correlation coefficient because we would need to use the new data values (with inches) to calculate it.

C) The correlation coefficient would increase because we there are 2.54 centimeters in 1 inch.

D) The correlation coefficient would be unchanged because it is not affected by changes in units.

Objective: (1) Apply Concepts for Linear Models

33

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

The scatterplot below shows the relationship between the average monthly temperature and the monthly cost of a gas bill. The correlation coefficient between the values is -0.92.

The regression equation for the data is ^

Gas Bill = 225.78 - 2.97 · (Temperature)

105) Do lower monthly temperature cause gas bills to be more expensive? Explain your reasoning.

Objective: (1) Apply Concepts for Linear Models

106) If appropriate, calculate the expected gas bill cost for a month with an average temperature of -20°. If it's not appropriate, explain why.

Objective: (1) Apply Concepts for Linear Models

107) Determine the value of the coefficient of determination (r2 ) and explain its meaning in context?

Objective: (1) Apply Concepts for Linear Models

34

The following scatterplot shows the relationship between heights (in cm) and weights (in kg) of 100 Americans.

The coefficient of determination was found to be 37.9%.

108) Calculate the value of the correlation coefficient between height and weight.

Objective: (1) Apply Concepts for Linear Models

109) If we converted the x-axis to inches, instead of centimeters, what would happen to the value of the correlation coefficient?

Objective: (1) Apply Concepts for Linear Models

Solve the problem.

110) Create a data set of 2 variables (X and Y) such that the relationship between X and Y would have a perfect negative correlation of -1. Note: The data set can be very small (three to four X and Y values).

Objective: (1) Apply Concepts for Linear Models

111) For the following scatterplot, what effect would the outlier have on the slope of the regression equation?

Explain your reasoning.

Objective: (1) Apply Concepts for Linear Models

35

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

112) The data in the table represent the amount of pressure (psi) exerted by a stamping machine (x), and the amount of scrap brass shavings (in pounds) that are collected from the machine each hour (y). Also shown below are the outputs from two different statistical technologies (TI-83/84 Calculator and Excel). A scatterplot of the data confirms that there is a linear association. Report the equation for predicting scrap brass shavings using words such as scrap, not x and y. State the slope and intercept of the prediction equation. Round all calculations to the nearest thousandth.

A) scrap = -2.019 + 2.134(pressure); slope = -2.019 and the intercept is 2.134.

B) scrap = -2.019 + 2.134(pressure); slope = 2.134 and the intercept is -2.019.

C) scrap = 2.134 - 2.019(pressure); slope = -2.019 and the intercept is 2.134.

D) scrap = 2.134 - 2.019(pressure); slope = 2.134 and the intercept is -2.019.

Objective: (2) Perform a Linear Regression

36

113) The data in the table represent the amount of raw material (in tons) put into an injection molding machine each day (x), and the amount of scrap plastic (in tons) that is collected from the machine every four weeks (y). Also shown below are the outputs from two different statistical technologies (TI-83/84 Calculator and Excel). A scatterplot of the data confirms that there is a linear association. Report the equation for predicting scrap from raw material using words such as scrap, not x and y. State the slope and intercept of the prediction equation. Round all calculations to the nearest hundredth.

A) scrap = 2.19 - 2.38(raw material); slope = -2.38 and the intercept is 2.19.

B) scrap = -2.38 + 2.19(raw material); slope = 2.19 and the intercept is -2.38.

C) scrap = 2.19 - 2.38(raw material); slope = 2.19 and the intercept is -2.38.

D) scrap = -2.38 + 2.19(raw material); slope = -2.38 and the intercept is 2.19.

Objective: (2) Perform a Linear Regression

37

Answer Key Testname: GOULDCH4TESTGEN

1) A 2) A 3) D 4) A 5) B 6) There are two possible answers here: (1) The number of crimes committed is the explanatory variable and the number of police on patrol is the response because the amount of crime can explain a need for more or less police officers.

(2) The number of police on patrol is the explanatory variable and the amount of crime is the response because the more police that are on patrol could explain a reduction in the amount of crime.

7) Scatterplot (ii) shows a stronger linear relationship because it has less vertical variation between points. As a tree's diameter increases, its volume typically increases as well.

8) B 9) D 10) C 11) C 12) D 13) A 14) B 15) A 16) A 17) C

18) Answers may vary.

Example: People who spend more time working out tend to lose more weight.

19) C 20) A 21) C 22) A 23) C 24) B 25) B 26) B 27) C 28) D 29) A 30) D 31) C 32) D 33) C 34) A 35) C 36) A correlation coefficient will be negative when there is a negative linear trend in a scatterplot.

So, as the values of x increase, the values of y tend to decrease.

37) Scatterplot (i) has the highest correlation because it is more linear than scatterplot (ii). The points have less vertical variation in scatterplot (i), so the relationship is stronger.

38) The correlation coefficient, r, will get closer to 1 because the point is an outlier. Since the rest of the points show a strongly positive linear relationship, r would reflect that and get closer to 1.

39) A 40) B 41) C 42) B 43) C 44) A 45) C 46) C 47) D 48) C 49) D 50) A 51) A 52) The correlation coefficient between the heights of the teenagers in 2003 and 2008 is equal to 1 because for every person, the height increased exactly 6 inches (15.24 cm) from 2003 to 2008. If we plotted the data, the points would form a straight line.

53) B 54) D 55) A 56) B ^

57) Price = 49 + 0.22 · (Distance) = 49 + 0.22 · (2448.3) = 49 + 538.63 = $587.63

38

58) Using the regression equation, we find that she has held her current position in the company for approximately 17 years.

Salary = 19250 + 3875 · (Years in Position) 85,000 = 19,250 + 3875 · (Years in Position) 65,750 = 3875 · (Years in Position) 16.97 = (Years in Position) 59) A 60) B 61) C 62) C 63) A 64) C 65) B 66) B 67) C 68) B 69) A 70) C 71) A 72) B 73) A 74) B 75) B 76) A 77) B 78) A 79) The slope is 0.22. For every additional mile of flight travel, the price of the airline ticket is predicted to increase by $0.22.

Answer Key Testname: GOULDCH4TESTGEN

80) The intercept is 49. If you are traveling 0 miles, the price of an airline ticket is predicted to be $49.

The value is not meaningful because you would not pay for an airline ticket if you are not traveling anywhere. sy = 0.93 · 81) b = r · sx 12500 = 0.93 · 3 4166.67 = 3875.

So, the slope is $3875.

For every additional year an employee has held his/her current position in the company, he/she is expected to earn $3875 more for their annual salary.

82) a = y - bx = 58000 3875(10) = 58000 38750 = 19,250.

So, the intercept is $19,250. If an employee has worked for 0 years in the current position, he/she is predicted to earn a salary of $19,250. This is reasonable because $19,250 could be the employee's starting salary.

83) D 84) D 85) B 86) B 87) C 88) B 89) B 90) B 91) C

92) A 93) D 94) B 95) B 96) B 97) D 98) A 99) B 100) D 101) A 102) A 103) B 104) D 105) No, lower monthly temperatures do not cause gas bills to be more expensive.

Correlation never implies causation.

We can say that lower temperatures are associated with higher gas bills, but we cannot say that the temperature causes the price.

106) It would not be appropriate to make a prediction because a temperature of -20° is outside the range of our data. We would be extrapolating.

107) r2 = (-0.92)2 = 0.8464.

109) The correlation coefficient would be unchanged because it is not affected by changes in units.

110) Answers may vary.

Example:

111) The outlier would decrease the slope because it would influence the lower left hand side of the regression line to move closer to it.

This would make the line less steep, which results in a smaller slope value.

112) B 113) B

This means that 84.64% of the variation in the cost of a gas bill can be explained by the monthly average temperature.

108) r = r2 = 0.379 =

0.6156. Since the plot shows a positive relationship between height and weight, r = 0.6156.

39

Gould/Ryan/Wong Essentials Statistics 3e Chapter 5 Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

1) If 20 babies are born, how often are there 8 or less male babies? Assume that the gender of a baby is a random event. Which of the following experiments would not simulate this situation?

A) Choose the first twenty digits from a row in the random number table. Designate odd numbers to mean "female" and even numbers to mean "male".

B) Roll a die twenty times. Designate a 1, 2, or 3 to mean "female" and a 4, 5, or 6 to mean "male".

C) Flip a coin twenty times. Designate a head to mean "female" and a tail to mean "male".

D) All of these will simulate the gender of twenty babies.

Objective: (1) Use Simulations to Calculate Probabilities

2) A certain baseball player has a hit 10 times in every 30 times at bat on average. Assume that having a hit is a random event. Which of the following experiments would not simulate this situation?

A) Choose the first 30 digits from a row in the random number table. Designate odd numbers to mean "hit" and even numbers to mean "non-hit".

B) Flip a coin thirty times. Designate a head to mean "hit" and a tail to mean "non-hit".

C) All of these will simulate the number of hits.

D) None of these will simulate the number of hits.

Objective: (1) Use Simulations to Calculate Probabilities

3) Is the following an example of theoretical probability or empirical probability? A card player declares that there is a one in thirteen chance that the next card pulled from a well-shuffled, full deck will be a queen.

A) Theoretical B) Empirical Objective: (2) Identify Empirical and Theoretical Probabilities

4) Is the following an example of theoretical probability or empirical probability? A homeowner notes that five out of seven days the newspaper arrives before 5 pm. He concludes that the probability that the newspaper will arrive before 5 pm tomorrow is about 71%.

A) Theoretical B) Empirical Objective: (2) Identify Empirical and Theoretical Probabilities

5) Is the following an example of theoretical probability or empirical probability? A fisherman notes that eight out of ten times that he uses a certain lure he catches a fish within an hour. He concludes that the probability that the lure will catch a fish on his fishing next trip is about 80% A) Empirical B) Theoretical Objective: (2) Identify Empirical and Theoretical Probabilities

6) Is the following an example of theoretical probability or empirical probability? At a carnival shell game the player can pay three dollars and choose the shell that he or she believes is hiding the prize. There are four shells that are thoroughly mixed up after each guess. The player concludes that there is a one in four chance of randomly picking the winning shell.

A) Empirical B) Theoretical Objective: (2) Identify Empirical and Theoretical Probabilities

1

7) A student tosses two coins 20 times and records the number of tails.

Outcome Frequency

2 tails 1 tail 0 tails 2 2 16

The student concludes that the probability of getting exactly 1 tail when tossing two coins is of empirical probability or theoretical probability?

A) Theoretical

1 . Is this an example 10

B) Empirical

Objective: (2) Identify Empirical and Theoretical Probabilities

8) A bag contains 9 red marbles, 5 blue marbles, and 9 green marbles. Jeffery claims that if a marble is selected at 5 random from the bag, the probability of choosing a blue marble is . Is this an example of empirical probability 23 or theoretical probability?

A) Empirical

B) Theoretical

Objective: (2) Identify Empirical and Theoretical Probabilities

9) A homeowner notices that 8 out of 14 days the mail arrives before 3pm. She concludes that the probability that the mail will arrive before 3pm tomorrow is about 57%. Is this an example of a theoretical or empirical probability?

A) Empirical B) Theoretical Objective: (2) Identify Empirical and Theoretical Probabilities

10) A six-sided die is rolled and a coin is tossed. The probability of getting a tail on the coin and a 2 on the die is 8.3%.

Is this an example of a theoretical or empirical probability?

A) Empirical B) Theoretical Objective: (2) Identify Empirical and Theoretical Probabilities

11) Is the following an example of theoretical probability or empirical probability? A survey was conducted to determine a group of elderly adults' favorite breeds of dogs. He concludes that the probability that the elderly adults prefer a poodle is about 30%.

A) Empirical B) Theoretical Objective: (2) Identify Empirical and Theoretical Probabilities

12) Is the following an example of theoretical probability or empirical probability? Joyce and Joel roll two dice 50 times and record their results in the accompanying chart. They calculate the number of times 7 was rolled. This is an example of what type of probability?

A) Empirical B) Theoretical Objective: (2) Identify Empirical and Theoretical Probabilities

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

13) Describe the difference between a theoretical probability and an empirical probability. Give at least one example of each type of probability.

Objective: (2) Identify Empirical and Theoretical Probabilities

14) A card player claims that the probability of choosing a red jack from a well-shuffled deck of cars is 1/26 because choosing any card is equally likely and there are two red jacks in the deck of fifty-two cards. Is this an example of a theoretical probability or an empirical probability? Explain.

Objective: (2) Identify Empirical and Theoretical Probabilities

2

15) A researcher wants to compare experimental results with a theoretical value for the probability of getting a tail on a coin and a 1 on a die. Design an experiment to compare the probabilities. Define which one is theoretical and which one is an empirical probability? Explain.

Objective: (2) Identify Empirical and Theoretical Probabilities

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

16) Which of the following statements is not true about probability?

A) Probabilities are always numbers between 0 and 1 inclusive.

B) A probability of zero means that an event will not happen, a probability of one means that an event is certain to happen.

C) Probability is used to measure how often random events occur.

D) All of these are true statements Objective: (1) Find Theoretical Probabilities

17) The National Center for Health Statistics has found that there is a 0.41% chance that an American citizen will die from falling. What is the probability that you will not die from a fall? (Round to the nearest hundredth of a percent) A) 99.59% B) Can't be determined with the given information.

C) 59.00% D) 93.31% Objective: (1) Find Theoretical Probabilities

18) The National Center for Health Statistics has found that there is a 5.01% chance that an American citizen will die from an accident (unintentional injury). What is the probability that you will not die from an accident? (Round to the nearest hundredth of a percent) A) Can't be determined with the given information.

B) 95.00% C) 99.50% D) 94.99% Objective: (1) Find Theoretical Probabilities

Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other.

19) If one student is randomly chosen from the group, what is the probability that the student is female?

A) 0.50 B) 0.52 C) 0.48 D) None of these Objective: (1) Find Theoretical Probabilities

20) If one student is randomly chosen from the group, what is the probability that the student chose "outside employment" as their most likely activity on a Saturday morning?

A) 0.23 B) 0.43 C) 0.13 D) None of these Objective: (1) Find Theoretical Probabilities

21) If one student is randomly chosen from the group, what is the probability that the student is male?

A) 0.48 B) 0.50 C) 0.52 D) None of these Objective: (1) Find Theoretical Probabilities

3

22) If one student is randomly chosen from the group, what is the probability that the student chose "recreation" as their most likely activity on a Saturday morning?

A) 0.310 B) 0.115 C) 0.195 D) None of these Objective: (1) Find Theoretical Probabilities

23) What is the probability that a randomly chosen survey respondent is male or chose "recreation" as their most likely activity on Saturday mornings?

A) 0.480 B) 0.675 C) 0.790 D) None of these Objective: (1) Find Theoretical Probabilities

24) If one student is randomly chosen from the group, what is the probability that the student chose "recreation" or "other" as their most likely activity on a Saturday morning?

A) 0.275 B) 0.375 C) 0.395 D) None of these Objective: (1) Find Theoretical Probabilities

25) If one student is randomly chosen from the group, what is the probability that the student chose "homework" or "housework" as their most likely activity on a Saturday morning?

A) 0.395 B) 0.075 C) 0.145 D) None of these Objective: (1) Find Theoretical Probabilities

26) If one student is randomly chosen from the group, what is the probability that the student is female or chose "homework" as their most likely activity on a Saturday morning?

A) 0.900 B) 0.755 C) 0.665 D) None of these Objective: (1) Find Theoretical Probabilities

27) If one student is randomly chosen from the group, what is the probability that the student is female and chose "outside employment" as their most likely activity on a Saturday morning?

A) 0.43 B) 0.13 C) 0.23 D) None of these Objective: (1) Find Theoretical Probabilities

28) If one student is randomly chosen from the group, what is the probability that the student is male and chose "outside employment" as their most likely activity on a Saturday morning?

A) 0.23 B) 0.10 C) 0.13 D) None of these Objective: (1) Find Theoretical Probabilities

Provide an appropriate response.

29) Use the spinner below to answer the question. Assume that it is equally probable that the pointer will land on any one of the five numbered spaces. If the pointer lands on a borderline, spin again.

Find the probability that the arrow will land on 4 or 3.

A) 4

B) 1

C)

Objective: (1) Find Theoretical Probabilities

4

3 4

D)

2 5

30) You are dealt one card from a standard 52-card deck. Find the probability of being dealt an ace or a 9.

5 2 13 A) B) C) D) 10 13 13 2 Objective: (1) Find Theoretical Probabilities

31) A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting a 2.

1 1 A) 0 B) C) D) 2 6 3 Objective: (1) Find Theoretical Probabilities

32) A die is rolled. The set of equally likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of getting a 10.

10 A) 10 B) 0 C) D) 1 6 Objective: (1) Find Theoretical Probabilities

Find the indicated probability.

33) The following table shows the career and age of retirement for a group of retired people.

10

43

81

33

167

10

50

71

43

174

59

182

285

175

701

Suppose one of these people is selected at random. Compute the probability that the person selected was a store clerk.

A) 0.305 B) 0.260 C) 0.099 D) 0.026 Objective: (1) Find Theoretical Probabilities

5

34) The Book Industry Study Group, Inc., performs sample surveys to obtain information on characteristics of book readers. A book reader is defined to be one who read one or more books in the six months prior to the survey; a non-book reader is defined to be one who read newspapers or magazines but no books in the six months prior to the survey; a nonreader is defined to be one who did not read a book, newspaper, or magazine in the six months prior to the survey.

The following data were obtained from a random sample of people 16 years old and over.

142

167

20

329

156

141

8

305

215

97

8

320

686

672

91

1449

Suppose one of these people is selected at random. Compute the probability that the person is a nonreader.

A) 0.063 B) 0.111 C) 0.604 D) 0.038 Objective: (1) Find Theoretical Probabilities

Solve the problem.

35) The Social Security Administration reported in 2014 that if you are a 70 year old man, there is a 65.8% chance of making it to your 80th birthday. What is the probability that you will die before reaching your 80th birthday? (round to the nearest hundredth place) A) 0.66% B) Can't be determined with the given information.

C) 0.34% D) 34.20% Objective: (1) Find Theoretical Probabilities

6

A random sample of adults was asked to respond to a survey about whether they use their cell phones to shop for a specific item. One question, summarized in the table below reflecting probabilities, asked each respondent to choose whether or not they use a cell phone app to shop. The major age groupings were under 40 or 40 years or older.

36) If one adult is randomly chosen from the group, what is the probability that the adult is 40 years or older?

A) 40% B) 50% C) 60% D) 0.40% Objective: (1) Find Theoretical Probabilities

37) If one adult is randomly chosen from the group, what is the probability that the adult uses a cell phone app for shopping and is under 40 years of age?

A) 60% B) 30% C) 40% D) 10% Objective: (1) Find Theoretical Probabilities

38) What type of probability is the 0.30 shown in the table?

A) Theoretical

B) Empirical

Objective: (1) Find Theoretical Probabilities

39) If one adult is randomly chosen from the group, what is the probability that if the adult does not use a cell phone app for shopping and is over 40 years old?

A) 70% B) 40% C) 60% D) 30% Objective: (1) Find Theoretical Probabilities

40) Find the probability that an adult randomly chosen from the group uses a cell phone app to shop? (round to the nearest thousandth) A) 40% B) 0.50% C) 50% D) 60% Objective: (1) Find Theoretical Probabilities

A random sample of car buyers was asked to respond to a survey about what was the most important quality of the car they purchased. This question is summarized in the table below. The important contributors were fuel efficiency, looks, manufacturer reputation, price or other.

41) If one car buyer is randomly chosen from the group, what is the probability that the buyer is female?

A) 0.50 B) 0.52 C) 0.48 D) 0.38 Objective: (1) Find Theoretical Probabilities

42) If one car buyer is randomly chosen from the group, what is the probability that the buyer chose a car based on "looks" as their most important factor for the purchase?

A) 0.235 B) 0.640 C) 0.160 D) 0.320 Objective: (1) Find Theoretical Probabilities

7

43) If one car buyer is randomly chosen from the group, what is the probability that the buyer is male and chose "manufacturer reputation" as their most important factor for the purchase?

A) 0.100 B) 0.208 C) 0.130 D) 0.230 Objective: (1) Find Theoretical Probabilities

44) If one car buyer is randomly chosen from the group, what is the probability that the buyer is female and chose "fuel efficiency" or "other" as their most important factor for the purchase?

A) 0.212 B) 0.300 C) 0.173 D) 0.110 Objective: (1) Find Theoretical Probabilities

45) If one car buyer is randomly chosen from the group, what is the probability amongst female buyers that they chose "price" as their most important factor for the purchase?

A) 0.375 B) 0.240 C) 0.310 D) 0.629 Objective: (1) Find Theoretical Probabilities

46) Find the probability of those car buyers who chose "looks" as their most important factor was a female car buyer?

A) 0.163 B) 0.469 C) 0.160 D) 0.531 Objective: (1) Find Theoretical Probabilities

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Suppose that the typical work schedule for the wait staff at Sam's BBQ Shack, which is open seven days a week, is five days on with two days off each week. A week begins on Monday and ends on Sunday. Assume that any day of the week is equally likely to be a day off and the selection of a day off is independent.

47) What is the probability that Isaac, a waiter at Sam's BBQ Shack, will have Saturday or Sunday off? Show your work and round to the nearest tenth of a percent.

Objective: (1) Find Theoretical Probabilities

48) State the complement of the event given in the previous question and calculate the probability of the complement.

Show your work and round to the nearest tenth of a percent.

Objective: (1) Find Theoretical Probabilities

49) What is the probability that Issac will have Saturday and Sunday off? Show your work and round to the nearest tenth of a percent.

Objective: (1) Find Theoretical Probabilities

A random sample of college students was asked to respond to a survey about how they spend their free time on a week night. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Wednesday afternoon/evening. The activity choices were homework, housework, outside employment, recreation, or other.

50) If one person is chosen randomly from the group, what is the probability that the person is working on their homework on a Wednesday afternoon/evening? (round to the nearest thousandth) Objective: (1) Find Theoretical Probabilities

8

51) If one person is chosen randomly from the group, what is the probability that the student is female and working at outside employment on a Wednesday afternoon/evening? (round to the nearest thousandth) Objective: (1) Find Theoretical Probabilities

52) If one person is chosen randomly from the group, what is the probability that the person was male and doing housework on a Wednesday afternoon/evening? (round to the nearest thousandth) Objective: (1) Find Theoretical Probabilities

53) If one person is chosen randomly from the group, what is the probability that the person was either doing homework or outside employment on a Wednesday afternoon/evening? (round to the nearest thousandth) Objective: (1) Find Theoretical Probabilities

54) Compare the probability that a randomly chosen female student was engaged in recreation versus a male student on a Wednesday afternoon/evening. (Round to the nearest thousandth) Objective: (1) Find Theoretical Probabilities

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other.

55) Which of the following are mutually exclusive events?

A) Student is male and student chose "housework" as their most likely activity on Saturday mornings.

B) Student is male and student chose "outside employment" as their most likely activity on Saturday mornings.

C) Student chose "recreation" and student chose "other" as their most likely activity on Saturday mornings.

D) Student is female and student chose "housework" as their most likely activity on Saturday mornings.

Objective: (2) Identify Mutually Exclusive Events

56) Which of the following are mutually exclusive events?

A) Student chose "outside employment" and student chose "other" as their most likely activity on Saturday mornings.

B) Student is female and student chose "outside employment" as their most likely activity on Saturday mornings.

C) Student is female and student chose "housework" as their most likely activity on Saturday mornings.

D) Student is male and student chose "housework" as their most likely activity on Saturday mornings.

Objective: (2) Identify Mutually Exclusive Events

9

Determine whether the events are mutually exclusive.

57) The number of hours needed by sixth grade students to complete a research project was recorded. A student is selected at random. The events A and B are defined as follows.

A = event the student took at most 8 hours B = event the student took at least 6 hours Are the events A and B mutually exclusive?

A) Yes

B) No

Objective: (2) Identify Mutually Exclusive Events

58) The age distribution of students at a community college is recorded. A student from the community college is selected at random. The events A and B are defined as follows.

A = event the student is at most 24 B = event the student is at least 40 Are the events A and B mutually exclusive?

A) Yes

B) No

Objective: (2) Identify Mutually Exclusive Events

A random sample of adults was asked to respond to a survey about whether they use their cell phones to shop for a specific item. One question, summarized in the table below reflecting probabilities, asked each respondent to choose whether or not they use a cell phone app to shop. The major age groupings were under 40 or 40 years or older.

59) Which of the following are mutually exclusive events in this study?

A) Adult is over 40 years of age and does not use a cell phone app for shopping.

B) Adults over 40 years of age and uses a cell phone app for shopping.

C) Adult is under 40 years of age and does not use a cell phone app for shopping.

D) None of these choices.

Objective: (2) Identify Mutually Exclusive Events

Solve the problem.

60) A study asks a sample of adults whether they prefer cats or dogs or neither. Only one answer is allowed. Survey also records whether male or female. Which of the following are mutually exclusive events in this study?

A) Adult is male and likes cats and dogs.

B) Adult is female and likes dogs.

C) Adult is female and prefers cats.

D) Adult is male and adult prefers neither cats nor dogs.

Objective: (2) Identify Mutually Exclusive Events

10

61) Which of the following are mutually exclusive events?

A) A car buyer is female and a car buyer chose "fuel efficiency" as their most important factor for their purchase.

B) A car buyer is male and a car buyer chose "manufacturer reputation" as their most important factor for their purchase.

C) A car buyer chose "fuel efficiency" and "other" as their most important factor for their purchase.

D) A car buyer is female and a car buyer chose "looks" as their most important factor for their purchase.

Objective: (2) Identify Mutually Exclusive Events

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

A random sample of college students was asked to respond to a survey about how they spend their free time on a week night. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Wednesday afternoon/evening. The activity choices were homework, housework, outside employment, recreation, or other.

62) Using this example, state two events that are mutually exclusive.

Objective: (2) Identify Mutually Exclusive Events

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the following table to answer the question. A random sample of college students was asked to respond to a survey about how they spend their free time on weekends. One question, summarized in the table below, asked each respondent to choose the one activity that they are most likely to participate in on a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or other.

63) Find the probability that a female college student from the group chose "housework" as their most likely activity on Saturday mornings? (Round to the nearest thousandth) A) 0.163 B) 0.531 C) 0.520 D) None of these Objective: (1) Find Conditional Probabilities

64) Find the probability that a male college student from the group chose "housework" as their most likely activity on Saturday mornings? (Round to the nearest thousandth) A) 0.302 B) 0.145 C) 0.156 D) None of these Objective: (1) Find Conditional Probabilities

11

Find the conditional probability.

65) The table below describes the smoking habits of a group of asthma sufferers.

Light Heavy Nonsmoker smoker smoker Total Men 399 65 60 524 Women 383 86 62 531 Total 782 151 122 1055 If one of the 1055 subjects is randomly selected, find the probability that the person chosen is a nonsmoker given that the person is a woman.

A) 0.49 B) 0.363 C) 0.721 D) 0.503 Objective: (1) Find Conditional Probabilities

66) The table below describes the smoking habits of a group of asthma sufferers.

Light Heavy Nonsmoker smoker smoker Total Men 354 66 70 490 Women 389 89 76 554 Total 743 155 146 1044 If one of the 1044 subjects is randomly selected, find the probability that the person chosen is a woman given that the person is a light smoker.

A) 0.085 B) 0.148 C) 0.161 D) 0.574 Objective: (1) Find Conditional Probabilities

Suppose that a recent poll of American households about pet ownership found that for households with pets, 45% owned a dog, 34% owned a cat, and 10% owned a bird. Suppose that three households are selected randomly and with replacement and the ownership is mutually exclusive.

67) What is the probability that all three randomly selected households own a dog? (Round to the nearest hundredth) A) 0.09 B) 0.80 C) 0.91 D) 0.04 Objective: (1) Find Conditional Probabilities

68) What is the probability that none of the three randomly selected households own a cat? (Round to the nearest hundredth) A) 0.71 B) 0.29 C) 0.96 D) 0.17 Objective: (1) Find Conditional Probabilities

69) What is the probability that at least one of the three randomly selected households own a bird? (Round to the nearest hundredth) A) 0.92 B) 0.73 C) 0.27 D) 0.08 Objective: (1) Find Conditional Probabilities

70) What is the probability that at least two of the three randomly selected households own either a cat or a dog?

(Round to the nearest hundredth) A) 0.89 B) 0.06 C) 0.94 D) 0.97 Objective: (1) Find Conditional Probabilities

12

Suppose that a recent poll of American households about car ownership found that for households with a car, 39% owned a sedan, 33% owned a van, and 7% owned a sports car. Suppose that three households are selected randomly and with replacement.

71) What is the probability that all three randomly selected households own a van? (Round to the nearest thousandth) A) 0.036 B) 0.003 C) 0.964 D) 0.059 Objective: (1) Find Conditional Probabilities

72) What is the probability that none of the three randomly selected households own a van? (Round to the nearest thousandth) A) 0.036 B) 0.699 C) 0.060 D) 0.301 Objective: (1) Find Conditional Probabilities

73) What is the probability that at least one of the three randomly selected households own a sports car? (Round to the nearest thousandth) A) 0.003 B) 0.800 C) 0. 200 D) 0.627 Objective: (1) Find Conditional Probabilities

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Suppose that a recent poll of single people over the age of thirty-five were asked about their living arrangements. The poll found that 34% rented a house or apartment, 21% owned a house, and 17% owned a condominium. Suppose that four single people are selected randomly and with replacement.

74) What is the probability that all four people rent a house or apartment? Show your work and round to the nearest thousandth.

Objective: (1) Find Conditional Probabilities

75) What is the probability that none of the four randomly selected people rent a house or apartment? Show your work and round to the nearest thousandth.

Objective: (1) Find Conditional Probabilities

76) What is the probability that at least one of the four randomly selected people rents a house or apartment? Show your work and round to the nearest thousandth.

Objective: (1) Find Conditional Probabilities

Solve the problem.

77) A multiple choice quiz contains five questions. Each question has four answer choices. Michael is not prepared for the quiz and decides to guess for each question. What is the probability that Michael will get at least one question correct? What is the probability that Michael will get all five questions correct? Show your work and round to the nearest thousandth.

Objective: (1) Find Conditional Probabilities

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

78) Use your intuition to decide whether the following events are likely to be independent or associated.

Event A: A randomly selected person is married with no children.

Event B: A randomly selected person opposes a tax credit for children.

A) Independent B) Associated Objective: (2) Determine if Events are Independent or Associated

13

79) Use your intuition to decide whether the following events are likely to be independent or associated.

Event A: The randomly selected carton of milk you purchased from the store is sour.

Event B: Your car won't start on a randomly selected morning.

A) Independent B) Associated Objective: (2) Determine if Events are Independent or Associated

80) Use your intuition to decide whether the following two events are likely to be independent or associated.

Event A: You reach into your dark closet, without looking, and pull out a black shirt.

Event B: You reach into your sock drawer, without looking, and pull out black socks.

A) Independent B) Associated Objective: (2) Determine if Events are Independent or Associated

81) Use your intuition to decide whether the following two events are likely to be independent or associated.

Even A: A randomly selected registered voter's political party affiliation is Republican Event B: A randomly selected registered voter opposes a new tax on fuel.

A) Independent B) Associated Objective: (2) Determine if Events are Independent or Associated

82) Classify the events as independent or not independent: Events A and B where the probability of event A occurring is 0.7, the probability of event B occurring is 0.6, and the probability of both event occurring is 0.42.

A) not independent B) independent Objective: (2) Determine if Events are Independent or Associated

83) Classify the events as independent or not independent: Events A and B where the probability of event A occurring is 0.2, the probability of event B occurring is 0.9, and the probability of both event occurring is 0.17.

A) not independent B) independent Objective: (2) Determine if Events are Independent or Associated

84) Use your intuition to decide whether the following two events are likely to be independent or associated.

Event A: You roll a number larger than four on a die.

Event B: Rolling a six on a die.

A) Independent B) Associated Objective: (2) Determine if Events are Independent or Associated

85) Use your intuition to decide whether the following two events are likely to be independent or associated.

Event A: Drawing a club from a deck of cards.

Event B: Drawing a card with a black symbol from a deck of cards.

A) Associated B) Independent Objective: (2) Determine if Events are Independent or Associated

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

86) Suppose you would like a mug of hot chocolate with cinnamon. You reach into the kitchen cupboard containing twenty mixed up mismatched mugs without looking and pull out a pink coffee cup. You also reach into a kitchen drawer containing 30 different mixed up spice jars without looking and pull out the cinnamon. Use your intuition and state whether these two events are associated or independent. Explain.

Objective: (2) Determine if Events are Independent or Associated

14

87) Use your intuition and state whether these two events are likely to be associated or independent. Explain.

Event A: A randomly selected adult is a pet owner.

Event B: A randomly selected adult responds favorably to the survey question "Should a portion of the beach be set aside as an (unleashed) dog beach?".

Objective: (2) Determine if Events are Independent or Associated

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the following information to answer the question. Suppose that a recent poll of American households about pet ownership found that for households with one pet, 39% owned a dog, 33% owned a cat, and 7% owned a bird. Suppose that three households are selected randomly and with replacement.

88) What is the probability that all three randomly selected households own a dog? (Round to the nearest hundredth) A) 0.23 B) 0.06 C) 0.39 D) None of these Objective: (3) Find the Probabilities of Sequences of Events

89) What is the probability that none of the three randomly selected households own a cat? (Round to the nearest hundredth) A) 0.46 B) 0.70 C) 0.30 D) None of these Objective: (3) Find the Probabilities of Sequences of Events

90) What is the probability that all three randomly selected households own a cat? (Round to the nearest hundredth) A) 0.04 B) 0.06 C) 0.03 D) None of these Objective: (3) Find the Probabilities of Sequences of Events

91) What is the probability that none of the three randomly selected households own a bird? (Round to the nearest hundredth) A) 0.86 B) 0.93 C) 0.80 D) None of these Objective: (3) Find the Probabilities of Sequences of Events

92) What is the probability that at least one of the three randomly selected households own a dog? (Round to the nearest hundredth) A) 0.70 B) 0.61 C) 0.77 D) 0.27 Objective: (3) Find the Probabilities of Sequences of Events

93) What is the probability that at least one of the three randomly selected households own a bird? (Round to the nearest hundredth) A) 0.80 B) 0.40 C) 0.20 D) 0.60 Objective: (3) Find the Probabilities of Sequences of Events

Solve the problem.

94) A true/false pop quiz contains five questions. What is the probability that when guessing, a student will get at least one question correct? (Round to the nearest hundredth) A) 1.00 B) 0.50 C) 0.76 D) 0.97 Objective: (3) Find the Probabilities of Sequences of Events

95) A true/false pop quiz contains seven questions. What is the probability that when guessing, a student will get at least one question correct? (Round to the nearest hundredth) A) 0.99 B) 0.50 C) 0.97 D) 1.00 Objective: (3) Find the Probabilities of Sequences of Events

15

Find the indicated probability.

96) In one town, 27% of all voters are Democrats. If two voters are randomly selected for a survey, find the probability that they are both Democrats. Round to the nearest thousandth if necessary.

A) 0.270 B) 0.070 C) 0.540 D) 0.073 Objective: (3) Find the Probabilities of Sequences of Events

97) Find the probability of correctly answering the first 3 questions on a multiple choice test if random guesses are made and each question has 5 possible answers.

5 3 1 1 A) B) C) D) 3 5 125 243 Objective: (3) Find the Probabilities of Sequences of Events

98) In one town, 70% of adults have health insurance. What is the probability that 4 adults selected at random from the town all have health insurance? Round to the nearest thousandth if necessary.

A) 0.057 B) 0.7 C) 2.8 D) 0.24 Objective: (3) Find the Probabilities of Sequences of Events

99) In a homicide case 3 different witnesses picked the same man from a line up. The line up contained 5 men. If the identifications were made by random guesses, find the probability that all 3 witnesses would pick the same person.

A) 0.6 B) 0.04 C) 0.008 D) 0.0041152 Objective: (3) Find the Probabilities of Sequences of Events

Solve the problem.

100) If 20 babies are born, how often are there 12 or more female babies? Assume that the gender of a baby is a random event. Which of the following experiments would not simulate this situation?

A) Roll a die twenty times. Designate a 1, 2, or 3 to mean "female" and a 4, 5, or 6 to mean "male."

B) Choose the first twenty digits from a row in the random number table. Designate odd numbers to mean "female" and even numbers to mean "male."

C) Flip a coin twenty times. Designate a head to mean "female" and a tail to mean "male."

D) All of these will simulate the gender of twenty babies.

Objective: (1) Use Simulations to Compute Probabilities

101) If 20 babies are born, how often are there 8 or less male babies? Assume that the gender of a baby is a random event. Which of the following experiments would not simulate this situation?

A) Roll a die twenty times. Designate a 1, 2, or 3 to mean "female" and a 4, 5, or 6 to mean "male."

B) Choose the first twenty digits from a row in the random number table. Designate odd numbers to mean "female" and even numbers to mean "male."

C) Flip a coin twenty times. Designate a head to mean "female" and a tail to mean "male."

D) All of these will simulate the gender of twenty babies.

Objective: (1) Use Simulations to Compute Probabilities

16

102) Which of the following statements is true about the Law of Large Numbers (LLN)?

A) The LLN states that if you simulate or conduct an experiment or simulation enough times the empirical probability observed will always match the theoretical probability that is expected.

B) The LLN is almost always true, but there are special occasions, even when outcomes are random, when the LLN can be broken.

C) The LLN states that the empirical probability that is observed will simulate the theoretical probability that is expected for any finite number of trials, so a simulation or experiment need not have an excessive number of trials.

D) The LLN states that if an experiment with a random outcome is repeated a large number of times, the empirical probability that is observed is likely to be close to the theoretical probability.

Objective: (1) Use Simulations to Compute Probabilities

Answer the question about the Law of Large Numbers.

103) A fair coin is tossed 1000 times. What can you say about getting the outcome of exactly 500 tails? a. Since the probability of a tail is 0.5 for each toss, you should expect exactly 500 tails in 1000 tosses. b. You should not expect exactly 500 tails in 1000 tosses, but the proportion of tails should approach 0.5 as the number of tosses increases. c. You should expect between 400 and 600 tails in 1000 tosses. d. Getting 500 tails is no more likely than getting any other number of tails in 1000 tosses.

A) c B) b C) d D) a Objective: (1) Use Simulations to Compute Probabilities

Solve the problem.

104) Swinging Sammy Skor's batting prowess was simulated to get an estimate of the probability that Sammy will get a hit. Let 1 = HIT and 0 = OUT. The output from a simulation was as follows.

1 0 0 0 1 0 0 1 0 0 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 1 1 1 1 Estimate the probability that he gets a hit.

A) 0.452 B) 0.286

C) 0.476

D) 0.301

Objective: (1) Use Simulations to Compute Probabilities

105) Which of the following statements is true about the "law of large numbers" (LLN)?

A) If you simulate or conduct an experiment or simulation enough times the empirical probability observed will always match the theoretical probability that is expected.

B) If you repeat a random experiment many, many times, your outcomes should on average approach the theoretical average.

C) If you repeat a random experiment many, many times, your outcomes should be a unique value that is separate from the theoretical average.

D) If an experiment with a random outcome is repeated a large number of times, the empirical probability that is observed is consistently different from the theoretical probability.

Objective: (1) Use Simulations to Compute Probabilities

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

106) Jody flips a coin ten times and observes the outcome of heads three times. Yvonne flips a coin one hundred times and observes the outcome of heads forty-eight times. Jody states that his coin must not be fair because so few heads were observed. Pretend you are Yvonne and explain to Jody why his results do not indicate that he has an unfair coin by explaining to him what the Law of Large Numbers is, and how it justifies the results that were observed in both experiments.

Objective: (1) Use Simulations to Compute Probabilities

17

Answer Key Testname: GOULDCH5TESTGEN

1) D 2) D 3) A 4) B 5) A 6) B 7) B 8) B 9) A 10) B 11) A 12) A 13) An empirical probability is short-run relative frequency based on an experiment. A theoretical probability is a long-run relative frequency of an event after infinitely many trials.

14) This is a theoretical probability because it is not based on a short-run experiment.

15) The probability of each independent event is 1/2 for P(tail) and 1/6 for P(1). The probability of both events together would be 1/2 * 1/6 = 1/12 or 8.3%. This is a theoretical value. An experiment can be designed to throw each coin and die separately and record the results for 10 flips and rolls and compare to the theoretical value.

This will be the empirical probability.

16) D 17) A 18) D

19) B 20) A 21) A 22) A 23) B 24) B 25) A 26) C 27) B 28) B 29) D 30) B 31) B 32) B 33) B 34) A 35) D 36) A 37) C 38) B 39) D 40) C 41) B 42) C 43) A 44) D 45) A 46) D 47) 1/7 + 1/7 = 0.286 48) Complement: Isaac will work Saturday and will work Sunday (not(A or B) = (not A AND not B)); 0.714 49) 1/7 * 1/7 = 0.020 50) 77/200 = 0.385 51) 30/200 = 0.150 52) 2/200 = 0.010 53) (77+70)/200 = 0.735 54) (10/88) versus (11/112) = 0.114 versus 0.098 55) C 56) A 57) B 58) A 59) D 60) A 61) C

62) Various. Any combination of the events "student doing homework – type x" and "student engaged in outside employment – type y".

63) A 64) A 65) C 66) D 67) A 68) B 69) C 70) A 71) A 72) D 73) C 74) 0.013 75) 0.190 76) 0.810 77) 0.763, 0.001 78) B 79) A 80) A 81) B 82) B 83) A 84) B 85) A 86) These two events are most likely independent.

87) These two events are most likely associated.

88) B 89) C 90) A 91) C 92) C 93) C 94) D 95) A 96) D 97) C 98) D 99) B 100) D 18

101) D 102) D 103) B 104) C 105) B 106) The LLN states that if an experiment with a random outcome is repeated a large number of times, the empirical probability is likely to be close to the true (theoretical) probability. A pattern of heads in the short run (like ten trials) can be highly variable, but the more trials that are conducted the closer the empirical probability will tend to approach the theoretical probability. Yvonne did ten times as many trials as Jody and observed an empirical probability that is much closer to the theoretical probability of one half.

Gould/Ryan/Wong Essentials Statistics 3e Chapter 6 Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

1) Determine whether the variable would best be modeled as continuous or discrete: The temperature of a greenhouse at a certain time of the day.

A) Discrete B) Continuous Objective: (1) Determine if a Variable is Continuous or Discrete

2) Determine whether the variable would best be modeled as continuous or discrete: The number of tomatoes harvested each week from a greenhouse tomato plant.

A) Continuous B) Discrete Objective: (1) Determine if a Variable is Continuous or Discrete

3) Determine whether the variable would best be modeled as continuous or discrete: The number of cups dispensed from a beverage vending machine during a 24-hour period.

A) Discrete B) Continuous Objective: (1) Determine if a Variable is Continuous or Discrete

4) Determine whether the variable would best be modeled as continuous or discrete: The temperature of a cup of coffee dispensed from a beverage vending machine, taken four times during a 24-hour period.

A) Continuous B) Discrete Objective: (1) Determine if a Variable is Continuous or Discrete

Provide an appropriate response.

5) The peak shopping time at home improvement store is between 8:00am-11:00 am on Saturday mornings.

Management at the home improvement store randomly selected 105 customers last Saturday morning and decided to observe their shopping habits. They recorded the number of items that each of the customers purchased as well as the total time the customers spent in the store. Identify the types of variables recorded by the home improvement store.

A) number of items - continuous; total time - continuous B) number of items - discrete; total time - continuous C) number of items - discrete; total time - discrete D) number of items - continuous; total time - discrete Objective: (1) Determine if a Variable is Continuous or Discrete

Solve the problem.

6) Determine whether the variable would best be modeled as continuous or discrete: The number of tails when flipping ten coins.

A) Continuous B) Discrete Objective: (1) Determine if a Variable is Continuous or Discrete

7) Determine whether the variable would best be modeled as continuous or discrete: The amount of time it takes students to get to school.

A) Discrete B) Continuous Objective: (1) Determine if a Variable is Continuous or Discrete

1

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

8) Explain the difference between a discrete random variable and a continuous random variable and give an example of each.

Objective: (1) Determine if a Variable is Continuous or Discrete

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

9) A box containing recipes from five categories is dropped so that the recipe cards are thoroughly mixed up. The following table shows the possible categories and the associated probability for a recipe randomly chosen. Does the table represent a probability distribution?

A) Can't be determined with the given information B) No C) Yes Objective: (2) Create a Probability Density Function Table or Graph

10) An MP3 playlist, containing several songs from five genres, is set to shuffle. The following table shows the genre and the associated probability for the first song played. Does the table represent a probability distribution?

A) Can't be determined with the given information B) Yes C) No Objective: (2) Create a Probability Density Function Table or Graph

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied.

11) If a person is randomly selected from a certain town, the probability distribution for the number, x, of siblings is as described in the accompanying table. x P(x) 0 0.26 1 0.28 2 0.20 3 0.12 4 0.08 5 0.03 A) Yes B) Can't be determined with the given information C) No Objective: (2) Create a Probability Density Function Table or Graph

2

12) In a certain town, 30% of adults have a college degree. The accompanying table describes the probability distribution for the number of adults (among 4 randomly selected adults) who have a college degree. x P(x) 0 0.2401 1 0.4116 2 0.2646 3 0.0756 4 0.0081 A) Can't be determined with the given information B) No C) Yes Objective: (2) Create a Probability Density Function Table or Graph

Provide an appropriate response.

13) Students at a local high school were asked how many living grandparents they have and the results are shown below. Find the probability of each number of living grandparents for a randomly selected student in the school, and record the results in table form. Be sure the total of all the probabilities is 1.

Number of living grandparents 0 1 2 3 4 Frequency 34 76 151 207 160 A) Grandparents Probability 0 0.2 1 0.2 2 0.2 3 0.2 4 0.2 C) Grandparents Probability 0 0.054 1 0.121 2 0.240 3 0.330 4 0.255 Objective: (3) Find Probabilities for Discrete-Valued Outcomes

3

B)

D)

Grandparents Probability 0 0.062 1 0.137 2 0.240 3 0.314 4 0.247 Grandparents Probability 1 0.128 2 0.254 3 0.348 4 0.269

14) Students at a local middle school were asked how many siblings they have and the results are shown below. Find the probability of each number of siblings for a randomly selected student in the school, and record the results in table form. Be sure the total of all the probabilities is 1.

Number of siblings 0 1 2 3 4 5 6 7 Frequency 198 252 120 50 22 8 5 1 A) Siblings Probability 0 0.302 1 0.384 2 0.183 3 0.076 4 0.034 5 0.012 6 0.008 7 0.002 C) Siblings Probability 0 0.317 1 0.369 2 0.195 3 0.064 4 0.034 5 0.012 6 0.008 7 0.002

B)

D)

Siblings Probability 0 0.125 1 0.125 2 0.125 3 0.125 4 0.125 5 0.125 6 0.125 7 0.125 Siblings Probability 1 0.550 2 0.262 3 0.109 4 0.048 5 0.017 6 0.011 7 0.002

Objective: (3) Find Probabilities for Discrete-Valued Outcomes

Solve the problem.

15) A summary of the types of movies showing in a small city, contains five genres. The following table shows the genres and the associated probability for that type of movie available on a particular weekend. The table is a probability distribution. If we chose a theater and movie to attend at random, what probability would we have of seeing anything other than a romantic or sci-fi movie?

A) 0.677

B) 0.880

C) 0.323

Objective: (3) Find Probabilities for Discrete-Valued Outcomes

4

D) 0.646

A box contains recipes from five categories. The following table shows the possible categories and the associated probability for a recipe randomly chosen.

16) What is the probability of randomly selecting either an appetizer or salad category? Round to the nearest tenth of a percent.

A) 61.7% B) 3.8% C) 38.3% D) 3.7% Objective: (3) Find Probabilities for Discrete-Valued Outcomes

17) What is the probability of randomly selecting anything but a vegetable or main dish category? Round to the nearest tenth of a percent.

A) 51.4% B) 5.1% C) 4.9% D) 48.6% Objective: (3) Find Probabilities for Discrete-Valued Outcomes

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Solve the problem.

18) A suit of standard playing cards has thirteen cards. Suppose the suit of hearts is thoroughly shuffled and that you have the opportunity to play the following game: You win $10 if you choose the ten or queen of hearts, you lose $5 if you choose the jack or king of hearts, you win $2 if you choose the five or seven of hearts, and you lose $10 if you choose the ace of hearts. With any other outcome you will win or lose nothing. Complete the table that shows the probability distribution. Would it be sensible to play this game?

Objective: (3) Find Probabilities for Discrete-Valued Outcomes

19) A researcher summarized the genres of movies showing in a particular city. The following table shows the possible genres and the associated probability for a movie randomly chosen. What type of distribution does this table represent? What are its characteristics?

What is the probability of randomly selecting a movie genre other than drama or foreign? Round to the nearest tenth of a percent.

Objective: (3) Find Probabilities for Discrete-Valued Outcomes

5

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

20) At a course in public speaking, the instructor always gives an opening speech that lasts between fifteen and eighteen minutes. The length of the speech can be modeled by a uniform distribution, that is, the speech is just as likely to last fifteen minutes as it is to last eighteen minutes. The probability density curve is shown below. What is the probability that the speech will last at least seventeen minutes? What is the probability that the speech will last between fifteen and sixteen minutes?

A) 0.25; 0.50 C) 0.50; 0.75

B) Can't be determined with the given information D) 0.50; 0.25

Objective: (4) Find Probabilities for Continuous-Valued Outcomes

21) At a course in public speaking, the instructor always gives an opening speech that lasts between fifteen and eighteen minutes. The length of the speech can be modeled by a uniform distribution, that is, the speech is just as likely to last fifteen minutes as it is to last eighteen minutes. The probability density curve is shown below. What is the probability that the speech will last sixteen minutes or more? What is the probability that the speech will last between eighteen and nineteen minutes?

A) 0.75; 0.25 C) Can't be determined with the given information Objective: (4) Find Probabilities for Continuous-Valued Outcomes

6

B) 0.50; 0.75 D) 0.50; 0.25

Using the following probability density curve, answer the question.

22) What is the probability that the random variable has a value greater than 6?

A) 0.250 B) 0.125 C) 0.200

D) 0.375

Objective: (4) Find Probabilities for Continuous-Valued Outcomes

23) What is the probability that the random variable has a value less than 2?

A) 0.125 B) 0.000 C) 0.250

D) 0.375

Objective: (4) Find Probabilities for Continuous-Valued Outcomes

A package delivery service divides their packages into weight classes. Suppose that the packages in the 14-20 pound class are uniformly distributed, meaning that all weights within that class are equally likely to occur. The probability density curve is shown below.

24) Find the probability that a randomly selected package will weigh less than 18 pounds.

A) 0.30 B) 0.67 C) 0.80

D) 0.20

Objective: (4) Find Probabilities for Continuous-Valued Outcomes

25) Find the probability that a randomly selected package will weigh between 16 and 18 pounds.

A) 0.80 B) 0.20 C) 3.60 D) 0.33 Objective: (4) Find Probabilities for Continuous-Valued Outcomes

26) the probability that a package weighs less than 20 pounds?

A) 1.00 B) 0.80

C) 0.40

D) 0.20

27) the probability that a package weighs between 14 and 18 pounds?

A) 0.33 B) 0.67 C) 0.80

D) 0.40

Objective: (4) Find Probabilities for Continuous-Valued Outcomes

Objective: (4) Find Probabilities for Continuous-Valued Outcomes

7

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

When exposed to heat, the reaction time of a certain chemical always occurs after thirteen minutes, but before 17 minutes.

Reaction times for this chemical can be modeled by a uniform distribution, that is, the reaction time is just as likely to occur at thirteen minutes as it is to occur at seventeen minutes.

28) Find the probability that the reaction will happen after fifteen minutes. Shade the appropriate area and calculate the numerical value of the probability.

Objective: (4) Find Probabilities for Continuous-Valued Outcomes

29) Find the probability that the reaction time will occur after fourteen minutes, but before fifteen minutes. Shade the appropriate area and calculate the numerical value of the probability.

Objective: (4) Find Probabilities for Continuous-Valued Outcomes

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the following information for the question. The average travel time to work for a person living and working in Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately normally distributed.

30) Which of these statements is asking for a measurement (i. e. is an inverse normal question)?

A) If 15% of people living and working in Kokomo have travel time to work that is below a certain number of minutes, how many minutes would that be?

B) What percentage of people living and working in Kokomo have a travel time to work that is between thirteen and fifteen minutes?

Objective: (1) Understand the Empirical Rule and Normal Distributions

8

31) Which of these statements is asking for a probability?

A) If 15% of people living and working in Kokomo have travel time to work that is below a certain number of minutes, how many minutes would that be?

B) What percentage of people living and working in Kokomo have a travel time to work that is between thirteen and fifteen minutes?

Objective: (1) Understand the Empirical Rule and Normal Distributions

Use the empirical rule to solve the problem.

32) At one college, GPA's are normally distributed with a mean of 2.7 and a standard deviation of 0.4. What percentage of students at the college have a GPA between 2.3 and 3.1?

A) 84.13% B) Almost all C) 95% D) 68% Objective: (1) Understand the Empirical Rule and Normal Distributions

33) The amount of Jen's monthly phone bill is normally distributed with a mean of $78 and a standard deviation of $ 10. What percentage of her phone bills are between $48 and $108?

A) 68% B) 50% C) Almost all D) 95% Objective: (1) Understand the Empirical Rule and Normal Distributions

34) Solar energy is considered by many to be the energy of the future. A recent survey was taken to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $107 and a standard deviation of $12. If the distribution is normal, what percentage of homes will have a monthly utility bill of more than $95?

A) approximately 32% B) approximately 84% C) approximately 95% D) approximately 16% Objective: (1) Understand the Empirical Rule and Normal Distributions

A police radar gun is used to measure the speeds of cars on a highway. The speeds of cars are normally distributed with a mean of 55 mi/hr and a standard deviation of 5 mi/hr.

35) Roughly what percentage of cars are driving less than 45 mi/hr? (Round to the nearest tenth of a percent) A) 95.0% B) 2.5% C) 18.0% D) 5.0% Objective: (1) Understand the Empirical Rule and Normal Distributions

36) Roughly what proportion of cars are driving between 60 and 70 mi/hr? Round to the nearest thousandth) A) .0843 B) 0.314 C) 0.157 D) 0.628 Objective: (1) Understand the Empirical Rule and Normal Distributions

Solve the problem.

37) Some statisticians use a guideline that says that events that happen 5% of the time or less often should be considered "unusual." By this standard, is it unusual to have a car speed of 75 mi/hr or greater?

A) No, this would not be unusual because it is only 2 standard deviations higher than the mean.

B) Yes, this would be unusual because it is 4 standard deviations higher than the mean.

C) No, this would not be unusual because is only 1 standard deviation higher than the mean.

D) Yes, this would be unusual because it is 3 standard deviations higher than the mean.

Objective: (1) Understand the Empirical Rule and Normal Distributions

9

The Normal distribution below models the distribution of highway gas consumption (in miles per gallon) for a large collection of SUVs when driving on level roads. The center is shown at 24.8 mpg and the standard deviations reflect the spread of the data.

38) Choose the most accurate statement.

A) The bottom 0.3% of SUVs get 6.2 mpg or lower.

C) The top 2.5% of SUVs get 37.2 mpg or higher.

B) The top 5% of SUVs get 37.2 mpg or higher.

D) The bottom 32% of SUVs get 18.6 mpg or lower.

Objective: (1) Understand the Empirical Rule and Normal Distributions

39) What percent of SUVs consume 37.2 mpg or less?

A) 90% B) 95%

C) 50%

D) 97.5%

Objective: (1) Understand the Empirical Rule and Normal Distributions

40) Choose the most accurate statement.

A) Approximately 99.7% of all SUVs have gas consumption between 12.4 and 37.2 mpg.

B) The bottom 30% gas consumption of all SUVs is less than 18.6 mpg.

C) Approximately 95% of all SUVs have gas consumption between 12.4 and 37.2 mpg.

D) The top 25% of gas consumption of SUVs is greater than 31.0 mpg.

Objective: (1) Understand the Empirical Rule and Normal Distributions

Solve the problem.

41) The distribution of gas consumption for SUVs driving on flat highways is approximately Normal with a center of 24.8 mpg and a standard deviation of 5 mpg. Which one of the following statements would explain a larger spread of the normal distribution?

A) The standard deviation was 7.5 mpg.

B) The standard deviation was 2.5 mpg.

C) The center of the distribution is less than 24.8 mpg.

D) The center of the distribution is greater than 24.8 mpg.

Objective: (1) Understand the Empirical Rule and Normal Distributions

10

42) The distribution of gas consumption for SUVs (in miles per gallon) is approximately normally distributed with a center of 24.8 mpg and a standard deviation of 5 mpg. A similar data set for a group of sedans is approximately normally distributed with a center of 28 mpg and a standard deviation of 4 mpg. Which one of the following statements is true when the distributions are compared on a number line?

A) The normal distribution for the sedans is shifted to the right and not as spread out.

B) The normal distribution for the sedans is shifted to the right and more spread out.

C) The normal distribution for the SUVs is centered at the same value as for the sedans but spreads out further.

D) The normal distribution of the SUVs is centered at the same value as for the sedans but does not spread out as far.

Objective: (1) Understand the Empirical Rule and Normal Distributions

43) A data set of gas consumption for trucks (in miles per gallon) is approximately normally distributed with a center of 24.8 mpg and a standard deviation of 5 mpg. Which one of the following statements would explain a smaller spread of the normal distribution?

A) The center of the distribution would be less than 24.8 mpg.

B) The center of the distribution would be greater than 24.8 mpg.

C) The standard deviation was 2.5 mpg.

D) The standard deviation was 7.5 mpg.

Objective: (1) Understand the Empirical Rule and Normal Distributions

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

44) The normal distribution below reflects a data set of gas consumption (in miles per gallon) for a group of SUVs. a. State the specifics of what is shown on the bell-shaped curve below, addressing the 68%, 95%, and 99.7% intervals and what they represent. b. Specify what the middle and the standard deviation of this distribution are and what they mean.

Objective: (1) Understand the Empirical Rule and Normal Distributions

45) A study about commuting time for workers in a certain city. The distribution is clustered on the left with most of the values less than about 40 minutes commute. There are a fairly large number of values that are much higher, even stretching out to 150 minutes. There is a 15% chance that a random worker has a commute time of greater than 45 minutes. If you were to sketch this distribution, what would it look like, how would you describe it, and how do you represent the 15% probability?

Objective: (1) Understand the Empirical Rule and Normal Distributions

11

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the following information for the question. Male players at the high school, college and professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballs are approximately normally distributed.

46) Roughly what percentage of regulation basketballs weigh less than 20.7 ounces? Round to the nearest tenth of a percent.

A) 5.7% of the basketballs will weigh less than 20.7 ounces.

B) 9.7% of the basketballs will weigh less than 20.7 ounces.

C) 22.3% of the basketballs will weigh less than 20.7 ounces.

D) 40.3% of the basketballs will weigh less than 20.7 ounces.

Objective: (2) Solve Applications of Normal Distributions

47) Roughly what percentage of regulation basketballs weigh more than 23.1 ounces? Round to the nearest tenth of a percent.

A) Roughly 15.1% of the basketballs will weigh more than 23.1 ounces.

B) Roughly 42.3% of the basketballs will weigh more than 23.1 ounces.

C) Roughly 13.6% of the basketballs will weigh more than 23.1 ounces.

D) Roughly 36.4% of the basketballs will weigh more than 23.1 ounces.

Objective: (2) Solve Applications of Normal Distributions

48) If a regulation basketball is randomly selected, what is the probability that it will weigh between 20.5 and 23.5 ounces? Round to the nearest thousandth.

A) 0.134 B) 0.704 C) 0.267 D) 0.866 Objective: (2) Solve Applications of Normal Distributions

49) If a regulation basketball is randomly selected, what is the probability that it will weigh between 19.5 and 22.5 ounces? Round to the nearest thousandth.

A) 0.723 B) 0.547 C) 0.685 D) 0.315 Objective: (2) Solve Applications of Normal Distributions

50) Would it be unusual to randomly select a regulation basketball and find that it weighs 17.9 ounces?

A) Yes, this would be unusual.

B) No, this would not be unusual.

Objective: (2) Solve Applications of Normal Distributions

51) Would it be unusual to randomly select a regulation basketball and find that it weighs 23.75 ounces?

A) No, this would not be unusual.

B) Yes, this would be unusual.

Objective: (2) Solve Applications of Normal Distributions

Use the following information for the question. The average travel time to work for a person living and working in Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately normally distributed.

52) Approximately what percentage of people living and working in Kokomo have a travel time to work of at least 20 minutes? Round to the nearest whole percent.

A) 75% B) 15% C) 25% D) None of these.

Objective: (2) Solve Applications of Normal Distributions

12

53) Approximately what percentage of people living and working in Kokomo have a travel time to work that is less than 15.5 minutes? Round to the nearest whole percent.

A) 25% B) 37% C) 63% D) None of these.

Objective: (2) Solve Applications of Normal Distributions

Solve the problem.

54) Suppose that weights of cans of AJ's brand whipped cream have a population mean of 7.5 ounces and a population standard deviation of 0.27 ounces and are approximately normally distributed. Which of the following statements are correct? Choose the best statement.

A) The probability that a randomly selected can of AJ's whipped cream will weigh between 7.8 ounces and 8.3 ounces is approximately 0.131.

B) Approximately 95% of all cans of AJ's whipped cream will weigh between 6.96 ounces and 8.04 ounces.

C) Less than 1% of all cans of AJ's whipped cream will weigh more than 8.3 ounces.

D) All of these statements are true.

Objective: (2) Solve Applications of Normal Distributions

13

55) Suppose that weights of cans of Benneke brand peaches have a population mean of 13.5 ounces and a population standard deviation of 0.33 ounces and are approximately normally distributed. Which of the following statements are correct? Choose the best statement.

A) About 4% of all cans of Benneke peaches will weigh less than 12.9 ounces B) Approximately 95% of all Benneke brand canned peaches will weigh between 12.85 ounces and 14.15 ounces.

C) The probability that a randomly selected can of Benneke peaches will weigh between 12.9 ounces and 13.6 ounces is approximately 0.585.

D) All of these statements are true.

Objective: (2) Solve Applications of Normal Distributions

Use a table or technology to answer the question.

56) Find the area to the left of a z-score of -0.47.

A) 0.3192 B) 06808

C) 09871

D) 03446

C) 0.0487

D) 0.9299

58) Find the probability that a z-score will be between 0.3 and 1.4.

A) 0.3821 B) 0.3013 C) 0.9192

D) 0.6179

Objective: (2) Solve Applications of Normal Distributions

57) Find the probability that a z-score will be more than 2.30.

A) 0.0107 B) 0.0701 Objective: (2) Solve Applications of Normal Distributions

Objective: (2) Solve Applications of Normal Distributions

Provide an appropriate response.

59) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 470 seconds and a standard deviation of 40 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 378 seconds.

A) 0.4893 B) 0.5107 C) 0.9893 D) 0.0107 Objective: (2) Solve Applications of Normal Distributions

14

60) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 40 seconds. Find the probability that a randomly selected boy in secondary school will take longer than 368 seconds to run the mile.

A) 0.4893 B) 0.5107 C) 0.0107 D) 0.9893 Objective: (2) Solve Applications of Normal Distributions

61) The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 5.0 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will take between 3.5 and 6.0 minutes to find a parking spot in the library lot.

A) 0.0919 B) 0.2255 C) 0.7745 D) 0.4938 Objective: (2) Solve Applications of Normal Distributions

62) The amount of soda a dispensing machine pours into a 12 ounce can of soda follows a normal distribution with a mean of 12.24 ounces and a standard deviation of 0.16 ounce. The cans only hold 12.40 ounces of soda. Every can that has more than 12.40 ounces of soda poured into it causes a spill and the can needs to go through a special cleaning process before it can be sold. What is the probability a randomly selected can will need to go through this process?

A) 0.1587 B) 0.8413 C) 0.6587 D) 0.3413 Objective: (2) Solve Applications of Normal Distributions

The mean time it takes for workers at a factory to insert a delicate bolt into an engine is 15 minutes. The standard deviation of time to insert the bolt is 4.0 minutes and the distribution of time is approximately normally distributed.

63) For a randomly selected worker, what's the approximate probability the bolt will be inserted in 19 minutes or less?

Round to the nearest whole percent.

A) 18% B) 84% C) 50% D) 16% Objective: (2) Solve Applications of Normal Distributions

64) 97.5% of the time, the bolt is inserted in less than which time value? Round to the nearest whole number.

A) 19 minutes B) 15 minutes C) 7 minutes D) 23 minutes Objective: (2) Solve Applications of Normal Distributions

Solve the problem.

65) Admission to a certain university is determined by an entry exam. The scores of this test are Normally distributed with a mean of 400 and a standard deviation of 60. Only students who score in the top 30% will be offered admission. Amy scores 425 on the test. Choose the most accurate statement.

A) The top 30% of all students have scores greater than or equal to 520 so she will not be admitted.

B) The top 30% is defined with a score greater than or equal to 431.4 so she will not be admitted.

C) The top 30% is defined with a score less than or equal to 431.4 so she will be admitted.

D) The top 30% of all students have scores greater than or equal to 460 so she will not be admitted.

Objective: (2) Solve Applications of Normal Distributions

The average travel time to work for a person living and working in Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately normally distributed.

66) Approximately what percentage of people living and working in Kokomo have a travel time to work that is less than 12.5 minutes? Round to the nearest whole percent.

A) 84% B) 16% C) 68% D) 5% Objective: (2) Solve Applications of Normal Distributions

15

Solve the problem.

67) The normal distribution below reflects a data set of gas consumption (in miles per gallon) for a group of trucks.

The center is shown at 24 mpg and the standard deviation is 4 mpg. Choose the most accurate statement.

A) Approximately 68% of all of the trucks miles per gallon is between 20 and 28.

B) The top 2.5% of all of the trucks miles per gallon is greater than 32.

C) Approximately 99.7% of all of the trucks miles per gallon is between 12 and 36.

D) All of these statements are accurate.

Objective: (2) Solve Applications of Normal Distributions

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Circumferences of regulation soccer balls have a mean of 69 cm with as standard deviation of 1.50 cm. Assume that the circumferences of soccer balls are approximately normally distributed.

68) Roughly what percentage of regulation soccer balls has a circumference that is greater than 69.9 cm? Round to the nearest tenth of a percent.

Objective: (2) Solve Applications of Normal Distributions

69) If a regulation soccer ball is randomly selected, what is the probability that it will have a circumference between 66.9 and 68.9 cm? Round to the nearest thousandth.

Objective: (2) Solve Applications of Normal Distributions

70) Would it be unusual to randomly select a regulation soccer ball and find that it has a circumference that is greater than 72.3 cm?

Objective: (2) Solve Applications of Normal Distributions

Suppose that weights of jars of Puff brand marshmallow cream has a population mean of 24.5 ounces and a population standard deviation of 0.19 ounces and are approximately normally distributed. Use the figure below to find determine the specified probabilities.

71) What is the probability that a randomly selected jar of Puff marshmallow cream will be greater than 24.45 ounces?

What is the probability that a randomly selected jar of Puff marshmallow cream will be less than 24.22 ounces?

Round to the nearest thousandth.

Objective: (2) Solve Applications of Normal Distributions

16

72) If a large random sample of Puff marshmallow cream jars were weighed, approximately what percentage of the jars would weigh between 24.22 and 24.45 ounces? Round to the nearest tenth of a percent.

Objective: (2) Solve Applications of Normal Distributions

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the following information for the question. The average travel time to work for a person living and working in Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately normally distributed.

73) Suppose that it is reported in the news that 12% of the people living and working in Kokomo feel that their commute is too long. What is the travel time to work that separates the top 12% of people with the longest travel times and the lower 88%? Round to the nearest tenth of a minute.

A) 22.3 minutes B) 18.1 minutes C) 26.0 minutes D) None of these Objective: (3) Use the Normal Distribution to Find Percentiles

74) Suppose that it is reported in the news that 8% of the people living and working in Kokomo feel "very satisfied" with their commute time to work. What is the travel time to work that separates the bottom 8% of people with the shortest travel times and the upper 92%? Round to the nearest tenth of a minute.

A) 13.8 minutes B) 17.2 minutes C) 10.7 minutes D) None of these Objective: (3) Use the Normal Distribution to Find Percentiles

Solve the problem.

75) The normal model N(58, 21) describes the distribution of weights of chicken eggs in grams. Suppose that the weight of a randomly selected chicken egg has a z-score of 1.78. What is the weight of this egg in grams? Round to the nearest hundredth of a gram.

A) 89.50 grams B) 65.25 grams C) 79.50 grams D) 95.38 grams Objective: (3) Use the Normal Distribution to Find Percentiles

76) The normal model N(58, 21) describes the distribution of weights of chicken eggs in grams. Suppose that the weight of a randomly selected chicken egg has a z-score of -2.01. What is the weight of this egg in grams? Round to the nearest hundredth of a gram.

A) 31.20 grams B) 38.10 grams C) 28.50 grams D) 15.80 grams Objective: (3) Use the Normal Distribution to Find Percentiles

Provide an appropriate response.

77) Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test). Find the IQ score separating the bottom 20% from the top 80%.

A) 88.7 B) 87.4 C) 86.1 D) 87.9 Objective: (3) Use the Normal Distribution to Find Percentiles

78) Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test). Find the IQ score separating the top 16% from the others.

A) 99.8 B) 106.6 C) 85.0 D) 114.9 Objective: (3) Use the Normal Distribution to Find Percentiles

79) The amount of rainfall in January in a certain city is normally distributed with a mean of 4.2 inches and a standard deviation of 0.5 inches. Find the value of the 25th percentile, rounded to the nearest tenth.

A) 3.9 B) 1.1 C) 4.0 D) 4.5 Objective: (3) Use the Normal Distribution to Find Percentiles

17

80) The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2200 miles. What warranty should the company use if they want 96% of the tires to outlast the warranty?

A) 57,800 mi B) 62,200 mi C) 63,850 mi D) 56,150 mi Objective: (3) Use the Normal Distribution to Find Percentiles

The average travel time to work for a person living and working in Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately normally distributed.

81) What is the travel time to work that separates the bottom 2.5% of people with the median or 50%? Round to the nearest tenth of a minute.

A) 12.5 to 17 minutes B) 8 to 17 minutes C) 7 to 17 minutes D) 3.5 to 17 minutes Objective: (3) Use the Normal Distribution to Find Percentiles

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Solve the problem.

82) The normal model N (210, 45) describes the weights of baby elephants in pounds. Suppose that the weight of a randomly selected baby elephant has a zscore of -1.35. What is the weight of this baby elephant in pounds? Round to the nearest tenth of a pound.

Objective: (3) Use the Normal Distribution to Find Percentiles

On a busy day, the average roller coaster wait time at a large amusement park is 27 minutes. Suppose the standard deviation of wait time is 11.9 minutes and the distribution of wait times is approximately normally distributed.

83) If it is a busy day, approximately what percentage of people at the amusement park will have a wait time that is at least 30 minutes? Round to the nearest whole percent.

Objective: (3) Use the Normal Distribution to Find Percentiles

84) To improve customer satisfaction, the amusement park manager has decided to give food coupons to customers with long wait times. The manager decides to give the coupons to the top 10% of people waiting the longest. What is the minimum wait time for the top 10%? Round to the nearest tenth of a minute.

Objective: (3) Use the Normal Distribution to Find Percentiles

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

85) Which of the following characteristics are not required for the binomial model?

A) There are a fixed number of trials.

B) The trials must be independent.

C) The probability of success must be the same as the probability of failure.

D) Only two outcomes are possible at each trial.

Objective: (1) Understand the Binomial Model

86) Which of the following characteristics are not required for the binomial model?

A) The outcome must be a discrete numerical variable.

B) The probability of success is the same at each trial.

C) The trials must be independent.

D) There are a fixed number of trials.

Objective: (1) Understand the Binomial Model

18

87) Determine which of the given procedures describe a binomial distribution.

A) Observing that five out of the next ten customers at a hotdog stand order hot peppers given that the probability of ordering hot peppers is 0.18.

B) Record the number of ear piercings in a group of 30 randomly selected college students.

C) Surveying customers leaving a hardware store until a customer responds that he or she spent more than fifty dollars.

Objective: (1) Understand the Binomial Model

88) Determine which of the given procedures describe a binomial distribution.

A) Observing that ten out of the next twenty customers at a grocery store checkout use a credit card given that the probability of using a credit card is 0.58.

B) Record the number of songs downloaded in a month for a group of 30 randomly selected college students.

C) Surveying customers entering a sporting equipment store until a customer responds that he or she was shopping for a bicycle.

Objective: (1) Understand the Binomial Model

Provide an appropriate response.

89) Decide whether the experiment is a binomial experiment. If it is not, explain why. You observe the gender of the next 450 babies born at a local hospital. The random variable represents the number of boys.

A) Not a binomial experiment. The trials are not independent.

B) Not a binomial experiment. There are more than two outcomes.

C) Binomial experiment D) Not a binomial experiment. The probability of success is not the same for each trial.

Objective: (1) Understand the Binomial Model

90) Decide whether the experiment is a binomial experiment. If it is not, explain why. You draw a marble 300 times from a bag with three colors of marbles. The random variable represents the color of marble that is drawn.

A) Not a binomial experiment. There are more than two outcomes.

B) Not a binomial experiment. The probability of success is not the same for each trial.

C) Binomial experiment D) Not a binomial experiment. The trials are not independent.

Objective: (1) Understand the Binomial Model

91) Decide whether the experiment is a binomial experiment. If it is not, explain why. In a game you spin a wheel that has 18 different letters 450 times. The random variable represents the selected letter on each spin of the wheel.

A) Not a binomial experiment. The trials are not independent.

B) Not a binomial experiment. There are more than two outcomes.

C) Not a binomial experiment. The probability of success is not the same for each trial.

D) Binomial experiment Objective: (1) Understand the Binomial Model

92) Decide whether the experiment is a binomial experiment. If it is not, explain why. Testing a cough suppressant using 240 people to determine if it is effective. The random variable represents the number of people who find the cough suppressant to be effective.

A) Not a binomial experiment. The probability of success is not the same for each trial.

B) Not a binomial experiment. There are more than two outcomes.

C) Binomial experiment D) Not a binomial experiment. The trials are not independent.

Objective: (1) Understand the Binomial Model

19

Solve the problem.

93) Determine which of the given procedures describe a binomial distribution.

A) The number out of the next ten customers at a hotdog stand order who order onions, assuming that each has the same probability of ordering onions.

B) The number of customers surveyed, while leaving a grocery store, until a customer responds that he or she spent more than fifty dollars.

C) The ages of every 5th person entering a department store.

D) The number of tattoos in a group of 30 randomly selected college students.

Objective: (1) Understand the Binomial Model

94) Can the following problem be solved by using a binomial model? Let's say that the probability that a student will arrive on time for a statistics class is 70%. How many students out of 30 would be on time for the last day of class?

A) A binomial model is only valid for the average probability rather than a particular day's probability.

B) This problem can be solved using the binomial model because the students are not independent.

C) Not enough information is provided to determine if the binomial model can be used.

D) This problem cannot be solved using the binomial model because the students are not independent.

Objective: (1) Understand the Binomial Model

95) Which of the following characteristics is not required for the binomial model?

A) The probability of success and of failure must be equal.

B) The probability of success is the same at each trial.

C) There are a fixed number of trials.

D) The trials must be independent.

Objective: (1) Understand the Binomial Model

96) Determine which of the given procedures describe a binomial distribution.

A) Record the number of songs downloaded in a month for a group of 30 randomly selected college students.

B) Observing that ten out of the next twenty customers at a grocery store checkout use a credit card given that the probability of using a credit card is 0.58.

C) Surveying every 5th person going into a department store to determine age groups of customers.

D) Surveying customers entering a sporting equipment store until a customer responds that he or she was shopping for a bicycle.

Objective: (1) Understand the Binomial Model

97) Assume 80% of adults with arthritis symptoms report relief with a specific medication. If a new medication is given to 10 new patients with symptoms, what is the probability that the medication effectively relieves their symptoms? Select the most accurate statement to investigate the assumptions for using a binomial distribution model.

A) The outcome is relief from symptoms, yes or no with relief as a yes.

B) It is reasonable to assume that the replications are independent.

C) The probability of success for each new patient is 0.8.

D) All of these assumptions are true.

Objective: (1) Understand the Binomial Model

20

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

98) a. List the four characteristics of the binomial model. b. At a county animal shelter, the probability that a stray cat comes into the shelter with rabies is 0.145 and the probability that a stray dog comes into the shelter with rabies is 0.157. A volunteer at the shelter records whether the next thirty cats or dogs delivered to the shelter has rabies. Which of the condition or conditions for use of the binomial model is or are not met?

Objective: (1) Understand the Binomial Model

Suppose that the probability that the train travelling from Holland, Michigan to Chicago, Illinois arrives on time is 0.80.

For the questions that follow, consider a sample of twenty randomly selected train trips.

99) Approximately how many trips would you expect to arrive on time out of twenty randomly selected trips, give or take how many trips? Round to the nearest whole trip.

Objective: (1) Understand the Binomial Model

Suppose that a binomial distribution is illustrated by the figure below:

100) a. What is displayed in this graph, being as specific as possible? b. How would you determine the probability for x being less than 5? Round to the nearest hundredth place.

Objective: (1) Understand the Binomial Model

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the following information to answer the question. Suppose that the probability that a person books a hotel using an online travel website is 0.68. For the questions that follow, consider a sample of fifteen randomly selected people who recently booked a hotel.

101) What is the probability that exactly ten people out of fifteen people used an online travel website when they booked their hotel? Round to the nearest thousandth.

A) 0.048 B) 0.552 C) 0.213 D) 0.287 Objective: (2) Find Binomial Probabilities

102) What is the probability that at least fourteen out of fifteen people used an online travel website when they booked their hotel? Round to the nearest thousandth.

A) 0.028 B) 0.978 C) 0.323 D) 0.025 Objective: (2) Find Binomial Probabilities

21

103) What is the probability that no more than four out of fifteen people used an online travel website when they booked their hotel? Round to the nearest thousandth.

A) 0.321 B) 0.001 C) 0.111 D) None of these Objective: (2) Find Binomial Probabilities

Use the following information to answer the question. Suppose that the probability that a person books an airline ticket using an online travel website is 0.72. For the questions that follow, consider a sample of ten randomly selected people who recently booked an airline ticket.

104) What is the probability that exactly seven out of ten people used an online travel website when they booked their airline ticket? Round to the nearest thousandth.

A) 0.480 B) 0.998 C) 0.264 D) 0.035 Objective: (2) Find Binomial Probabilities

105) What is the probability that at least nine out of ten people used an online travel website when they booked their airline ticket? Round to the nearest thousandth.

A) 0.183 B) 0.935 C) 0.065 D) 0.857 Objective: (2) Find Binomial Probabilities

106) What is the probability that no more than three out of ten people used an online travel website when they book their airline ticket? Round to the nearest thousandth.

A) 0.007 B) 0.115 C) 0.733 D) None of these Objective: (2) Find Binomial Probabilities

Solve the problem.

107) Five identical poker chips are tossed in a hat and mixed up. Two of the chips have been marked with an X to indicate that if drawn a valuable prize will be awarded. If you and two of your friends each draws a chip (with replacement), what is the probability that at least one of your group of three will win the valuable prize? Round to the nearest thousandth.

A) 0.978 B) 0.784 C) 0.216 D) None of these Objective: (2) Find Binomial Probabilities

108) Five identical poker chips are tossed in a hat and mixed up. Two of the chips have been marked with an X to indicate that if drawn a valuable prize will be awarded. If you and three of your friends each draws a chip (with replacement), what is the probability that at least one of your group of four will win the valuable prize? Round to the nearest thousandth.

A) 0.758 B) 0.130 C) 0.870 D) None of these Objective: (2) Find Binomial Probabilities

Find the indicated probability. Round to three decimal places.

109) Assume that male and female births are equally likely and that the birth of any child does not affect the probability of the gender of any other children. Find the probability of exactly nine girls in ten births.

A) 0.020 B) 0.09 C) 0.9 D) 0.010 Objective: (2) Find Binomial Probabilities

110) In a recent survey, 72% of the community favored building a health center in their neighborhood. If 14 citizens are chosen, find the probability that exactly 10 of them favor the building of the health center.

A) 0.714 B) 0.720 C) 0.001 D) 0.230 Objective: (2) Find Binomial Probabilities

22

111) The probability that an individual has 20-20 vision is 0.19. In a class of 23 students, what is the probability of finding five people with 20-20 vision?

A) 0.217 B) 0.188 C) 0.000 D) 0.19 Objective: (2) Find Binomial Probabilities

112) According to insurance records a car with a certain protection system will be recovered 95% of the time. Find the probability that 5 of 6 stolen cars will be recovered.

A) 0.95 B) 0.833 C) 0.232 D) 0.05 Objective: (2) Find Binomial Probabilities

113) The probability that a football game will go into overtime is 13%. What is the probability that two of three football games will go to into overtime?

A) 0.13 B) 0.0169 C) 0.044 D) 0.295 Objective: (2) Find Binomial Probabilities

114) Fifty percent of the people that use the Internet order something online. Find the probability that only five of 8 Internet users will order something online.

A) 1.750 B) 0.004 C) 0.219 D) 0.625 Objective: (2) Find Binomial Probabilities

115) The probability that a house in an urban area will develop a leak is 3%. If 29 houses are randomly selected, what is the probability that none of the houses will develop a leak?

A) 0.001 B) 0.413 C) 0.000 D) 0.030 Objective: (2) Find Binomial Probabilities

116) Sixty-five percent of men consider themselves knowledgeable soccer fans. If 13 men are randomly selected, find the probability that exactly three of them will consider themselves knowledgeable fans.

A) 0.002 B) 0.231 C) 0.165 D) 0.65 Objective: (2) Find Binomial Probabilities

117) A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?

A) 0.172 B) 0.205 C) 0.828 D) 0.377 Objective: (2) Find Binomial Probabilities

118) A machine has 7 identical components which function independently. The probability that a component will fail is 0.2. The machine will stop working if more than three components fail. Find the probability that the machine will be working.

A) 0.033 B) 0.967 C) 0.996 D) 0.029 Objective: (2) Find Binomial Probabilities

119) Find the probability of at least 2 girls in 7 births. Assume that male and female births are equally likely and that the births are independent events.

A) 0.938 B) 0.773 C) 0.063 D) 0.164 Objective: (2) Find Binomial Probabilities

23

120) An airline estimates that 94% of people booked on their flights actually show up. If the airline books 78 people on a flight for which the maximum number is 76, what is the probability that the number of people who show up will exceed the capacity of the plane?

A) 0.040 B) 0.008 C) 0.048 D) 0.146 Objective: (2) Find Binomial Probabilities

Use the following information to answer the question.

121) What is the approximate probability that x is equal to 5 or less? Round to nearest hundredth place.

A) 0.17 B) 0.13 C) 0.71 D) 0.29 Objective: (2) Find Binomial Probabilities

122) What is the approximate probability that x is equal to more than 10? Round to the nearest hundredth place.

A) 0.20 B) 0.10 C) 0.88 D) 0.02 Objective: (2) Find Binomial Probabilities

123) What is the approximate probability that x = 6 or less? Round to nearest hundredth place.

A) 0.13 B) 0.44 C) 0.76

D) 0.56

Objective: (2) Find Binomial Probabilities

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Suppose that the probability that the train travelling from Holland, Michigan to Chicago, Illinois arrives on time is 0.80.

For the questions that follow, consider a sample of twenty randomly selected train trips.

124) What is the probability that exactly fifteen trips out of twenty will arrive in Chicago on time? Round to the nearest thousandth.

Objective: (2) Find Binomial Probabilities

24

Suppose that a binomial distribution is illustrated by the figure below:

125) a. What is the approximate probability that x = between 7 and 15? Round to the nearest hundredth place. b. Does this probability make sense when looking at the graph of the distribution? Why? Objective: (2) Find Binomial Probabilities

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the following information to answer the question. Suppose that the probability that a person books a hotel using an online travel website is 0.68. For the questions that follow, consider a sample of fifteen randomly selected people who recently booked a hotel.

126) Out of fifteen randomly selected people, how many would you expect to use an online travel website to book their hotel, give or take how many? Round to the nearest whole person.

A) 10 people, give or take 2 people B) 9 people, give or take 3 people C) 10 people, give or take 3 people D) 5 people, give or take 2 people Objective: (3) Find the Expected Number and Standard Deviation for a Binomial Distribution

Use the following information to answer the question. Suppose that the probability that a person books an airline ticket using an online travel website is 0.72. For the questions that follow, consider a sample of ten randomly selected people who recently booked an airline ticket.

127) Out of ten randomly selected people, how many would you expect to use an online travel website to book their hotel, give or take how many? Round to the nearest whole person.

A) 7 people, give or take 1 person B) 3 people, give or take 4 people C) 7 people, give or take 2 people D) 8 people, give or take 2 people Objective: (3) Find the Expected Number and Standard Deviation for a Binomial Distribution

Solve the problem.

128) Suppose that the probability that a person between the ages of 19 and 24 checks their daily horoscope is 0.12. If 400 randomly selected people between the ages of 19 and 24 were asked "Do you check your daily horoscope?", would you be surprised if 63 or more said yes to this question? Why? A) No, 63 is within the expected range of people.

B) Yes, 63 would be an unusually small number of people given the known probability of 0.12.

C) Yes, 63 would be an unusually large number of people given the known probability of 0.12.

D) Cannot be determined with the given information.

Objective: (3) Find the Expected Number and Standard Deviation for a Binomial Distribution

25

129) Suppose that the probability that a person between the ages of 19 and 24 buys at least one tabloid magazine per week is 0.115. If 500 randomly selected people between the ages of 19 and 24 were asked "Do you buy at least one tabloid magazine per week?", would you be surprised if 45 or more said yes to this question? Why? A) No, 45 is within the expected range of people.

B) Yes, 45 would be an unusually large number of people given the known probability of 0.12.

C) Yes, 45 would be an unusually small number of people given the known probability of 0.115.

D) Cannot be determined with the given information.

Objective: (3) Find the Expected Number and Standard Deviation for a Binomial Distribution

130) On a multiple choice test with 12 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the expected number of correct answers.

A) 6 B) 4 C) 9 D) 3 Objective: (3) Find the Expected Number and Standard Deviation for a Binomial Distribution

131) The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 3. Find the expected number of seeds germinating in each batch.

A) 2.1 B) 0.9 C) 2.13 D) 2.7 Objective: (3) Find the Expected Number and Standard Deviation for a Binomial Distribution

132) The probability that a person has immunity to a particular disease is 0.4. Find the expected number of people who have immunity in samples of size 13.

A) 6.5 B) 0.4 C) 5.2 D) 7.8 Objective: (3) Find the Expected Number and Standard Deviation for a Binomial Distribution

133) The probability is 0.4 that a person shopping at a certain store will spend less than $20. For groups of size 22, find the expected number of shoppers who spend less than $20.

A) 13.2 B) 8.0 C) 12.0 D) 8.8 Objective: (3) Find the Expected Number and Standard Deviation for a Binomial Distribution

134) In a certain town, 60 percent of voters are in favor of a given ballot measure and 40 percent are opposed. For groups of 280 voters, find the expected number of voters who oppose the measure.

A) 60 B) 40 C) 168 D) 112 Objective: (3) Find the Expected Number and Standard Deviation for a Binomial Distribution

135) On a multiple choice test with 7 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the standard deviation for the number of correct answers.

A) 1.3 B) 13.1 C) 1.1 D) 1.7 Objective: (3) Find the Expected Number and Standard Deviation for a Binomial Distribution

136) The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 8. Find the standard deviation for the number of seeds germinating in each batch.

A) 1.3 B) 16.8 C) 2.8 D) 1.7 Objective: (3) Find the Expected Number and Standard Deviation for a Binomial Distribution

26

Answer Key Testname: GOULDCH6TEST

1) B 2) B 3) A 4) A 5) B 6) B 7) B 8) A discrete random variables has a numerical outcome that can be listed or counted, A continuous random variable occurs over an infinite range of values and cannot be listed or counted.

Examples will vary.

9) C 10) C 11) C 12) C 13) C 14) A 15) A 16) C 17) D 18) The probability column should contain the following values: 2/13, 2/13, 2/13, 1/13, 6/13. Your chances of winning money are slightly better than losing.

19) a. This is a probability distribution. b. Characteristics are that it must list all the possible outcomes and list all the associated probabilities. c. The probability of randomly selecting a movie genre other than drama or foreign is 1 – (0.421+0.093) = 0.486 or 4.9% 20) D 21) A 22) A 23) C 24) B 25) D 26) A 27) B 28) 0.50, the right half of the distribution should be shaded.

29) 0.25, the rectangle between 14 and 15 should be shaded.

30) A 31) B 32) D 33) C 34) B 35) B 36) C 37) B 38) C 39) D 40) C 41) A 42) A 43) C

44) a. The intervals shown represent +/1 standard deviation or the middle 68% (68% of middle values range from 18.6 to 31.0 mpg), +/2 standard deviations or the middle 95% (95% of middle values range from 12.4 to 37.2 mpg), +/3 standard deviations or the middle 99.7% (99.7% of middle values range from 6.2 to 43.4 mpg). b. The normal distribution shown has a center (mean, median) of 24.8 mpg with a standard deviation of 6.2 mpg (representing the spread).

45) The distribution should be sketched as a right skewed distribution (most of the values clustered on the left side (zero to about 40 minutes) and then stretched out to the right showing 150 minutes on far right. The 15% probability is the shaded area under the curve from a vertical line at 45 all the way to the right end.

46) B 47) C 48) D 49) C 50) A 51) A 52) C 53) B 27

54) D 55) D 56) A 57) A 58) B 59) D 60) D 61) C 62) A 63) B 64) D 65) B 66) B 67) D 68) 27.4% 69) 0.393 70) Yes, 72.3 cm would be unusual. It is more the two standard deviations from the mean.

71) 0.604; 0.070 72) 32.6% 73) A 74) C 75) D 76) D 77) B 78) D 79) A 80) D 81) B 82) 149.3 lbs.

83) 40% will have at least a 30 minute wait time.

84) 42.3 minutes 85) C 86) A 87) A 88) A 89) C 90) A 91) B 92) C 93) A 94) D 95) A 96) B 97) D

Answer Key Testname: GOULDCH6TEST

98) a. (1) A fixed number of trials, (2) Only two possible outcomes for each trial, (3) The probability of success is the same from trial to trial, and (4) The trials are independent. b. There are a fixed number of trials, there are only two outcomes (rabies or no rabies). The probability of success is not the same from trial to trial since the trials include cats and dogs.

99) 16 trips give or take 2 trips 100) a. The graph shows the binomial distribution for each event. It displays the specific probabilities for each x value. b. The method to determine the probability for x less than 5 is to add all of the probabilities for x = 4, x = 3, x = 2, etc.

The result is approximately 0.16 or 16%?

101) C 102) D 103) B 104) C 105) A 106) A 107) B 108) C 109) D 110) D 111) B 112) C 113) C 114) C

115) B 116) A 117) D 118) B 119) A 120) C 121) D 122) B 123) B 124) 0.175 125) a. The probability of x being between 7 and 15 is approximately 0.56 or 56%. b. The shape of the distribution shows that the probability is greater than approximately half of the distribution since the probabilities skew slightly to the right.

126) A 127) A 128) C 129) A 130) D 131) A 132) C 133) D 134) D 135) C 136) A

28

Gould/Ryan/Wong Essentials Statistics 3e Chapter 7 Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Fill in the blank to complete the statement.

1) The collection of the ages of all the U.S. first ladies when they married is a A) Sample

B) Parameter

C) Statistic

.

D) Population

Objective: (1) Understand the Difference Between a Sample and a Population

2) Suppose that the age of all the U.S. first ladies when they married was recorded. The mean age of U.S. first ladies when they married would be a .

A) Statistic

B) Parameter

C) Sample

D) Population

Objective: (1) Understand the Difference Between a Sample and a Population

3) Researchers are interested in learning more about the age of women when they marry for the first time so they survey 500 married or divorced women and ask them how old they were when they first married. The collection of the ages of the 500 women when they first married is a .

A) Sample

B) Statistic

C) Parameter

D) Population

Objective: (1) Understand the Difference Between a Sample and a Population

4) Suppose that the age of all the U. S. vice presidents when they took office was recorded. The collection of the ages of all the U. S. vice presidents when they took office is a .

A) Population

B) Sample

C) Statistic

D) Parameter

Objective: (1) Understand the Difference Between a Sample and a Population

5) The mean age of all the U. S. vice presidents when they took office would be a A) Sample

B) Parameter

C) Statistic

.

D) Population

Objective: (1) Understand the Difference Between a Sample and a Population

6) Researchers are interested in learning more about the age of men when they marry for the first time so they survey 500 married or divorced men and ask them how old they were when they first married. The mean of age of the 500 men when they married for the first time would be a .

A) Statistic

B) Population

C) Sample

D) Parameter

Objective: (1) Understand the Difference Between a Sample and a Population

7) Researchers want to find out which U. S. movie has the most positive audience reaction for the current week. As they exited a randomly selected movie theater, movie-goers were asked to give the movie they had just viewed a letter grade of A, B, C, D, or F. In this scenario, the movie-goers are an example of a .

A) Variable

B) Population

Objective: (1) Understand the Difference Between a Sample and a Population

1

C) Sample

Solve the problem.

8) The deacons at a local church surveyed the congregation to find out if members would be willing to fund a new construction project. In this example, what is the population of interest?

A) The deacons B) The survey respondents C) The congregation D) None of these Objective: (1) Understand the Difference Between a Sample and a Population

Answer the question.

9) A magazine publisher mails a survey to every subscriber asking about the timeliness of its subscription service.

The publisher finds that only 3% of the subscribers responded. This 3% represents what?

A) The population B) The sample Objective: (1) Understand the Difference Between a Sample and a Population

10) A magazine publisher always mails out a questionnaire six months before a subscription ends. This questionnaire asks its subscribers if they are going to renew their subscriptions. On average, only 10% of the subscribers respond to the questionnaire. Of the 10% who do respond, an average of 47% say that they will renew their subscription.

This 10% who respond to the questionnaire are known as what?

A) The population B) The sample Objective: (1) Understand the Difference Between a Sample and a Population

11) A computer network manager wants to test the reliability of some new and expensive fiber-optic Ethernet cables that the computer department just received. The computer department received 3 boxes containing 40 cables each.

The manager does not have the time to test every cable in each box. The manager will choose one box at random and test 8 cables chosen randomly within that box. What is the population?

A) The 8 cables chosen randomly for testing B) 120 cables C) The 3 boxes D) The one box that was chosen at random from the 3 boxes Objective: (1) Understand the Difference Between a Sample and a Population

12) A computer network manager wants to test the reliability of some new and expensive fiber-optic Ethernet cables that computer department just received. The computer department received 5 boxes containing 30 cables each.

The manager does not have the time to test every cable in each box. The manager will choose one box at random and test 6 cables chosen randomly within that box. What is the sample?

A) The 5 boxes B) The one box that was chosen at random from the 5 boxes C) The 6 cables chosen for testing D) 150 cables Objective: (1) Understand the Difference Between a Sample and a Population

Solve the problem.

13) All daily maximum temperatures in August last year for all major U.S. cities were recorded. The mean of all maximum temperatures would be a _____________.

A) Sample B) Statistic C) Population D) Parameter Objective: (1) Understand the Difference Between a Sample and a Population

2

14) Understand survey terminology] Researchers are interested in learning more about the age of young adults who watch a certain television program. By interviewing people at a shopping mall, they can identify people who watch this show. The collection of the ages of these young adults who watch this television program is a _____________.

A) Parameter B) Sample C) Statistic D) Population Objective: (1) Understand the Difference Between a Sample and a Population

15) A factory manager is monitoring the quality of production of a small battery powered toy. The factory produces 600 toys in an hour. Thirty toys are tested from each hour's production. Which one of the following statements is the most accurate?

A) The toys being tested are the population. All toys produced in that hour is the sample and the sample size is 600.

B) The toys being tested are the sample. The factory's total production is the population.

C) The toys being tested are the sample and the sample size is 30. All toys produced in that hour is the population.

D) None of these statements accurately describe this situation.

Objective: (1) Understand the Difference Between a Sample and a Population

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

16) Explain the difference between a population and a sample. Give an example of each.

Objective: (1) Understand the Difference Between a Sample and a Population

17) Describe the importance of how survey questions are phrased – in particular, the effect on the sample results.

Explain how such a sample may not be reflective of the population.

Objective: (1) Understand the Difference Between a Sample and a Population

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

18) Max is interested in whether there is community interest in having local musicians perform music in the park in the evenings during the summer. Max goes to the park for several evenings in a row and asks people visiting the park whether they would like to hear music in the evening. Out of the 200 people he surveys, 58% respond favorably. This scenario is describing what type of sampling bias?

A) Simple random sampling B) Measurement bias C) Survey bias D) Voluntary response bias Objective: (2) Understand Surveys and Sampling

Provide an appropriate response.

19) The government of a town needs to determine if the city's residents will support the construction of a new town hall. The government decides to conduct a survey of a sample of the city's residents. Which one of the following procedures would be most appropriate for obtaining a sample of the town's residents?

A) Survey the first 300 people listed in the town's telephone directory.

B) Survey a random sample of persons within each geographic region of the city.

C) Survey a random sample of employees at the old city hall.

D) Survey every 9th person who walks into city hall on a given day.

Objective: (2) Understand Surveys and Sampling

3

20) The city council of a small town needs to determine if the town's residents will support the building of a new library. The council decides to conduct a survey of a sample of the town's residents. Which one of the following procedures would be most appropriate for obtaining a sample of the town's residents?

A) Survey 300 individuals who are randomly selected from a list of all people living in the state in which the town is located.

B) Survey a random sample of librarians who live in the town.

C) Survey a random sample of persons within each neighborhood of the town.

D) Survey every 11th person who enters the old library on a given day.

Objective: (2) Understand Surveys and Sampling

Solve the problem.

21) A researcher is interested in knowing how many students of a particular college would be interested in having a sandwich shop open within a block of campus. She surveys 300 students on campus at different times of day by asking students randomly if they would answer a few questions. She receives a response from 35. Of those who responded, 65% favored having a sandwich shop within a block of campus. This scenario describes sampling bias.

Which statement most accurately describes the bias?

I. The researcher asked only one question which results in bias.

II. The students voluntarily responded which could result in bias.

III. Not enough students responded which can result in bias.

A) I only B) II only C) both II and III D) III only Objective: (2) Understand Surveys and Sampling

22) Max organizes weekly concerts in the local park. He is interested in knowing what type of music people enjoy.

Before one particular concert, he makes an announcement to the audience, and asks people to visit a web page and take a survey to vote on whether or not they liked the concert. 75 people take the survey, and 58% respond favorably. Max claims that 58% of all of those who were at the concert liked the music. This scenario describes sampling bias. Which statement most accurately describes the bias in Max's method?

I. The Max asked only one question which results in bias.

II. The attendees voluntarily responded which could result in bias.

III. Not enough attendees responded which can result in bias.

A) I only B) III only C) II only D) both II and III Objective: (2) Understand Surveys and Sampling

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

23) Explain the difference between a statistic and a parameter. Give an example of each.

Objective: (2) Understand Surveys and Sampling

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

24) If it is being used to make inferences about a population, a good statistic (or estimator) should A) Be accurate and precise.

B) Show correlation.

C) Be derived from population data.

D) None of these.

Objective: (1) Understand Bias and Precision

25) Which of the following statements is not true about a sampling distribution?

A) It is used for making inferences about a population.

B) It is the probability distribution of a statistic.

C) It tells us how often we can expect to see particular values of our estimator.

D) All these statements are true.

Objective: (1) Understand Bias and Precision

4

26) Which of the following statements is not true about a sampling distribution?

A) It gives probabilities for a statistic.

B) It gives characteristics of the estimator, such as bias and precision.

C) It is the probability distribution of a statistic.

D) It is used for making inferences about a sample.

Objective: (1) Understand Bias and Precision

27) According to a snack cracker manufacturer, a batch of butter crackers has a defect rate of 8%. Suppose a quality inspector randomly inspects 500 crackers. Complete the following statement: The quality inspector should expect defective crackers, give or take crackers.

A) 60; 16

B) 60; 12

C) 40; 6

D) 40; 16

Objective: (1) Understand Bias and Precision

28) According to a snack cracker manufacturer, a batch of butter crackers has a defect rate of 6%. Suppose a quality inspector randomly inspects 400 crackers. Complete the following statement: The quality inspector should expect defective crackers, give or take crackers.

A) 25; 12

B) 48; 5

C) 24; 5

D) 45; 6

Objective: (1) Understand Bias and Precision

29) There are four colors in a bag containing 500 plastic chips. It is known that 28% of the chips are green. On average, how many chips from a random sample of 50 (with replacement) would be expected to be green?

A) 14 B) Not enough information to determine expected value.

C) 18 D) 28 Objective: (1) Understand Bias and Precision

30) There are four colors in a bag containing 600 plastic chips. It is known that 34% of the chips are yellow. On average, how many chips from a random sample of 30 (with replacement) would be expected to be yellow? Round to the nearest whole chip.

A) About 5 B) About 16 C) About 10 D) Not enough information to determine expected value.

Objective: (1) Understand Bias and Precision

Use the following information to answer the question. A pescatarian is a person who eats fish and seafood but no other animal. An event planner does some research and finds that approximately 2.75% of the people in the area where a large event is to be held are pescatarian. Treat the 250 guests expected at the event as a simple random sample from the local population of about 150,000.

31) On average, what proportion of the guests would be expected to be pescatarian, give or take how many? Round to the nearest whole person.

A) 8 people, give or take 4 people B) 6 people, give or take 5 people C) There is not enough information given to calculate expected value.

D) 7 people, give or take 3 people Objective: (1) Understand Bias and Precision

5

Use the following information to answer the question. A pollotarian is a person who eats poultry but no red meat. A wedding planner does some research and finds that approximately 3.5% of the people in the area where a large wedding is to be held are pollotarian. Treat the 300 guests expected at the wedding as a simple random sample from the local population of about 200,000.

32) On average, what proportion of the guests would be expected to be pollotarian, give or take how many? Round to the nearest whole person.

A) There is not enough information given to calculate expected value.

B) 15 people, give or take 4 people C) 20 people, give or take 5 people D) 11 people, give or take 3 people Objective: (1) Understand Bias and Precision

Use the following information to answer the question. In a recent poll of 1100 randomly selected home delivery truck drivers, 26% said they had encountered an aggressive dog on the job at least once.

33) What is the standard error for the estimate of the proportion of all home delivery truck drivers who have encountered an aggressive dog on the job at least once? Round to the nearest ten-thousandth.

A) 0.0132 B) 0.0141 C) 0.0002 D) 0.1322 Objective: (1) Understand Bias and Precision

Use the following information to answer the question. In a recent poll of 1200 randomly selected adult office workers, 32% said they had worn a Halloween costume to the office at least once.

34) What is the standard error for the estimate of the proportion of all American adult office workers that have worn a Halloween costume to the office? Round to the nearest ten-thousandth.

A) 0.4672 B) 0.0143 C) 0.0135 D) 0.0002 Objective: (1) Understand Bias and Precision

Solve the problem.

35) If you use an instrument to measure 1 ml of water and do it 3 times, weighing the water each time, you get 0.751, 0.753, and 0.750 grams. One ml of water should weigh 1.0 grams. The measurements are _________.

A) accurate but not precise B) neither precise nor accurate C) both precise and accurate D) precise but not accurate Objective: (1) Understand Bias and Precision

36) Which of the following statements is characteristics of the sampling distribution of a sample proportion?

A) The standard deviation of the sampling distribution is the same as the standard deviation of the population from which the data were sampled.

B) The mean of the sampling distribution is the same as the mean of the population from which the data were sampled.

C) It cannot be used for making inferences about a population.

D) It is the probability distribution of a parameter.

Objective: (1) Understand Bias and Precision

^

37) The bias of p is zero if certain conditions are met. Identify which condition is not required.

I. The sample is randomly selected from the population of interest.

II. The population must be at least 100 times bigger than the sample size.

III. The standard error of the sampling distribution is the same as the standard deviation of the population.

IV. The mean of the sampling distribution is the mean of the population from which the data were sampled.

A) I only B) II only C) I and IV D) II and III Objective: (1) Understand Bias and Precision

6

38) A survey recently reported that 35% of U.S. citizens believe that we never landed on the moon. The pertinent question in the survey was "Do you think it was possible or impossible that the event of the U.S. landing on the moon never happened?" Select the most accurate statement about this survey.

A) The question worded in a confusing way caused sampling bias.

B) The question worded in a confusing way caused measurement bias.

C) The question worded in a confusing way caused response bias.

D) The results are significant.

Objective: (1) Understand Bias and Precision

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

39) A sampling method should be as precise and accurate as possible. Explain what these two terms mean and how each is measured.

Objective: (1) Understand Bias and Precision

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

40) What generally happens to the sampling error as the sample size is decreased?

A) It gets more predictable.

B) It gets smaller.

C) It gets larger.

D) It gets less predictable.

Objective: (2) Find the Error in a Sample

Solve the problem.

41) A group of screwdrivers produced in a day at a particular factory has a defect rate of 0.7%. Suppose a quality inspector randomly inspects 500 screwdrivers. Complete the following statement: The quality inspector should expect ____defective screwdrivers, with an error of ____.

A) 3.5; 0.4% B) 1; 4.0% C) 35; 0.4% D) 1; 0.4% Objective: (2) Find the Error in a Sample

42) A group of battery powered toys produced in a day at a factory has a defect rate of 0.5%. Suppose a quality inspector randomly inspects 200 of the toys. Complete the following statement: The quality inspector should expect ____defective toys, with an error of ____.

A) 10; 0.5% B) 1; 0.5% C) 1; 5% D) 10; 5% Objective: (2) Find the Error in a Sample

43) There are five colors available in each bag of Skittles. It is known that the 18% of the Skittles are red. On average, how many Skittles from a random sample of 40 (with replacement) would be expected to be red? Round to the nearest whole Skittle.

A) About 1 B) About 8 C) About 16 D) About 7 Objective: (2) Find the Error in a Sample

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

A marble manufacturer advertises that its bags of marbles will contain 25% "milky-white" marbles. Suppose that a bag containing 80 marbles is inspected.

44) What value should we expect for our sampling percentage of milky-white marbles? How many marbles would this be? Round to the nearest whole marble.

Objective: (2) Find the Error in a Sample

7

45) What is the standard error? Round to the nearest tenth of a percent.

Objective: (2) Find the Error in a Sample

46) Use your answers to fill in the blanks: We expect ________% milky-white marbles, give or take ________%.

Objective: (2) Find the Error in a Sample

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

47) Suppose that New Mexico lawmakers survey 160 randomly selected registered voters to see if they favor stricter laws regarding motorcycle helmet use for riders over the age of 17. The lawmakers believe the population proportion in favor of changing the law is 6% (based on historical data and previous votes). Which of the following conditions for the Central Limit theorem are not met?

A) The population proportion is too small and will not have enough expected successes.

B) The population proportion is too small and will not have enough expected failures.

C) Relative to the population, the sample is not large enough.

D) None of these, all the conditions of the CLT are met.

Objective: (1) Use the Central Limit Theorem for Sample Proportions

48) Suppose that Illinois lawmakers survey 130 randomly selected registered voters to see if they favor charging a deposit on aluminum cans to encourage recycling. The lawmakers believe the population proportion in favor of changing the law is 93% (based on historical data and previous votes). Which of the following conditions for the Central Limit theorem are not met?

A) The population proportion is too small and will not have enough expected successes.

B) Relative to the population, the sample is not large enough.

C) The population proportion is too small and will not have enough expected failures.

D) None of these, all the conditions of the CLT are met.

Objective: (1) Use the Central Limit Theorem for Sample Proportions

Use the following information to answer the question. A pollotarian is a person who eats poultry but no red meat. A wedding planner does some research and finds that approximately 3.5% of the people in the area where a large wedding is to be held are pollotarian. Treat the 300 guests expected at the wedding as a simple random sample from the local population of about 200,000.

49) Suppose the wedding planner assumes that 5% of the guests will be pollotarian so she orders 15 pollotarian meals.

What is the approximate probability that more than 5% of the guests are pollotarian and therefore she will not have enough pollotarian meals? Round to the nearest thousandth.

A) 0.489 B) 0.421 C) 0.079 D) None of these Objective: (1) Use the Central Limit Theorem for Sample Proportions

50) Suppose the wedding planner assumes that only 3% of the guests will be pollotarian so she orders 9 pollotarian meals. What is the approximate probability that she will have too many pollotarian meals? Round to the nearest thousandth.

A) 0.681 B) 0.477 C) 0.251 D) 0.319 Objective: (1) Use the Central Limit Theorem for Sample Proportions

8

Use the following information to answer the question. A pescatarian is a person who eats fish and seafood but no other animal. An event planner does some research and finds that approximately 2.75% of the people in the area where a large event is to be held are pescatarian. Treat the 250 guests expected at the event as a simple random sample from the local population of about 150,000.

51) Suppose the event planner assumes that 4% of the guests will be pescatarian so he orders 10 pescatarian meals.

What is the approximate probability that more than 4% of the guests are pescatarian and that he will not have enough pescatarian meals? Round to the nearest thousandth.

A) 0.470 B) 0.113 C) 0.387 D) None of these Objective: (1) Use the Central Limit Theorem for Sample Proportions

52) Suppose the event planner assumes that only 1.6% of the guests will be pescatarian so he orders 4 pescatarian meals. What is the approximate probability that he will have too many pescatarian meals? Round to the nearest thousandth.

A) 0.387 B) 0.613 C) 0.113 D) 0.245 Objective: (1) Use the Central Limit Theorem for Sample Proportions

Solve the problem.

53) It is thought that 10% of all children have some level of nearsightedness. 200 randomly selected children, selected without replacement, had their eyesight tested. Can the Central Limit Theorem be used to find a good approximation of the probability that more than 15% of the children will be nearsighted? Which statement is not true?

I.Relative to the population, the sample is not large enough.

II. The sample does not need to be randomized since all children are likely to have vision problems.

III. Sample size should be large enough so np>10 and nq>10. This condition is met.

A) I and II B) II and III C) I and III D) I only Objective: (1) Use the Central Limit Theorem for Sample Proportions

54) A survey investigates whether residents of a certain city support an educational tax increase. Which of the following statements are true?

A) The proportions of "Yes" in many samples of size n will be approximately normally distributed with mean = p and standard deviation equal to the square root of p*(1-p)/n.

B) The proportion of "Yes" in one sample of size n will be close to p if the Central Limit Theorem conditions are satisfied.

C) The true proportion of "Yes" in the population is p.

D) All of these statements are true.

Objective: (1) Use the Central Limit Theorem for Sample Proportions

55) According to the manufacturer of the candy Skittles, 20% of the candy produced are red. If we take a random sample of 100 bags of Skittles, what is the probability that the proportion in our sample of red candies will be less than 20%? Which statement, if any, is not true for the conditions to use the Central Limit Theorem?

A) The success/failure conditions are satisfied.

B) Though not from a random sample, we can assume that the bags are representative of the population.

C) The sample size is small compared to the population.

D) All of these statements are true.

Objective: (1) Use the Central Limit Theorem for Sample Proportions

9

56) Suppose that Illinois lawmakers survey 130 randomly selected registered voters to see if they favor charging a deposit on aluminum cans to encourage recycling. The lawmakers believe the population proportion in favor of changing the law is 93% (based on historical data and previous votes). Which of the following conditions for the Central Limit theorem are not met?

A) Relative to the population, the sample is not large enough.

B) The population proportion is too small and will not have enough expected successes.

C) The population proportion is too small and will not have enough expected failures.

D) None of these, all the conditions of the CLT are met.

Objective: (1) Use the Central Limit Theorem for Sample Proportions

57) According to the manufacturer of the candy Skittles, 25% of the candy produced are green. If we take a random sample of 10 bags of Skittles, what is the probability that the proportion in our sample of green candies will be more than 25%? Which statement, if any, is true for the conditions to use the Central Limit Theorem?

A) Though not from a random sample, we can assume that the bags are representative of the population.

B) The success/failure conditions may not be satisfied.

C) The sample size is small compared to the population.

D) All of these statements are not true.

Objective: (1) Use the Central Limit Theorem for Sample Proportions

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

58) Suppose that Michigan lawmakers survey 500 randomly selected registered voters to see if they favor an extension of the fall duck hunting season. The lawmakers believe the population proportion in favor of extending the duck hunting season is 45% (based on historical data and previous votes). State the three conditions of the Central Limit Theorem and explain whether each condition is satisfied in this scenario.

Objective: (1) Use the Central Limit Theorem for Sample Proportions

An event planner does some research and finds that in the area where a large children's event is to be held, approximately 1.75% of the children are lactose intolerant. Treat the 250 children expected at the event as a simple random sample from the local population of about 100,000 children.

59) On average, how many of the children attending the event would be expected to be lactose intolerant, give or take how many? Round to the nearest whole person.

Objective: (1) Use the Central Limit Theorem for Sample Proportions

60) Suppose the event planner assumes that 2.8% of the children attending the event will be lactose intolerant so he orders 7 lactose-free meals. What is the approximate probability that more than 2.8% of the children attending the event are lactose intolerant and that he will not have enough lactose-free meals? Round to the nearest thousandth.

Objective: (1) Use the Central Limit Theorem for Sample Proportions

61) Suppose the event planner assumes that only 0.8% of the children attending the event will be lactose intolerant so he orders 2 lactose-free meals. What is the approximate probability that he will have too many lactose-free meals?

Round to the nearest thousandth.

Objective: (1) Use the Central Limit Theorem for Sample Proportions

10

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

62) Which of the following statements is true about the confidence interval for a population proportion?

A) It is equal to the population proportion plus or minus a calculated amount called the standard error.

B) The confidence interval for a proportion does not need a specified confidence level.

C) It is equal to the sample proportion plus or minus a calculated amount called the margin of error.

D) The confidence interval for a proportion will always contain the true population proportion.

Objective: (1) Find Confidence Intervals for Population Proportions

63) Complete the statement by filling in the blank. When constructing a confidence interval, if the level of confidence increases the margin of error will and the confidence interval will be . A larger sample size will improve the accuracy of the confidence interval, therefore margin of error will and the confidence interval will be

.

A) Increase, narrower. Decrease, wider.

C) Increase, wider. Decrease, narrower.

B) Decrease, narrower. Increase, wider.

D) Decrease, wider. Increase, narrower

Objective: (1) Find Confidence Intervals for Population Proportions

Use the following information to answer the question. In a recent poll of 1200 randomly selected adult office workers, 32% said they had worn a Halloween costume to the office at least once.

64) What is the margin of error, using a 95% confidence level, for estimating the true population proportion of adult office workers who have worn a Halloween costume to the office at least once? (Round to the nearest thousandth) A) 0.053 B) 0.158 C) 0.026 D) 0.013 Objective: (1) Find Confidence Intervals for Population Proportions

65) Report the 95% confidence interval for the proportion of all adult office workers who have worn a Halloween costume to the office at least once. (Round final calculations to the nearest tenth of a percent) A) (30.7%, 33.4%) B) (29.4%, 34.6%) C) (28.0%, 36.1%) D) None of these Objective: (1) Find Confidence Intervals for Population Proportions

Use the following information to answer the question. In a recent poll of 1100 randomly selected home delivery truck drivers, 26% said they had encountered an aggressive dog on the job at least once.

66) What is the margin of error, using a 95% confidence level, for estimating the true population proportion of home delivery truck drivers who have encountered an aggressive dog on the job at least once? (Round to the nearest thousandth) A) 0.004 B) 0.026 C) 0.053 D) 0.013 Objective: (1) Find Confidence Intervals for Population Proportions

67) Report the 95% confidence interval for the proportion of all home delivery truck drivers who have encountered an aggressive dog on the job at least once. (Round final calculations to the nearest tenth of a percent) A) (24.7 %, 27.3%) B) (20.7%, 31.3%) C) (23.4%, 28.6%) D) None of these Objective: (1) Find Confidence Intervals for Population Proportions

11

Solve the problem.

68) A random sample of 830 adult television viewers showed that 52% planned to watch sporting event X. The margin of error is 3 percentage points with a 95% confidence. Does the confidence interval support the claim that the majority of adult television viewers plan to watch sporting event X? Why? A) Yes; the confidence interval means that we are 95% confident that the population proportion of adult television viewers who plan to watch sporting event X is between 49% and 55%. Since the confidence interval is mostly above 50% it is likely that the true proportion is greater than 50%.

B) No; the confidence interval means that we are 95% confident that the population proportion of adult television viewers who plan to watch sporting event X is between 49% and 55%. The true proportion could be less than 50%.

C) No; the confidence interval means that we are 95% confident that the population proportion of adult television viewers who plan to watch sporting event X is between 50.5% and 53.5%. The lower limit of the confidence interval is just too close to 50% to say for sure.

D) Yes; the confidence interval means that we are 95% confident that the population proportion of adult television viewers who plan to watch sporting event X is between 50.5% and 53.5%. This is strong evidence that the true proportion is greater than 50% Objective: (1) Find Confidence Intervals for Population Proportions

69) A random sample of 950 adult television viewers showed that 48% planned to watch sporting event X. The margin of error is 4 percentage points with a 95% confidence. Does the confidence interval support the claim that the majority of adult television viewers plan to watch sporting event X? Why? A) Yes; the confidence interval means that we are 95% confident that the population proportion of adult television viewers who plan to watch sporting event X is between 44% and 52%.

B) No; the confidence interval means that we are 95% confident that the population proportion of adult television viewers who plan to watch sporting event X is between 44% and 52%.

C) No; the confidence interval means that we are 95% confident that the population proportion of adult television viewers who plan to watch sporting event X is between 46% and 50%.

D) Yes; the confidence interval means that we are 95% confident that the population proportion of adult television viewers who plan to watch sporting event X is between 46% and 50%.

Objective: (1) Find Confidence Intervals for Population Proportions

70) Suppose that in a recent poll of 1200 adults between the ages of 35 and 45, 38% surveyed said they have thought about getting elective plastic surgery. Find the 95% confidence interval for the proportion of adults ages 35 to 45 who have thought about getting elective plastic surgery then choose the correct interpretation. (Round to the nearest tenth of a percent) A) The population proportion of adults ages 35 to 45 who have thought about getting elective plastic surgery is between 28.5% and 47.5%, with a confidence level of 95%.

B) There is a 95% chance that the population of adults ages 35 to 45 who have thought about getting elective plastic surgery is between 35.2% and 40.7%.

C) There is a 95% chance that the population of adults ages 35 to 45 who have thought about getting elective plastic surgery is between 28.5% and 47.5%.

D) The population proportion of adults ages 35 to 45 who have thought about getting elective plastic surgery is between 35.2% and 40.7%, with a confidence level of 95%.

Objective: (1) Find Confidence Intervals for Population Proportions

12

71) Suppose that in a recent poll of 900 adults between the ages of 35 and 45, 22% surveyed said they have thought about participating in an extreme sport such as bungee jumping. Find the 95% confidence interval for the proportion of adults ages 35 to 45 who have thought about participating in an extreme sport such as bungee jumping then choose the correct interpretation. (Round to the nearest tenth of a percent) A) There is a 95% chance that the population of adults aged 35 to 45 who have thought about participating in an extreme sport such as bungee jumping is between 19.3% and 24.7%.

B) The population proportion of adults aged 35 to 45 who have thought about participating in an extreme sport such as bungee jumping is between 19.3% and 24.7%, with a confidence level of 95%.

C) There is a 95% chance that the population of adults aged 35 to 45 who have thought about participating in an extreme sport such as bungee jumping is between 13.9% and 30.1%.

D) The population proportion of adults aged 35 to 45 who have thought about participating in an extreme sport such as bungee jumping is between 13.9% and 30.1%, with a confidence level of 95%.

Objective: (1) Find Confidence Intervals for Population Proportions

Find the required confidence interval.

72) A researcher wishes to estimate the proportion of adults in the city of Darby who are vegetarian. In a random sample of 1053 adults from this city, the proportion that are vegetarian is 0.046. Find a 95% confidence interval for the proportion of all adults in the city of Darby that are vegetarians.

A) (0.0395, 0.0525) B) (0.0370, 0.0550) C) (0.0158, 0.0762) D) (0.0333, 0.0587) Objective: (1) Find Confidence Intervals for Population Proportions

73) In a sample of 1004 patients who underwent a certain type of surgery, 25% experienced complications. Find a 95% confidence interval for the proportion of all those undergoing this surgery who experience complications.

A) (0.2309, 0.2691) B) (0.2191, 0.2809) C) (0.2232, 0.2768) D) (0.2363, 0.2637) Objective: (1) Find Confidence Intervals for Population Proportions

Solve the problem.

74) Which of the following statements is true about the confidence interval for a population proportion?

A) It is equal to the population proportion plus or minus a calculated amount called the standard error.

B) The confidence interval for a proportion will always contain the true population proportion.

C) It is equal to the sample proportion plus or minus a calculated amount called the margin of error.

D) The confidence interval for a proportion does not need a specified confidence level.

Objective: (1) Find Confidence Intervals for Population Proportions

75) Complete the statement by filling in the blanks.

When constructing a confidence interval, if the level of confidence increases, the margin of error must _____ and the confidence interval will be _____.

A) Decrease, wider.

B) Increase; narrower.

C) Decrease, narrower.

D) Increase; wider.

Objective: (1) Find Confidence Intervals for Population Proportions

76) Complete the statement by filling in the blanks.

A larger sample size will improve the precision of the confidence interval, therefore, assuming no other values change, the margin of error will _____ and the confidence interval will be _____.

A) Decrease, wider.

B) Decrease; narrower.

C) Increase, wider.

D) Increase, narrower.

Objective: (1) Find Confidence Intervals for Population Proportions

13

77) Complete the statement by filling in the blanks.

When constructing a confidence interval, if the level of confidence decreases, the margin of error will _________ and the confidence interval will be _________.

A) Decrease, wider.

B) Increase; narrower.

C) Increase; wider.

D) Decrease, narrower Objective: (1) Find Confidence Intervals for Population Proportions

78) Complete the statement by filling in the blanks.

When constructing a confidence interval, a larger sample size will _________ the margin of error and the confidence interval will be _________.

A) Increase; narrower.

B) Decrease, wider.

C) Increase; wider.

D) Decrease, narrower Objective: (1) Find Confidence Intervals for Population Proportions

From a random sample of workers at a large corporation you find that 58% of 200 went on a vacation last year away from home for at least a week.

79) An approximate 95% confidence interval is (0.50, 0.66). Which of the following statements is a correct interpretation?

A) There is a 95% chance that a random selected coworker has gone on a vacation last year away from home for at least a week.

B) We are 95% confident that between 50% and 66% of the samples will have a proportion near 58%.

C) 95% of the coworkers fall in the interval (0.50, 0.66).

D) We are 95% confident that the proportion of coworkers who went on a vacation last year away from home for at least a week is between 50% and 66%.

Objective: (1) Find Confidence Intervals for Population Proportions

80) Which of the following statements are correct concerning the 95% confidence interval of (0.50, 0.66) of coworkers who went on a vacation last year away from home for at least a week?

A) If the confidence level were changed from 95% to 99%, the confidence interval would become wider.

B) If the confidence level were changed from 95% to 90%, the confidence interval would become wider.

C) If the sample size is 500 instead of 200, the confidence interval will be larger.

D) A maximum of 66% of the coworkers went on a vacation last year away from home for at least a week.

Objective: (1) Find Confidence Intervals for Population Proportions

81) What is the margin of error for the 95% confidence interval of (0.50, 0.66) of coworkers who went on a vacation last year away from home for at least a week?

A) 0.16 B) 0.58 C) 0.04 D) 0.08 Objective: (1) Find Confidence Intervals for Population Proportions

In a recent poll of 1100 randomly selected home delivery truck drivers, 26% said they had encountered an aggressive dog on the job at least once.

82) What is the standard error for the estimate of the proportion of all home delivery truck drivers who have encountered an aggressive dog on the job at least once? Round to the nearest ten-thousandth.

A) 0.1322 B) 0.0141 C) 0.0002 D) 0.0132 Objective: (1) Find Confidence Intervals for Population Proportions

14

Solve the problem.

83) Is it plausible that more than 10% of Americans believe in aliens? A random sample of 2000 adult Americans were surveyed and 15% of them said that they believed in aliens. Find the 95% confidence interval for the proportion of Americans who believe in aliens then choose the correct interpretation. (Round to the nearest tenth of a percent) A) The population proportion of Americans who believe in aliens is between 10% +/- 1.6% with a confidence level of 95%. The interval includes 10% and therefore, it is plausible that at least 10% of Americans believe in aliens.

B) The population proportion of Americans who believe in aliens is between 15% +/- 1.6% with a confidence level of 95%. The interval is higher than 10% and therefore, it is plausible that more than 10% of Americans believe in aliens.

C) The population proportion of Americans who believe in aliens is between 15% +/- 1.6% with a confidence level of 95%. The interval includes 10% and therefore, it is plausible that at least 10% of Americans believe in aliens.

D) The population proportion of Americans who believe in aliens is between 15% +/- 0.8% with a confidence level of 95%. The interval does not include 10% and therefore, it is not plausible that at least 10% of Americans believe in aliens.

Objective: (1) Find Confidence Intervals for Population Proportions

84) Which of the following statements is true about the confidence interval for a population proportion?

A) The confidence interval for a proportion does not need a specified confidence level.

B) It is equal to the sample proportion plus or minus a calculated amount called the margin of error.

C) The confidence interval for a proportion will always contain the true population proportion.

D) It is equal to the population proportion plus or minus the standard error.

Objective: (1) Find Confidence Intervals for Population Proportions

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

85) Suppose a city manager conducts a poll and finds that a 95% confidence interval for the proportion of residents who support parking restrictions during snow removal periods as 63% to 71%. Explain what this confidence interval means – the 95% and what the interval represents.

Objective: (1) Find Confidence Intervals for Population Proportions

86) Explain the difference between the standard error of a sample proportion and the margin of error of a confidence interval for a population proportion.

Objective: (1) Find Confidence Intervals for Population Proportions

In a recent poll of 900 randomly selected adults, 37% reported that they could not swim 24 yards (the length of a typical gymnasium lap pool).

87) What is the margin of error, using a 95% confidence level, for estimating the true proportion of adults who self-report that they cannot swim 24 yards? Round to the nearest thousandth.

Objective: (1) Find Confidence Intervals for Population Proportions

88) Report the 95% confidence interval for the proportion of adults who self-report that they cannot swim 24 yards.

Round final calculations to the nearest tenth of a percent.

Objective: (1) Find Confidence Intervals for Population Proportions

15

Solve the problem.

89) A survey of 800 randomly selected senior citizens showed that 55% said they planned to watch an upcoming political debate on television. The margin of error for the 95% confidence interval is 3.5 percentage points. Does the confidence interval support the claim that the majority of senior citizens plan to watch the upcoming political debate on television? Explain why or why not.

Objective: (1) Find Confidence Intervals for Population Proportions

90) Suppose that you and a friend read the following statement in a news report, "A recent poll found that 54% of voters, give or take 3%, plan to vote for candidate X in the next election (with a confidence level of 95%)". Your friend then makes the statement, "Hey, look, there's a 95% chance that somewhere between 51% and 57% of voters plan to vote for candidate X!" How would you explain to your friend why his statement is incorrect, be sure to provide your friend with the correct interpretation of the confidence interval.

Objective: (1) Find Confidence Intervals for Population Proportions

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Obtain the required confidence interval for the difference between two population proportions. Assume that independent simple random samples have been selected from the two populations.

91) In a random sample of 39 Democrats from one city, 30 approved of the mayor's performance. In a random sample of 50 Republicans from the city, 32 approved of the mayor's performance. Find a 90% confidence interval for the difference between the proportions of Democrats and Republicans who approve of the mayor's performance.

A) (0.609, 0.929) B) (0.579, 0.957) C) (-0.028, 0.287) D) (0.582, 0.957) Objective: (1) Find and Interpret Confidence Intervals for Two Population Proportions

92) A survey found that 27 of 71 randomly selected women and 48 of 72 randomly selected men follow a regular exercise program. Find a 95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program.

A) (-0.443, -0.130) B) (0.194, 0.567) C) (-0.473, 0.567) D) (0.223, 0.537) Objective: (1) Find and Interpret Confidence Intervals for Two Population Proportions

Solve the problem.

93) A polling agency wants to compare support for the president's foreign policies between men and women. They surveyed 2500 U.S. citizens and found a 95% confidence interval for the difference in proportions between men and women who support the president's foreign policies as (-0.05 to -0.025) where population 1 is men and population 2 is women. Select the correct interpretation of this result.

A) The interval does not contain 0, which shows that there is no significant difference in the proportions between men and women.

B) The number surveyed should be increased to increase the accuracy of the confidence interval.

C) The interval estimates that p 1 – p 2 < 0 which shows that women are more likely than men to support with the president's foreign policies.

D) The interval estimates that p 1 – p 2 < 0 which shows that men are more likely than women to support with the president's foreign policies.

Objective: (1) Find and Interpret Confidence Intervals for Two Population Proportions

16

94) Confidence intervals can be used to determine whether different sample proportions reflect a "real" difference in the population. The basic approach is to...

A) find the margin of error for each proportion and see if the difference is less than zero.

B) find the difference in the proportions and see if the difference is greater than zero.

C) find the difference in the proportions and see if the difference is less than zero.

D) find a confidence interval at the significance level desired for the difference in proportions.

Objective: (1) Find and Interpret Confidence Intervals for Two Population Proportions

95) A polling agency wants to estimate the proportion of U.S. citizens who support the president's domestic policies.

They surveyed 2500 U.S. citizens and found a 95% confidence interval for the difference in proportions between men and women who support the president's domestic policies as (-0.025 to 0.050) where population 1 is men and population 2 is women. Select the correct interpretation of this result.

A) The interval does not contain zero which shows that there is no significant difference in the proportions between men and women.

B) The interval contains zero which shows that men are more likely than women to disagree with the president's foreign policies.

C) The interval contains zero which shows that women are more likely than men to disagree with the president's foreign policies.

D) The interval contains zero which shows that there is no significant difference in the proportions between men and women.

Objective: (1) Find and Interpret Confidence Intervals for Two Population Proportions

96) A medical study examined data on patients with cardiovascular disease who were currently non-smokers and those who were current smokers. Population 1 were smokers and population 2 were non-smokers. After data analysis, the 95% confidence interval for the difference in proportions is 0.015 +/- 0.011. The most accurate interpretation is...

A) We are 95% confident that the difference in the proportion of smokers compared to nonsmokers is between 0.004 and 0.026. There is a significance difference indicating higher cardiovascular disease amongst smokers.

B) We are 95% confident that the interval of the difference in the proportions contains zero. There is not a significance difference between smokers and non-smokers.

C) We are 95% confident that the proportion of smokers compared to non-smokers is between 0.004 and 0.026.

D) We are 95% confident that the difference in the proportion of smokers compared to nonsmokers is between -0.004 and 0.026. There is not a significance difference in the proportions.

Objective: (1) Find and Interpret Confidence Intervals for Two Population Proportions

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

97) Confidence intervals can be used to determine whether different sample proportions reflect a "real" difference in the population. Explain the method of how this is accomplished and what the assumptions are.

Objective: (1) Find and Interpret Confidence Intervals for Two Population Proportions

98) A polling agency wants to estimate the proportion of U.S. citizens who support the president's educational policies. They surveyed 1500 U.S. citizens and found a 95% confidence interval for the difference in proportions between men and women who support the president's educational policies as (-0.075 to 0.025) where population 1 is men and population 2 is women. Interpret the result and state if the assumptions are satisfied.

Objective: (1) Find and Interpret Confidence Intervals for Two Population Proportions

17

Answer Key Testname: GOULDCH7TEST

1) D 2) B 3) A 4) A 5) B 6) A 7) C 8) C 9) B 10) B 11) B 12) C 13) D 14) B 15) C 16) A population is a group of objects or people which are being studied. A population is a total collection. A sample is a collection of objects or people taken from the population of interest. Examples will vary.

17) A persuasive survey question will result in biased results, which may not accurately reflect the true sentiments of the population. A confusing question with multiple negatives and irrelevant information can result in inaccurate responses.

18) D 19) B 20) C 21) C 22) D

23) A statistic is a summary of a sample of data, examples will vary. A parameter is a numerical value that characterizes some aspect of the population, examples will vary.

24) A 25) D 26) D 27) C 28) C 29) A 30) C 31) D 32) D 33) A 34) C 35) D 36) B 37) D 38) B 39) Precision means that sampling results are consistent when a sampling method is repeated. The precision of a sampling method is measured by the standard error.

Accuracy means sampling results are centered around the population parameter. Accuracy is measured in terms of bias.

40) C 41) A 42) B 43) D 44) 25%; 20 milky-white marbles 45) 4.8% 46) 25%; 4.8% 47) A

48) C 49) C 50) D 51) B 52) C 53) A 54) D 55) D 56) C 57) B 58) Sample is random and independent—it is stated that this is a random sample and voters are independent. The sample is large—a sample of 500 is large enough since it will have at least 10 successes and failures (0.45 × 500 . 10 and 0.55 × 500 . 10). The population is big—A sample of 500 is large enough because the population is at least ten times larger.

59) 4 children, give or take 2 children.

60) 0.103 61) 0.126 62) C 63) C 64) C 65) B 66) B 67) C 68) B 69) B 70) D 71) B 72) D 73) C 74) C 75) D 76) B 77) D 78) D 79) D 18

80) A 81) D 82) D 83) B 84) B 85) The 95% indicates that if many polls were taken, 95% of them would result in confidence intervals that include the true population proportion of residents that support parking restrictions during snow removal. The interval represents a population estimate +/- a margin of error which depends on the confidence level (95%) and the sample size.

86) The margin of error is an amount that is added and subtracted from the estimate which provides the range of plausible values around the sample proportion base on a chosen level of confidence.

The standard error of a sample proportion is the measure of variation for the data collected in a particular sample.

87) 0.032 88) The upper limit would be 37% + 3.2% = 40.2%. The lower limit would be 37% – 3.2% = 33.8%.

(33.8%, 40.2%)

Answer Key Testname: GOULDCH7TEST

89) Yes, a confidence interval of 55% ± 3.5% would include plausible population parameter values that are greater than 50% so the claim would not be unreasonable.

90) Answers will vary, but should reference the fact that there is no chance that the population parameter will change, which is implied when one interprets a confidence level as a probability. The correct interpretation is that the proportion of voters who plan to vote for candidate X is between 51% and 57%, with a confidence level of 95% which means the process used to produce the interval will capture the true population proportion 95% of the time.

91) C 92) A 93) C 94) D 95) D 96) A

97) The method for determining whether different sample proportions reflect a "real" difference in the population is find the difference between the two sample proportions taken from two populations, subtracting the sample proportion for population 2 from the sample proportion for population 1. Similar to the confidence interval for a single proportion, a margin of error is calculated that depends on the confidence level, the sample proportions, and the sample size.

The assumptions are that the samples are random and independent, are sufficiently large taken from big populations.

98) The interval contains zero which shows that there is no significant difference in the proportions between men and women. The assumptions are satisfied: the samples randomly drawn from their populations, samples are independent, with samples large enough from big populations.

19

Gould/Ryan/Wong Essentials Statistics 3e Chapter 8 Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

1) Read the following problem description then choose the correct null and alternative hypothesis. A new drug is being tested to see whether it can reduce the rate of asthma attacks in children ages 5 to 14. The rate of asthma attacks in the population of concern is 0.0744.

A) H0 : p > 0.0744; Ha: p 0.0744 B) H0 : p = 0.0744; Ha: p < 0.0744 C) H0 : p = 0.0744; Ha: p > 0.0744

D) H0 : p < 0.0744; Ha: p < 0.0744

Objective: (1) Identify Null and Alternative Hypotheses

2) Read the following problem description then choose the correct null and alternative hypothesis. A new drug is being tested to see whether it can reduce the rate of food-related allergic reactions in children aged 1 to 3 with food allergies. The rate of allergic reactions in the population of concern is 0.03.

A) H0 : p = 0.03; Ha : p < 0.03 B) H0 : p 0.03; Ha : p = 0.03 C) H0 : p < 0.03; Ha : p = 0.03

D) H0 : p = 0.03; Ha : p > 0.03

Objective: (1) Identify Null and Alternative Hypotheses

Express the null hypothesis and the alternative hypothesis in symbolic form.

3) An entomologist writes an article in a scientific journal which claims that fewer than 22 in ten thousand male fireflies are unable to produce light due to a genetic mutation.

A) H0 : p = 0.0022 B) H0 : p < 0.0022 C) H0 : p > 0.0022 D) H0 : p = 0.0022 Ha : p > 0.0022

Ha : p 0.0022

Ha : p 0.0022

Ha : p < 0.0022

Objective: (1) Identify Null and Alternative Hypotheses

4) A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 1 in every one thousand.

A) H0 : p = 0.001 B) H0 : p = 0.001 C) H0 : p > 0.001 D) H0 : p < 0.001 Ha : p > 0.001

Ha : p < 0.001

Ha : p 0.001

Ha : p 0.001

Objective: (1) Identify Null and Alternative Hypotheses

Solve the problem.

5) Read the following problem description then choose the correct null and alternative hypothesis. A new drug is being tested to see whether it can reduce the diastolic blood pressure measurement for adults age 45-60 years. The upper limit for diastolic blood pressure measurement should be 90 mmHg. A) H0 : p < 90 mmHg; Ha : p > 90 mmHg B) H0 : p = 90 mmHg; Ha : p 90 mmHg C) H0 : p 90 mmHg; Ha : p < 90 mmHg

D) H0 : p = 90 mmHg; Ha : p < 90 mmHg

Objective: (1) Identify Null and Alternative Hypotheses

6) Read the following problem description then choose the correct null and alternative hypothesis: A new drug is being tested to see whether it can reduce the rate of food-related allergic reactions in children ages 1 to 3 with food allergies. The rate of allergic reactions in the population of concern is 0.03.

A) H0 : p 0.03; Ha : p = 0.03 B) H0 : p < 0.03; Ha : p = 0.03 C) H0 : p = 0.03; Ha : p > 0.03

D) H0 : p = 0.03; Ha : p < 0.03

Objective: (1) Identify Null and Alternative Hypotheses

1

7) Which of the following is not true about the alternative hypothesis?

A) It is usually a statement that the researcher hopes to demonstrate is true.

B) It is sometimes called the research hypothesis.

C) It is assumed to be true.

D) Like the null hypothesis, it is always a statement about a population parameter.

Objective: (1) Identify Null and Alternative Hypotheses

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

8) The worker at a carnival game claims that he can communicate with a small magic rock and to prove it he tells you to hide it in your hand behind your back and he will identify the hand holding the rock. Being a wise student of statistics, you decide to stand back and observe the outcome of the next ten games before deciding whether to pay your three dollars to play the game. You have just conducted an informal hypothesis test. State the null and alternative hypothesis.

Objective: (1) Identify Null and Alternative Hypotheses

9) A researcher wishes to test the claim that the proportion of children with blue eyes in his region is different than one in six, the national rate of blue eyes in children. State and explain the null and alternative hypothesis that should be used to test the claim.

Objective: (1) Identify Null and Alternative Hypotheses

A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test whether the claim is true or not, a random sample of 100 doctors is obtained. Of these doctors, 82 indicated that they recommend aspirin for headaches. Is the claim accurate? Test with a significance level of 0.05.

10) State and explain the null and alternative hypothesis that should be used to test the claim.

Objective: (1) Identify Null and Alternative Hypotheses

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

11) Suppose that the following is to be tested: H0 : p = 0.35 and Ha : p > 0.35. Calculate the observed z-statistic for the following sample data: Forty out of eighty test subjects have the characteristic of interest. Round to the nearest hundredth.

A) z = -1.87 B) z = 2.81 C) z = -0.94 D) z = 1.88 Objective: (2) Find Test Statistics

12) Suppose that the following is to be tested: H0 : p = 0.72 and Ha : p 0.72. Calculate the observed z-statistic for the following sample data: Sixty-eight out of ninety test subjects have the characteristic of interest. Round to the nearest thousandth.

A) z = 0.751 B) z = 0.453 C) z = -0.751 D) z = 0.756 Objective: (2) Find Test Statistics

Use the following information to answer the question. A janitor at a large office building believes that his supply of light bulbs has too many defective bulbs. The janitor's null hypothesis is that the supply of light bulbs has a defect rate of p = 0.07 (the light bulb manufacturer's stated defect rate). Suppose he does a hypothesis test with a significance level of 0.05.

Symbolically, the null and alternative hypothesis are as follows: H0 : p = 0.07 and Ha : p > 0.07.

13) Suppose that the janitor tests 300 randomly selected light bulbs and finds that 27 bulbs are defective. What value of the test statistic should he report? Round to the nearest hundredth.

A) z = 1.96 B) z = -1.96 C) z = 1.36 D) z = -1.36 Objective: (2) Find Test Statistics

2

Use the following information to answer the question. A janitor at a large office building believes that his supply of light bulbs has a defect rate that is different than the defect rate stated by the manufacturer. The janitor's null hypothesis is that the supply of light bulbs has a defect rate of p = 0.09 (the light bulb manufacturer's stated defect rate). Suppose we do a hypothesis test with a significance level of 0.01. Symbolically, the null and alternative hypothesis are as follows: H0 : p = 0.09 and Ha : p > 0.09.

14) Suppose the janitor tests 300 light bulbs and finds that 33 bulbs are defective. What value of the test statistic should he report? Round to the nearest hundredth.

A) z = -2.17 B) z = -1.21 C) z = 1.21 D) z = 2.17 Objective: (2) Find Test Statistics

Find the value of the test statistic z.

15) A claim is made that the proportion of children who play sports is 0.5, and the sample statistics include 1761 subjects with 30% saying that they play a sport.

A) z = 34.26 B) z = -16.79 C) z = 16.79 D) z = -34.26 Objective: (2) Find Test Statistics

16) The claim is that the proportion of drowning deaths of children attributable to beaches is 0.25, and the sample statistics include 530 drowning deaths of children with 30% of them attributable to beaches.

A) z = 2.51 B) z = 2.66 C) z = -2.66 D) z = -2.51 Objective: (2) Find Test Statistics

A janitor at a large office building believes that his supply of light bulbs has a defect rate that is higher than the defect rate stated by the manufacturer. The janitor's null hypothesis is that the supply of light bulbs has a manufacturer's defect rate of p = 0.09. He performs a test at a significance level of 0.01. The null and alternative hypothesis are as follows: H0 : p = 0.09 and Ha: p > 0.09.

17) Suppose the janitor tests 300 light bulbs and finds that 33 bulbs are defective. The calculated test statistic is z = 1.21.

Select the appropriate interpretation of the test statistic.

A) A test statistic of 1.21 is 1.21 standard deviations greater than the mean (between 1 and 2) indicating that the result could be significant using a two-sided alternative hypothesis.

B) A test statistic of -1.21 is 1.21 standard deviations less than the mean (between 1 and 2) indicating that the result could be significant at a level of 0.01 using a one-sided alternative hypothesis.

C) A test statistic of 1.21 is 1.21 standard deviations greater than the mean (between 1 and 2) indicating that the result is not significant at a level of 0.01 using a one-sided alternative hypothesis.

D) A test statistic of 1.21 is 1.21 standard deviations less than the mean (between 1 and 2) indicating that the result is not significant.

Objective: (2) Find Test Statistics

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test whether the claim is true or not, a random sample of 100 doctors is obtained. Of these doctors, 82 indicated that they recommend aspirin for headaches. Is the claim accurate? Test with a significance level of 0.05.

18) Calculate the z test statistic for the sample results. Round to the nearest hundredth.

Objective: (2) Find Test Statistics

19) Explain how you can determine the significance by using the calculated z-value.

Objective: (2) Find Test Statistics

3

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the following information to answer the question. A janitor at a large office building believes that his supply of light bulbs has too many defective bulbs. The janitor's null hypothesis is that the supply of light bulbs has a defect rate of p = 0.07 (the light bulb manufacturer's stated defect rate). Suppose he does a hypothesis test with a significance level of 0.05.

Symbolically, the null and alternative hypothesis are as follows: H0 : p = 0.07 and Ha : p > 0.07.

20) Choose the statement that best describes the significance level in the context of the hypothesis test.

A) The significance level of 0.05 is the probability of concluding that the defect rate is equal to 0.07 when in fact it is greater than 0.07.

B) The significance level of 0.05 is the test statistic that we will use to compare the observed outcome to the null hypothesis.

C) The significance level of 0.05 is the defect rate we believe is the true defect rate.

D) The significance level of 0.05 is the probability of concluding that the defect rate is higher than 0.07 when in fact the defect rate is equal to 0.07.

Objective: (3) Find and Interpret p-Values

Use the following information to answer the question. A janitor at a large office building believes that his supply of light bulbs has a defect rate that is different than the defect rate stated by the manufacturer. The janitor's null hypothesis is that the supply of light bulbs has a defect rate of p = 0.09 (the light bulb manufacturer's stated defect rate). Suppose we do a hypothesis test with a significance level of 0.01. Symbolically, the null and alternative hypothesis are as follows: H0 : p = 0.09 and Ha : p > 0.09.

21) Choose the statement that best describes the significance level in the context of the hypothesis test.

A) The significance level of 0.01 is the defect rate we believe is the true defect rate.

B) The significance level of 0.01 is the probability of concluding that the defect rate is different than 0.09 when in fact the defect rate is equal to 0.09.

C) The significance level of 0.01 is the z-statistic that we will use to compare the observed outcome to the null hypothesis.

D) The significance level of 0.01 is the probability of concluding that the defect rate is equal to 0.09 when in fact it is greater than 0.09.

Objective: (3) Find and Interpret p-Values

Solve the problem.

22) A polling agency is interested in testing whether the proportion of women who support a female candidate for office is greater than the proportion of men. The null hypothesis is that there is no difference in the proportion of men and women who support the female candidate. The alternative hypothesis is that the proportion of women who support the female candidate is greater than the proportion of men. The test results in a p-value of 0.112.

Which of the following is the best interpretation of the p-value?

A) The p-value is the probability of getting a result that is as extreme as or more extreme than the one obtained, assuming that the proportion of women who support the female candidate is greater than the proportion of men.

B) The p-value is the probability that men will support the female candidate.

C) The p-value is the probability of getting a result that is as extreme as or more extreme than the one obtained, assuming that there is no difference in the proportions.

D) The p-value is the probability that women will support the female candidate.

Objective: (3) Find and Interpret p-Values

4

23) A polling agency is interested in testing whether the proportion of women who support a female candidate for office is less than the proportion of men. The null hypothesis is that there is no difference in the proportions of men and women who support the female candidate. The alternative hypothesis is that the proportion of women who support the female candidate is less than the proportion of men. The test results in a p-value of 0.041. Which of the following is the best interpretation of the p-value?

A) The p-value is the probability of getting a result that is as extreme as or more extreme than the one obtained, assuming that there is no difference in the proportions.

B) The p-value is the probability that the majority of men will support the female candidate.

C) The p-value is the probability of getting a result that is as extreme as or more extreme than the one obtained, assuming that the proportion of women who support the female candidate is less than the proportion of men.

D) The p-value is the probability that the majority of women will support the female candidate.

Objective: (3) Find and Interpret p-Values

24) Suppose a city official conducts a hypothesis test to test the claim that the majority of voters support a proposed tax to build sidewalks. Assume that all the conditions for proceeding with a one-sample test on proportions have been met. The calculated test statistic is approximately 1.40 with an associated p-value of approximately 0.081.

Choose the conclusion that provides the best interpretation for the p-value at a significance level of = 0.05.

A) If the null hypothesis is true, then the probability of getting a test statistic that is as extreme or more extreme than the calculated test statistic of 1.40 is 0.081. This result is surprising and could not easily happen by chance.

B) The p-value should be considered extreme; therefore the hypothesis test proves that the null hypothesis is true.

C) If the null hypothesis is true, then the probability of getting a test statistic that is as extreme or more extreme than the calculated test statistic of 1.40 is 0.081. This result is not surprising and could easily happen by chance.

D) None of these.

Objective: (3) Find and Interpret p-Values

25) Suppose a city official conducts a hypothesis test to test the claim that the majority of voters oppose a proposed school tax. Assume that all the conditions for proceeding with a one-sample test on proportions have been met.

The calculated test statistic is approximately 1.46 with an associated p-value of approximately 0.072. Choose the conclusion that provides the best interpretation for the p-value at a significance level of = 0.05.

A) The p-value should be considered extreme; therefore the hypothesis test proves that the null hypothesis is true.

B) If the null hypothesis is true, then the probability of getting a test statistic that is as extreme or more extreme than the calculated test statistic of 1.46 is 0.072. This result is surprising and could not easily happen by chance.

C) If the null hypothesis is true, then the probability of getting a test statistic that is as extreme or more extreme than the calculated test statistic of 1.46 is 0.072. This result is not surprising and could easily happen by chance.

D) None of these.

Objective: (3) Find and Interpret p-Values

5

Use the following information to answer the question. A janitor at a large office building believes that his supply of light bulbs has too many defective bulbs. The janitor's null hypothesis is that the supply of light bulbs has a defect rate of p = 0.07 (the light bulb manufacturer's stated defect rate). Suppose he does a hypothesis test with a significance level of 0.05.

Symbolically, the null and alternative hypothesis are as follows: H0 : p = 0.07 and Ha : p > 0.07.

26) The janitor calculates a p-value for the hypothesis test of approximately 0.087. Choose the correct interpretation for the p-value.

A) The p-value tells us that the probability of concluding that the defect rate is equal to 0.07, when in fact it is greater than 0.07, is approximately 0.087.

B) The p-value tells us that if the defect rate is 0.07, then the probability that the janitor will have 27 defective light bulbs out of 300 is approximately 0.087. At a significance level of 0.05, this would not be an unusual outcome.

C) The p-value tells us that the true population rate of defective light bulbs is approximately 0.087.

D) None of these Objective: (3) Find and Interpret p-Values

Use the following information to answer the question. A janitor at a large office building believes that his supply of light bulbs has a defect rate that is different than the defect rate stated by the manufacturer. The janitor's null hypothesis is that the supply of light bulbs has a defect rate of p = 0.09 (the light bulb manufacturer's stated defect rate). Suppose we do a hypothesis test with a significance level of 0.01. Symbolically, the null and alternative hypothesis are as follows: H0 : p = 0.09 and Ha : p > 0.09.

27) The janitor calculates a p-value for the hypothesis test of approximately 0.113. Choose the correct interpretation for the p-value.

A) The p-value tells us that the true population rate of defective light bulbs is approximately 0.113.

B) The p-value tells us that if the defect rate is 0.113, then the probability that the janitor will have 33 defective light bulbs out of 300 is approximately 0.113. At a significance level of 0.01, this would not be an unusual outcome.

C) The p-value tells us that the probability of concluding that the defect rate is equal to 0.09, when in fact it is greater than 0.09, is approximately 0.113.

D) None of these Objective: (3) Find and Interpret p-Values

Solve the problem.

28) A research firm carried out a hypothesis test on a population proportion using a right-tailed alternative hypothesis. Which of the following z-scores would be associated with a p-value of 0.04? Round to the nearest hundredth.

A) z = 2.50 B) z = 1.75 C) z = -1.75 D) z = -2.50 Objective: (3) Find and Interpret p-Values

29) A research firm carried out a hypothesis test on a population proportion using a left-tailed alternative hypothesis.

Which of the following z-scores would be associated with a p-value of 0.04? Round to the nearest hundredth.

A) z = 1.75 B) z = -1.75 C) z = -2.50 D) z = 2.50 Objective: (3) Find and Interpret p-Values

30) Complete the statement by filling in the blanks. The null hypothesis is is only rejected when the observed outcome is shown to be

A) Likely; false; extremely likely C) Proven; true; impossible

to be .

B) Assumed; true; extremely unlikely D) Known; true; the population parameter

Objective: (4) Know Concepts: The Essential Ingredients of Hypothesis Testing

6

and

31) Which statement best describes the significance level of a hypothesis test?

A) The probability of rejecting the null hypothesis when the null hypothesis is not true.

B) The probability of failing to reject the null hypothesis when the null hypothesis is not true.

C) The probability of rejecting the null hypothesis when the null hypothesis is true.

D) None of these Objective: (4) Know Concepts: The Essential Ingredients of Hypothesis Testing

32) Which of the following is not true about the alternative hypothesis?

A) Like the null hypothesis, it is always a statement about a population parameter.

B) It is assumed to be true based on the sample results.

C) It is usually a statement that the researcher hopes to demonstrate is true.

D) It is sometimes called the research hypothesis.

Objective: (4) Know Concepts: The Essential Ingredients of Hypothesis Testing

33) Complete the statement by filling in the blanks.

A research hypothesis is always expressed in terms of ________ __________ because we are interested in making statements about the _________ based on _______ statistics.

A) population; parameters; sample; population B) sample; statistics; population; sample C) population; parameters; population; sample D) population; statistics; population; parameter Objective: (4) Know Concepts: The Essential Ingredients of Hypothesis Testing

34) Complete the statement by filling in the blanks.

The null hypothesis H0 is the statement of _________ and always has a ______ sign. The alternative hypothesis Ha is the __________ hypothesis. It is a statement about the value of a __________ that we intend to test.

A) no change; = ; research; parameter B) no change; = ; research; sample C) change; = ; no change; parameter D) no consequence; > ; research; sample Objective: (4) Know Concepts: The Essential Ingredients of Hypothesis Testing

35) A quality control manager believes that there are too many defective light bulbs being produced, higher than the advertised rate. The manager's null hypothesis is that the production line of light bulbs has a defect rate of p = 0.025 (the light bulb's stated defect rate). He does a hypothesis test with a significance level of 0.05. Symbolically, the null and alternative hypothesis are as follows: H0 : p = 0.025 and Ha: p > 0.025.

Choose the statement that best describes the significance level in the context of the hypothesis test.

A) The significance level of 0.05 is the defect rate we believe is the true defect rate.

B) The significance level of 0.05 is the probability of concluding that the defect rate is higher than 0.025 when in fact the defect rate is equal to 0.025.

C) The significance level of 0.05 is the test statistic that we will use to compare the observed outcome to the null hypothesis.

D) The significance level of 0.05 is the probability of concluding that the defect rate is equal to 0.025 when in fact it is greater than 0.025.

Objective: (4) Know Concepts: The Essential Ingredients of Hypothesis Testing

7

A janitor at a large office building believes that his supply of light bulbs has a defect rate that is higher than the defect rate stated by the manufacturer. The janitor's null hypothesis is that the supply of light bulbs has a manufacturer's defect rate of p = 0.09. He performs a test at a significance level of 0.01. The null and alternative hypothesis are as follows: H0 : p = 0.09 and Ha: p > 0.09.

36) Choose the statement that best describes the significance level in the context of the hypothesis test.

A) The significance level of 0.01 is the z-statistic that we will use to compare the observed outcome to the null hypothesis.

B) The significance level of 0.01 is the probability of concluding that the defect rate is equal to 0.09 when in fact it is greater than 0.09.

C) The significance level of 0.01 is the defect rate we believe is the true defect rate.

D) The significance level of 0.01 is the probability of concluding the defect rate is more than 0.09 when it is equal to 0.09.

Objective: (4) Know Concepts: The Essential Ingredients of Hypothesis Testing

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test whether the claim is true or not, a random sample of 100 doctors is obtained. Of these doctors, 82 indicated that they recommend aspirin for headaches. Is the claim accurate? Test with a significance level of 0.05.

37) Write a statement describing the meaning of the level of significance in the context of the hypothesis test.

Objective: (4) Know Concepts: The Essential Ingredients of Hypothesis Testing

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the following information to answer the question. A researcher is wondering whether the drinking habits of adults in a certain region of the country are in the same proportion as the general population of adults. Suppose a recent study stated that the proportion of adults who reported drinking once a week or less in the last month was 0.26. The researcher's null hypothesis for this test is H0 : p = 0.26 and the alternative hypothesis is Ha : p > 0.26. The researcher collected data from a random sample of 75 adults in the region of interest.

38) Check that the conditions hold so that the sampling distribution of the z-statistic will approximately follow the standard normal distribution. Are the conditions satisfied? If not, choose the condition that is not satisfied.

A) No, the researcher did not collect a random sample.

B) No, the researcher did not collect a large enough sample.

C) Yes, all the conditions are satisfied.

D) No, the population of interest is not large enough to assume independence.

Objective: (1) Check the Conditions for a One-Proportion z-Test

Use the following information to answer the question. A researcher is wondering whether the drinking habits of adults in a certain region of the country are in the same proportion as the general population of adults. Suppose a recent study stated that the proportion of adults who reported drinking once a week or less in the last month was 0.26. The null hypothesis for this test is H0 : p = 0.26 and the alternative hypothesis is Ha : p < 0.26. The researcher collected data from 150 surveys he handed out at a busy park located in the region.

39) Check that the conditions hold so that the sampling distribution of the z-statistic will approximately follow the standard normal distribution. Are the conditions satisfied? If not, choose the condition that is not satisfied.

A) Yes, all the conditions are satisfied.

B) No, the researcher did not collect a large enough sample.

C) No, the population of interest is not large enough to assume independence.

D) No, the researcher did not collect a random sample.

Objective: (1) Check the Conditions for a One-Proportion z-Test

8

A researcher is wondering whether the smoking habits of young adults (18-25 years of age) in a certain city in the U.S. are the same as the proportion of the general population of young adults in the U.S. A recent study stated that the proportion of young adults who reported smoking at least twice a week or more in the last month was 0.16. The researcher collected data from a random sample of 75 adults in the city of interest.

40) Check that the conditions hold so that the sampling distribution of the z-statistic will approximately follow the standard normal distribution. Are the conditions satisfied? If not, choose the condition that is not satisfied.

A) Yes, all the conditions are satisfied.

B) No, the population of interest is not large enough to assume independence.

C) No, the researcher did not collect a random sample.

D) No, the researcher did not collect a large enough sample.

Objective: (1) Check the Conditions for a One-Proportion z-Test

A researcher is wondering whether the drinking habits of adults in a certain region of the country are in the same proportion as the general population of adults. Suppose a recent study stated that the proportion of adults in the general population who reported drinking once a week or less in the last month was 0.26. The null hypothesis for this test is H0 : p = 0.26 and the alternative hypothesis is Ha: p < 0.26. The researcher collected data from 150 surveys he handed out at a busy park located in the region.

41) Check that the conditions hold so that the sampling distribution of the z-statistic will approximately follow the standard Normal distribution. Are the conditions satisfied? If not, choose the condition that is not satisfied.

A) No, the population of interest is not large enough to assume independence.

B) Yes, all the conditions are satisfied.

C) No the conditions are not satisfied; the researcher did not collect a random sample.

D) Yes, the population of proportions can be assumed to be roughly symmetric.

Objective: (1) Check the Conditions for a One-Proportion z-Test

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

A health foods shop owner is wondering if his customer's daily vitamin supplement habits are in the same proportion as the general population of adults. The shop owner heard in a news report that 60% of all adults reported that they took a daily vitamin. The shop owner believes that his customers have a greater proportion of adults who take a daily vitamin, so he decides to conduct a hypothesis test using the following null and alternative hypothesis: H0 : p = 0.6 and Ha: p > 0.6.

The shope owner collected data from 50 randomly selected customers.

42) List and verify that the conditions hold so that the sampling distribution of the z test statistic will approximately follow the standard normal distribution.

Objective: (1) Check the Conditions for a One-Proportion z-Test

9

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the following information to answer the question. A researcher is wondering whether the drinking habits of adults in a certain region of the country are in the same proportion as the general population of adults. Suppose a recent study stated that the proportion of adults who reported drinking once a week or less in the last month was 0.26. The researcher's null hypothesis for this test is H0 : p = 0.26 and the alternative hypothesis is Ha : p > 0.26. The researcher collected data from a random sample of 75 adults in the region of interest.

43) To continue the study into the drinking habits of adults, the researcher decides to collect data from adults working in "blue collar" jobs to see whether their drinking habits are in the same proportion as the general public. The null hypothesis for this test is H0 : p = 0.26 and the alternative hypothesis is Ha : p > 0.26. The researcher collected data from a random sample of 90 adults with "blue collar" jobs of which 30 stated that they drank once a week or less in the last month. Assume that the conditions that must be met in order for us to use the N(0, 1) distribution as the ^

sampling distribution are satisfied. Find the values of the sample proportion, p, the test statistic, and the p-value associated with the test statistic. Round all values to the nearest thousandth. ^ ^ A) p = 0.333, z = 0.067, p-value = 0.946 B) p = 0.667, z = 8.795, p-value = 0.000+ ^

^

C) p = 0.289, z = -0.829, p-value = 0.407

D) p = 0.333, z = 1.586, p-value = 0.056

Objective: (2) Find the Test Statistic and Corresponding p-value for a One-Proportion z-Test

Use the following information to answer the question. A researcher is wondering whether the drinking habits of adults in a certain region of the country are in the same proportion as the general population of adults. Suppose a recent study stated that the proportion of adults who reported drinking once a week or less in the last month was 0.26. The null hypothesis for this test is H0 : p = 0.26 and the alternative hypothesis is Ha : p < 0.26. The researcher collected data from 150 surveys he handed out at a busy park located in the region.

44) To continue the study into the drinking habits of adults, the researcher decides to collect data from adults working in "white collar" jobs to see whether their drinking habits are in the same proportion as the general public. The null hypothesis for this test is H0 : p = 0.26 and the alternative hypothesis is Ha : p < 0.26. The researcher collected data from a random sample of 120 adults with "white collar" jobs of which 25 stated that they drank once a week or less in the last month. Assume that the conditions that must be met in order for us to use the N(0, 1) distribution as the ^

sampling distribution are satisfied. Find the values of the sample proportion, p, the test statistic, and the p-value associated with the test statistic. Round all values to the nearest thousandth. ^

B) p = 0.30, z = 0.803, p-value = 0.041

^

^

D) p = 0.75, z = -1.32, p-value = 0.599

A) p = 0.208, z = -1.290, p-value = 0.098

^

C) p = 0.208, z = -0.250, p-value = 0.401

Objective: (2) Find the Test Statistic and Corresponding p-value for a One-Proportion z-Test

Solve the problem.

45) Two researchers are comparing a blood pressure reducing drug with a two-sided alternative hypothesis. Their test statistics show that the following z values: z 1 = 1.87 and z 2 = 2.45. Which one of these have the smaller p-value and why?

A) z 1 = 1.87 because the area between 1.87 and 1.87 is smaller.

B) z 2 = 2.45 because the z-value indicates almost two and a half standard deviations away from the mean with the remaining areas smaller than 1.87.

C) z 2 = 2.45 because the bigger z-value has a bigger area between 2.45 and 2.45.

D) z 1 = 1.87 value because it is closer to the mean.

Objective: (2) Find the Test Statistic and Corresponding p-value for a One-Proportion z-Test

10

46) Suppose that the following is to be tested: H0 : p = 0.72 and Ha: p 0.72 . Calculate the observed z-statistic for the following sample data: Sixty-eight out of ninety test subjects have the characteristic of interest. Round to the nearest thousandth.

A) z = 0.453 B) z = 0.751 C) z = 0.756 D) z = -0.751 Objective: (2) Find the Test Statistic and Corresponding p-value for a One-Proportion z-Test

47) A research firm carried out a hypothesis test on a population proportion using a left-tailed alternative hypothesis.

Which of the following z-scores would be associated with a p-value of 0.025? Round to the nearest hundredth.

A) z = 1.96 B) z = -2.97 C) z = 2.97 D) z = -1.96 Objective: (2) Find the Test Statistic and Corresponding p-value for a One-Proportion z-Test

A researcher is wondering whether the drinking habits of adults in a certain region of the country are in the same proportion as the general population of adults. Suppose a recent study stated that the proportion of adults in the general population who reported drinking once a week or less in the last month was 0.26. The null hypothesis for this test is H0 : p = 0.26 and the alternative hypothesis is Ha: p < 0.26. The researcher collected data from 150 surveys he handed out at a busy park located in the region.

48) To continue the study into the drinking habits of adults, the researcher decides to collect data from adults working in "white collar" jobs to see whether their drinking habits are in the same proportion as the general public. The null hypothesis for this test is H0 : p = 0.26 and the alternative hypothesis is Ha: p < 0.26 . The researcher collected data from a random sample of 120 adults with "white collar" jobs of which 25 stated that they drank once a week or less in the last month. Assume that the conditions that must be met in order for us to use the N (0,1) distribution as the ^

sampling distribution are satisfied. Find the values of the sample proportion, p, and the test statistic. Round all values to the nearest thousandth. ^

A) p = 0.208, z = 0.250

^

B) p = 0.75, z = 1.32

^

C) p = 0.30, z = 0.803

^

D) p = 0.208, z = 1.290

Objective: (2) Find the Test Statistic and Corresponding p-value for a One-Proportion z-Test

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Solve the problem.

49) Two different students conduct a coin flipping experiment with a left-tailed alternative. They obtain the following test statistics: Student #1: z = 2.05 Student #2: z = 1.28 Which of the test statistics has a smaller p-value and why?

Objective: (2) Find the Test Statistic and Corresponding p-value for a One-Proportion z-Test

50) Suppose the following is to be tested: H0 : p = 0.4 and Ha : p 0.4. Calculate the observed z test statistic for the following sample data: n = 80 and 25 test subjects have the characteristic of interest. Round to the nearest thousandth.

Objective: (2) Find the Test Statistic and Corresponding p-value for a One-Proportion z-Test

11

A health foods shop owner is wondering if his customer's daily vitamin supplement habits are in the same proportion as the general population of adults. The shop owner heard in a news report that 60% of all adults reported that they took a daily vitamin. The shop owner believes that his customers have a greater proportion of adults who take a daily vitamin, so he decides to conduct a hypothesis test using the following null and alternative hypothesis: H0 : p = 0.6 and Ha: p > 0.6.

The shope owner collected data from 50 randomly selected customers.

51) To continue the study, the shop owner decides to collect data from 60 customers between the ages of 22 and 27 to see whether the proportion in this age group is different from the general population of adults. From this sample, 26 reported that they took a daily vitamin. The null hypothesis for this test is H0 : p = 0.6 and the alternative hypothesis is Ha : p 0.6 .

Assume that the conditions that must be met in order for us to use the N (0,1) distribution as the sampling ^

distribution are satisfied. Find the values of the sample proportion (p), the observed test statistic, and the associated p-value. Round all values to the nearest thousandth.

Objective: (2) Find the Test Statistic and Corresponding p-value for a One-Proportion z-Test

12

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

52) From the TI-84 graphing calculator screenshots below, choose the screenshot whose shaded area depicts a p-value for a left-tailed test.

A)

B)

C)

Objective: (3) Identify the Graph that Shows a p-value for a Given Alternative Hypothesis

13

53) From the TI-84 graphing calculator screenshots below, choose the screenshot whose shaded area correctly depicts the following hypothesis test results: H0 : p = 0.15, Ha : p 0.15,

= 0.05, z = -1.82, p-value = 0.0688

A)

B)

C)

Objective: (3) Identify the Graph that Shows a p-value for a Given Alternative Hypothesis

14

54) From the TI-84 graphing calculator screenshots below, choose the screenshot whose shaded area depicts a p-value for a two-tailed test.

A)

B)

C)

Objective: (3) Identify the Graph that Shows a p-value for a Given Alternative Hypothesis

55) From the TI-84 graphing calculator screenshots below, choose the screenshot whose shaded area correctly depicts the following hypothesis test results: H0 : p = 0.25, Ha : p > 0.25,

= 0.05, z = 2.01, p-value = 0.022

A)

15

B)

C)

Objective: (3) Identify the Graph that Shows a p-value for a Given Alternative Hypothesis

56) From the TI-84 graphing calculator screenshots below, there are specific shaded areas that represent p-values.

Choose the statement that best describes the interpretation of these p-values.

A) The p-value shown in graphic b displays a one-sided test with a small p-value.

B) The p-value shown in graphic c displays a one-sided test with a small p-value.

C) The p-value shown in graphic c displays a small two-sided p-value.

D) The p-values shown in graphics a and b display one-sided tests while c displays a shaded area showing a two-sided p-value.

Objective: (3) Identify the Graph that Shows a p-value for a Given Alternative Hypothesis

16

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Shade the approximate area that would represent the p-value for the alternative hypothesis and z-score, and then calculate the p-value. Round to the nearest thousandth.

57) The alternative hypothesis is a right-tailed with a z-score = 0.21

Objective: (3) Identify the Graph that Shows a p-value for a Given Alternative Hypothesis

58) The alternative hypothesis is a two-tailed with a z-score = 1.88

Objective: (3) Identify the Graph that Shows a p-value for a Given Alternative Hypothesis

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

59) A researcher conducts a hypothesis test on a population proportion. Her null and alternative hypothesis are H0 : p = 0.4 and Ha : p < 0.4. The test statistic and p-value for the test are z = -3.01 and p-value = 0.0013. For a significance level of = 0.05, choose the correct conclusion regarding the null hypothesis.

A) There is not sufficient evidence to reject the null hypothesis that the population proportion is equal to 0.04.

B) There is not sufficient evidence to conclude that the population proportion is significantly different from 0.04.

C) There is sufficient evidence to conclude that the population proportion is significantly different from 0.04.

D) There is sufficient evidence to accept the null hypothesis that the population proportion is equal to 0.04.

Objective: (4) Perform a One-Proportion z-Test

60) A researcher conducts a hypothesis test on a population proportion. Her null and alternative hypothesis are H0 : p = 0.6 and Ha : p < 0.6. The test statistic and p-value for the test are z = -1.51 and p-value = 0.0655. For a significance level of = 0.05, choose the correct conclusion regarding the null hypothesis.

A) There is sufficient evidence to accept the null hypothesis that the population proportion is equal to 0.6.

B) There is sufficient evidence to conclude that the population proportion is significantly different from 0.6.

C) There is insufficient evidence to reject the null hypothesis that the population proportion is equal to 0.6.

D) None of these.

Objective: (4) Perform a One-Proportion z-Test

17

Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level.

61) A manufacturer considers his production process to be out of control when defects exceed 3%. In a random sample of 85 items, the defect rate is 5.5% but the manager claims that this is only a sample fluctuation and production is not really out of control. Test whether the manufacturer's claim that production is out of control is supported or not supported.

A) not supported B) supported Objective: (4) Perform a One-Proportion z-Test

62) A supplier of 3.5" disks claims that no more than 1% of the disks are defective. In a random sample of 800 disks, it is found that 3% are defective, but the supplier claims that this is only a sample fluctuation. Test whether the supplier's claim that no more than 1% are defective is supported or not supported.

A) supported B) not supported Objective: (4) Perform a One-Proportion z-Test

63) According to a recent poll 53% of Americans would vote for the incumbent president. If a random sample of 100 people results in 25% who would vote for the incumbent, test whether the claim that the actual percentage is different from 53% is supported or not supported.

A) not supported B) supported Objective: (4) Perform a One-Proportion z-Test

Solve the problem.

64) Which of the following is not one of the four steps of the hypothesis test?

A) State the null and alternative hypothesis about the population parameter.

B) State the level of significance, choose a test, and check the conditions for the test.

C) Make a decision to reject or not reject the null hypothesis.

D) All of the these are steps of the hypothesis test.

Objective: (4) Perform a One-Proportion z-Test

A researcher is wondering whether the smoking habits of young adults (18-25 years of age) in a certain city in the U.S. are the same as the proportion of the general population of young adults in the U.S. A recent study stated that the proportion of young adults who reported smoking at least twice a week or more in the last month was 0.16. The researcher collected data from a random sample of 75 adults in the city of interest.

65) State the hypotheses to be tested for this study.

A) H0 : p = 0.16; Ha : p > 0.16 B) H0 : p = 0.16; Ha : p 0.16

C) H0 : p = 0.16; Ha : p < 0.16

D) H0 : p 0.16; Ha : p < 0.16

Objective: (4) Perform a One-Proportion z-Test

18

66) A researcher completes a hypothesis test with a resulting p-value = 0.076. Choose the best statement to interpret the results.

A) The p-value for a two-sided test is divided by 2 resulting in a value less than a standard cutoff value of = 0.05 supporting the hypothesis that the city of interest has a different proportion of smokers than the general public.

B) The p-value is above a standard cutoff value of = 0.05 and therefore there is sufficient evidence to support that the city of interest has a different proportion of smokers than the general public.

C) The p-value is above a standard cutoff value of = 0.05 and therefore there is insufficient evidence to support that the city of interest has a different proportion of smokers than the general public.

D) The standard cutoff value of = 0.05 is multiplied by two for a two-sided test and the resulting value of 0.10 is greater than the p-value. Therefore there is no evidence to support that the city of interest has a different proportion of smokers than the general public.

Objective: (4) Perform a One-Proportion z-Test

Solve the problem.

67) A medical researcher conducts a hypothesis test to test the claim that U.S. adult males have gained weight over the past 15 years. Assume that all the conditions for proceeding with a one-sample test on proportions have been met.

The calculated test statistic is approximately 1.71 with an associated p-value of approximately 0.0436. Choose the conclusion that provides the best interpretation for the p-value at a significance level of = 0.05.

A) If the null hypothesis is true, then the probability of getting a test statistic that is as extreme or more extreme than the calculated test statistic of 1.71 is 0.0436. This result is not surprising and could easily happen by chance.

B) If the null hypothesis is true, then the probability of getting a test statistic that is as extreme or more extreme than the calculated test statistic of 1.71 is 0.0436. The result should be doubled for a two-sided test. This result is not surprising and could easily happen by chance.

C) If the null hypothesis is true, then the probability of getting a test statistic that is as extreme or more extreme than the calculated test statistic of 1.71 is 0.0436. This result is surprising and could not easily happen by chance.

D) The p-value should be considered extreme; therefore the hypothesis test proves that the null hypothesis is true.

Objective: (4) Perform a One-Proportion z-Test

68) Which of the following is not one of the four steps of the hypothesis test?

A) Make a decision to either accept the null hypothesis or accept the alternative hypothesis.

B) State the null and alternative hypothesis about the population parameter.

C) Calculate the test statistic and the p-value.

D) State the level of significance, choose a test, and check the conditions for the test.

Objective: (4) Perform a One-Proportion z-Test

19

A researcher is wondering whether the drinking habits of adults in a certain region of the country are in the same proportion as the general population of adults. Suppose a recent study stated that the proportion of adults in the general population who reported drinking once a week or less in the last month was 0.26. The null hypothesis for this test is H0 : p = 0.26 and the alternative hypothesis is Ha: p < 0.26. The researcher collected data from 150 surveys he handed out at a busy park located in the region.

69) Suppose a city official conducts a hypothesis test to test the claim that the majority of voters support a proposed tax to build sidewalks. Assume that all the conditions for proceeding with a one-sample test on proportions have been met. The calculated test statistic is approximately 1.40 with an associated p-value of approximately 0.081.

Choose the conclusion that provides the best interpretation for the p-value at a significance level of = 0.05.

A) The p-value should be considered extreme; therefore the hypothesis test proves that the null hypothesis is true.

B) If the null hypothesis is true, then the probability of getting a test statistic as large or larger than 1.40 is 0.081.

This result is not surprising and could easily happen by chance.

C) If the null hypothesis is true, then the probability of getting a test statistic that is as extreme or more extreme than the calculated test statistic of 1.40 is 0.081. This result is surprising and could not easily happen by chance.

D) If the null hypothesis is true, then the probability of getting a test statistic that is as extreme or more extreme than the calculated test statistic of 1.40 is 0.081. The result should be doubled for a two-sided test. This result is not surprising and easily happen by chance.

Objective: (4) Perform a One-Proportion z-Test

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Solve the problem.

70) List and briefly summarize the four steps of the hypothesis test.

Objective: (4) Perform a One-Proportion z-Test

A health foods shop owner is wondering if his customer's daily vitamin supplement habits are in the same proportion as the general population of adults. The shop owner heard in a news report that 60% of all adults reported that they took a daily vitamin. The shop owner believes that his customers have a greater proportion of adults who take a daily vitamin, so he decides to conduct a hypothesis test using the following null and alternative hypothesis: H0 : p = 0.6 and Ha: p > 0.6.

The shope owner collected data from 50 randomly selected customers.

71) Based on a 5% significance level, write a conclusion by interpreting the p-value. Be sure to clearly state the decision regarding the null hypothesis.

Objective: (4) Perform a One-Proportion z-Test

20

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

72) A quality control manager thinks that there is a higher defective rate on the production line than the advertised value of p = 0.025. She does a hypothesis test with a significance level of 0.05. Symbolically, the null and alternative hypothesis are as follows: H0 : p = 0.025 and Ha : p > 0.025. She calculates a p-value for the hypothesis test of defective light bulbs to be approximately 0.067. Choose the correct interpretation for the p-value.

A) The p-value tells us that the result is significantly higher than the advertised value using a significance level of 0.05.

B) The p-value tells us that the probability of concluding that the defect rate is equal to 0.025, when in fact it is greater than 0.025, is approximately 0.067.

C) The p-value tells us that if the defect rate is 0.025, then the probability that she would observe the percentage she actually observed or higher is 0.067. At a significance level of 0.05, this would not be an unusual outcome.

D) The p-value tells us that the true population rate of defective light bulbs is approximately 0.067.

Objective: (1) Understand p-Values

A janitor at a large office building believes that his supply of light bulbs has a defect rate that is higher than the defect rate stated by the manufacturer. The janitor's null hypothesis is that the supply of light bulbs has a manufacturer's defect rate of p = 0.09. He performs a test at a significance level of 0.01. The null and alternative hypothesis are as follows: H0 : p = 0.09 and Ha: p > 0.09.

73) The janitor calculates a p-value for the hypothesis test of approximately 0.113. Choose the correct interpretation for the p-value.

A) The p-value tells us that if the defect rate is 0.09, then the probability that the janitor will have 33 or more defective light bulbs out of 300 is approximately 0.113.

B) The p-value tells us that the probability of concluding that the defect rate is equal to 0.09, when in fact it is greater than 0.09, is approximately 0.113.

C) The p-value tells us that the true population rate of defective light bulbs is approximately 0.113.

D) The p-value tells us that the result is significantly higher than the advertised value using a significance level of 0.05.

Objective: (1) Understand p-Values

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test whether the claim is true or not, a random sample of 100 doctors is obtained. Of these doctors, 82 indicated that they recommend aspirin for headaches. Is the claim accurate? Test with a significance level of 0.05.

74) Write a statement explaining what the p-value means and how it should be interpreted.

Objective: (1) Understand p-Values

21

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

For the given hypothesis test, explain the meaning of the kind of error, as requested.

75) Suppose you are testing your friend to see whether she can tell the difference between the name brand and generic peanut butter. You give her 40 samples selected randomly, half from the name brand and half from the generic brand. The null hypothese is that she is just guessing and should get about half right. Explain what the first kind of error would be in this case (when you reject the null hypothesis when it is actually true).

A) The first kind of error would be saying that your friend can tell the difference between the two kinds of peanut butter, when she really can.

B) The first kind of error would be saying that your friend can not tell the difference between the two kinds of peanut butter, when she really can.

C) The first kind of error would be saying that your friend can tell the difference between the two kinds of peanut butter, when she really cannot.

D) The first kind of error would be saying that your friend cannot tell the difference between the two kinds of peanut butter, when she really cannot.

Objective: (2) Identify Both Types of Errors

76) A statistics student has heard that about 19% of the students on his campus attend sporting events weekly. He wants to know if statistics students attend events in the same proportions as the general student body. Explain what the second type of error would be in this case (where the student fails to reject a null hypothesis that is actually false).

A) The second kind of error would be saying that statistics students attend sporting events in much higher proportions than the student body as a whole, even though they actually have the same attendance proportion.

B) The second kind of error would be saying that there is no difference in the attendance of statistics students and the student body as a whole at sporting events, even though statistics students actually go much less often.

C) The second kind of error would be saying that statistics students attend sporting events in different proportions than the student body as a whole, even though they actually have the same attendance proportion.

D) The second kind of error would be saying that there is no difference in the attendance of statistics students and the student body as a whole at sporting events, even though there really is.

Objective: (2) Identify Both Types of Errors

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Solve the problem.

77) Explain why failing to reject the null hypothesis does not prove that the null hypothesis is true.

Objective: (2) Identify Both Types of Errors

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

78) The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home, because if the proportion exceeds 35%, then the lab will scale back a proposed enlargement of its facilities. Suppose 300 business students were randomly sampled and 85 have PC's at home.

Should they use a hypothesis test or a confidence interval to answer this question?

A) Confidence interval.

B) Hypothesis test.

Objective: (3) Choose the Appropriate Test of Significance and Perform the Test

22

79) The city council wants to know what percentage of people in their town have health insurance. They take a poll, and of 87 adults selected randomly from the town, 60 have health insurance. Should the council use a hypothesis test or confidence interval to answer their question?

A) Confidence interval.

B) Hypothesis test.

Objective: (3) Choose the Appropriate Test of Significance and Perform the Test

Solve the problem.

80) Read the following then choose the appropriate test and name the population(s).

A researcher asks a random sample of 200 men whether they had made an online purchase in the last three months. He wants to determine whether the proportion of men who make online purchases is less than 0.18.

A) Two-proportion z-test; the population is the 200 men surveyed.

B) One-proportion z-test; the population is all adults who make online purchases.

C) Two-proportion z-test; one population is all men who make online purchases and the other population is all men who do not make online purchases.

D) One-proportion z-test; the population is all men.

Objective: (3) Choose the Appropriate Test of Significance and Perform the Test

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

81) For the following description, state whether a one-proportion z-test or a two-proportion z-test would be appropriate, and name the population. A researcher asks people who are 20-29 years old and senior citizens (people over 65) whether they support a new tax on income. He wants to determine whether the proportions that support the tax differ for these age groups.

Objective: (3) Choose the Appropriate Test of Significance and Perform the Test

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.

82) An entomologist writes an article in a scientific journal which claims that fewer than 12 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

A) There is not sufficient evidence to support the claim that the true proportion is greater than 12 in ten thousand.

B) There is sufficient evidence to support the claim that the true proportion is less than 12 in ten thousand.

C) There is not sufficient evidence to support the claim that the true proportion is less than 12 in ten thousand.

D) There is sufficient evidence to support the claim that the true proportion is greater than 12 in ten thousand.

Objective: (4) Understand Hypotheses and How to Interpret the Results of a Hypothesis Test

83) A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, p, is less than 1 in every ten thousand. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

A) There is sufficient evidence to support the claim that the true proportion is greater than 1 in ten thousand.

B) There is sufficient evidence to support the claim that the true proportion is less than 1 in ten thousand.

C) There is not sufficient evidence to support the claim that the true proportion is less than 1 in ten thousand.

D) There is not sufficient evidence to support the claim that the true proportion is greater than 1 in ten thousand.

Objective: (4) Understand Hypotheses and How to Interpret the Results of a Hypothesis Test

23

84) A psychologist claims that more than 55 percent of the population suffers from professional problems due to extreme shyness. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

A) There is not sufficient evidence to support the claim that the true proportion is less than 55 percent.

B) There is sufficient evidence to support the claim that the true proportion is less than 55 percent.

C) There is not sufficient evidence to support the claim that the true proportion is greater than 55 percent.

D) There is sufficient evidence to support the claim that the true proportion is greater than 55 percent.

Objective: (4) Understand Hypotheses and How to Interpret the Results of a Hypothesis Test

Solve the problem.

85) A researcher conducts a hypothesis test on a population proportion. Her null and alternative hypothesis are H0 : p = 0.6 and Ha: p < 0.6 . The test statistic and p-value for the test are z = 1.51 and p value = 0.0655. For a significance level of = 0.05, choose the correct conclusion regarding the null hypothesis.

A) There is insufficient evidence to reject the null hypothesis that the population proportion is equal to 0.6.

B) There is sufficient evidence to conclude that the population proportion is significantly different from 0.6.

C) There is sufficient evidence to accept the null hypothesis that the population proportion is equal to 0.6.

D) There is insufficient evident to determine the significance.

Objective: (4) Understand Hypotheses and How to Interpret the Results of a Hypothesis Test

86) Which statement best describes the significance level of a hypothesis test?

A) The probability of failing to reject the null hypothesis when the null hypothesis is not true.

B) The probability of rejecting the null hypothesis when the null hypothesis is not true.

C) The probability of rejecting the null hypothesis when the null hypothesis is true.

D) None of these Objective: (4) Understand Hypotheses and How to Interpret the Results of a Hypothesis Test

87) A researcher conducts a hypothesis test on a population proportion. Her null and alternative hypothesis are H0 : p = 0.4 and Ha: p < 0.4 . The test statistic and p-value for the test are z = 3.01 and p value = 0.0013. For a significance level of = 0.05 , choose the correct conclusion regarding the null hypothesis.

A) There is not sufficient evidence to reject the null hypothesis that the population proportion is equal to 0.4.

B) There is sufficient evidence to accept the null hypothesis that the population proportion is equal to 0.4.

C) There is not sufficient evidence to conclude that the population proportion is significantly different from 0.4.

D) There is sufficient evidence to conclude that the population proportion is significantly different from 0.4.

Objective: (1) Understand How to Interpret Two-Proportion z-Tests

88) A polling agency is interested in testing whether the proportion of women who support a female candidate for office is greater than the proportion of men. The null hypothesis is that there is no difference in the proportion of men and women who support the female candidate. The alternative hypothesis is that the proportion of women who support the female candidate is greater than the proportion of men. The test results in a p-value of 0.112.

Which of the following is the best interpretation of the p-value?

A) The p-value is the probability that men will support the female candidate.

B) The p-value is the probability of getting a result that is as extreme as or more extreme than the one obtained, assuming that the proportion of women who support the female candidate is greater than the proportion of men.

C) The p-value is the probability that women will support the female candidate.

D) The p-value is the probability of getting a result that is as extreme as or more extreme than the one obtained, assuming that there is no difference in the proportions.

Objective: (1) Understand How to Interpret Two-Proportion z-Tests

24

89) A polling agency is interested in testing whether the proportion of women who support a female candidate for office is less than the proportion of men. The null hypothesis is that there is no difference in the proportions of men and women who support the female candidate. The alternative hypothesis is that the proportion of women who support the female candidate is less than the proportion of men. The test results in a p-value of 0.041. Which of the following is the best interpretation of the p-value?

A) The p-value is the probability that the majority of men will support the female candidate.

B) The p-value is the probability that the majority of women will support the female candidate.

C) The p-value is the probability of getting a result that is as extreme as or more extreme than the one obtained, assuming that there is no difference in the proportions.

D) The p-value is the probability of getting a result that is as extreme as or more extreme than the one obtained, assuming that the proportion of women who support the female candidate is less than the proportion of men.

Objective: (1) Understand How to Interpret Two-Proportion z-Tests

90) Which of the following is not a condition that must be checked before proceeding with a two-sample test?

A) The samples must be independent of each other.

B) Each sample must be a random sample.

C) Both samples must be large enough so that the product of each sample size (n 1 and n 2 ) and the pooled ^

estimate, p, is greater than or equal to 10.

D) All of these are conditions that must be checked to proceed with a two-sample test.

Objective: (2) Perform a Two-Proportion z-Test

91) Which of the following is not a condition that must be checked before proceeding with a two-sample test?

A) Each sample must be a random sample.

B) The samples must be independent of each other.

C) The observations within each sample must be independent of one another.

D) All of these are conditions that must be checked to proceed with a two-sample test.

Objective: (2) Perform a Two-Proportion z-Test

92) A researcher believes that the proportion of women who exercise with a friend is greater than the proportion of men. He takes a random sample from each population and records the response to the question, "Have you exercised with a friend at least once in the last seven days?" The null hypothesis is H0 : pwomen = pmen. Choose the correct alternative hypothesis.

A) Ha : pwomen < pmen

B) Ha : p = 0

C) Ha : pwomen > pmen

D) Ha : pwomen pmen

Objective: (2) Perform a Two-Proportion z-Test

93) A researcher believes that the reading habits of men and women are different. He takes a random sample from each population and records the response to the question, "Did you read at least one book last month?" The null hypothesis is H0 : pwomen = pmen. Choose the correct alternative hypothesis.

A) Ha : p = 0

B) Ha : pwomen pmen D) Ha : pwomen > pmen

C) Ha : pwomen < pmen Objective: (2) Perform a Two-Proportion z-Test

25

94) A researcher believes that children who attend elementary school in a rural setting have lower obesity rates then children who attend elementary school in an urban setting. The researcher collects a random sample from each population and records the proportion of children in each sample who are clinically obese. The data is summarized in the table below. Assume that all conditions for proceeding with a two-sample test have been met.

Find the z-statistic (rounded to the nearest hundredth) and p-value (rounded to the nearest thousandth) for this hypothesis test. Using a 5% significance level, state the correct conclusion regarding the null hypothesis H0 : prural = purban.

A) z = -1.95, p = 0.026. There is not sufficient evidence to reject the null hypothesis.

B) z = -1.95, p = 0.026. There is sufficient evidence to reject the null hypothesis.

C) z = -1.85, p = 0.032. There is sufficient evidence to accept the null hypothesis.

D) z =1.95, p = 0.026. There is sufficient evidence to prove that the population proportions are the same.

Objective: (2) Perform a Two-Proportion z-Test

95) A researcher believes that children who attend elementary school in a rural setting are more physically active then children who attend elementary school in an urban setting. The researcher collects a random sample from each population and records the proportion of children in each sample who reported participating in at least one hour of rigorous activity a day. The data is summarized in the table below. Assume the all conditions for proceeding with a two-sample test have been met.

Find the z-statistic (rounded to the nearest hundredth) and p-value (rounded to the nearest thousandth) for this hypothesis test. Using a 5% significance level, state the correct conclusion regarding the null hypothesis, H0 : prural = purban.

A) z = 0.82, p = 0.073. There is sufficient evidence to accept the null hypothesis.

B) z = 1.79, p = 0.037. There is sufficient evidence to reject the null hypothesis.

C) z = 0.71, p = 0.073. There is sufficient evidence to reject the null hypothesis.

D) z = -1.79, p = 0.037. There is insufficient evidence to reject the null hypothesis.

Objective: (2) Perform a Two-Proportion z-Test

96) A researcher believes that the exercise habits of men and women are different. He takes a random sample from each population and records the response to the question, "Did you exercise for at least 30 minutes twice a week?"

The null hypothesis is H0 : pwomen = p men Choose the correct alternative hypothesis.

A) Ha: p women p men B) Ha: p women > pmen Objective: (2) Perform a Two-Proportion z-Test

26

C) Ha: p women < pmen

D) Ha: p = 0

97) Which of the following is not a condition that must be checked before proceeding with a two-sample test?

A) Each sample must be from populations with the same standard deviation.

B) Both samples must be large enough so that the product of each sample size (n1 and n2 ) and the pooled ^

estimate, p, is greater than or equal to 10.

C) Each sample must be a random sample.

D) The samples must be independent of each other.

Objective: (2) Perform a Two-Proportion z-Test

98) Which of the following is not a condition that must be checked before proceeding with a two-sample test?

A) Each sample must be a random sample.

B) The observations within each sample must be independent of one another.

C) The samples must be independent of each other.

D) All of these are conditions that must be checked to proceed with a two-sample test.

Objective: (2) Perform a Two-Proportion z-Test

99) Two movie reviewers give movies "thumbs up" and "thumbs down" ratings. You sample 100 movies that they both have rated and find that they both gave "thumbs up" to 25 movies, both gave "thumbs down" to 30 movies, Sarah gave "thumbs up" and Jessica "thumb down" to 28 movies, and the remaining movies Sarah gave "thumbs down" and Jessica "thumbs up". Test whether there is a tendency for one reviewer to give more movies "thumbs up" (proportion 1) than the other (proportion 2).

A) z = 1.56; For a two-sided test at = 0.05 level, there is insufficient evidence to reject the null hypothesis because the cutoff z-value is at 1.96.

B) z = 1.96 There is sufficient evidence to accept the null hypothesis.

C) z = 1.56; For a two-sided test at = 0.05 level, there is insufficient evidence to reject the null hypothesis because the cutoff z-value is at 1.96.

D) z = 1.96 There is sufficient evidence to reject the null hypothesis.

Objective: (2) Perform a Two-Proportion z-Test

100) A researcher asks random samples of residents of two separate counties as to whether they had purchased organically grown food in the last three months. He wants to determine whether the proportion of residents of one county who purchase organically grown food is greater than the proportion of residents of the second county who purchase organically grown food. Choose the appropriate test and name the population(s).

A) One-proportion z-test; the population is all residents of the first county.

B) Two-proportion z-test; one population is all residents of the first county and the other population is residents of the second county.

C) One-proportion z-test; the population is all residents of a state.

D) Two-proportion z-test; one population is all adults who buy organically grown food and the other population is all adults who do not buy organically grown food.

Objective: (2) Perform a Two-Proportion z-Test

27

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

101) A sociologist believes that families that eat at least one meal a day together (without the interference of any other media) will have better communication skills. The sociologist conducts a study to see if there is a difference in the proportion of meals that are eaten together as a family for families living in a rural setting compared to families living in an urban setting. She collects a random sample from each population and records the proportion of test subjects that reported that they had eaten at least 3 meals per week together as a family. The data are summarized in the table below. Assume the all conditions for proceeding with a two-sample test have been met.

Find the z test statistic (rounded to the nearest hundredth) and p-value (rounded to the nearest thousandth) for testing the hypothesis that the population proportions are different. At the 5% significance level, state the correct conclusion regarding the null hypothesis H0 : prural = p urban. Round all calculations to the nearest hundredth.

Objective: (2) Perform a Two-Proportion z-Test

102) A sociologist believes that the proportion of single men who attend church on a regular basis is less than the proportion of single women. She takes a random sample from each population and records the proportion from each that reported that they attended church on a regular basis. The null hypothesis is H0 : p men = p women. State the correct alternative hypothesis with a sentence and symbolically.

Objective: (2) Perform a Two-Proportion z-Test

103) When a two-sample test of proportions is conducted, there are two conditions of independence that must be checked. State the two conditions of independence. Be sure that your statement clearly states the difference between the two conditions.

Objective: (2) Perform a Two-Proportion z-Test

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Answer Key Testname: GOULDCH8TESTGEN

1) B 2) A 3) D 4) B 5) D 6) D 7) C 8) Null hypothesis is that the carnival worker has no special powers, therefore H0 : p = 0.5 . The alternative hypothesis is that he can communicate with a rock, therefore Ha: p > 0.5 .

9) H0 : p = 1 / 6 and Ha: p 1 / 6 ; The null hypothesis states that the population parameter is no different than what is expected and is assumed to be true.

The alternative hypothesis states that the population parameter may be different and contains the claim that the researcher is trying to show.

10) The null and alternative hypotheses are as follow: H0 : p = 0.90 and Ha: p 0.90.

19) The cutoff z-value for a significance level of 0.05 is +/-1.96. The calculated value of -2.667 is greater than the cutoff value and therefore the result is significant.

20) D 21) B 22) C 23) A 24) C 25) C 26) B 27) B 28) B 29) B 30) B 31) C 32) B 33) C 34) A 35) B 36) D 37) The significance level of 0.05 is the probability of concluding that the defect rate is different from 0.90, when in fact the defect rate is equal to 0.90.

38) C 39) D 40) A 41) C

42) Random Sample-stated in problem description; large enough sample size-since there are at least 10 expected success and failures (50 * 0.6 10 and 50 * 0.4 10); Large enough population-yes, it is reasonable to assume that there are at least 500 customers in the population; Independence-yes, reasonable to assume that customer responses are independent; Null hypothesis-yes, it is reasonable to assume the null hypothesis is true.

43) D 44) A 45) B 46) B 47) D 48) D 49) If the null hypothesis is correct, then the test statistic should be close to zero.

Values farther from zero are more surprising and so have smaller p-values. Since -2.05 is farther from zero than is -1.28, the area under the normal curve in the left tail is smaller for -2.05, therefore -2.05 will have a smaller p-value.

50) z = 1.598

11) B 12) A 13) C 14) C 15) B 16) B 17) C 18) z = -2.667

29

^

51) p = 0.433, z = 02.635, p = 0.008 52) C 53) C 54) B 55) C 56) D 57) The right tail of the curve should be shaded and should approximately represent the p-value of 0.417.

58) Both tails of the curve should be shaded and should approximately represent the p-value of 0.060.

59) C 60) C 61) A 62) B 63) B 64) D 65) B 66) C 67) C 68) A 69) B

Answer Key Testname: GOULDCH8TESTGEN

70) (1) State the null and alternative hypothesis about the population parameter; (2) State the significance level, an appropriate test statistic, check the required conditions, and state any assumptions; (3) Compute the test statistic and associated p-value; (4) State you conclusion regarding the null hypothesis.

Will you reject or fail to reject the null hypothesis? Explain in the context of the data.

71) If the null hypothesis is true, then the probability of getting a calculated z-score that is this far from zero is surprising and could not easily happen by chance.

The null hypothesis should be rejected.

There is sufficient evidence to support the claim that the proportion of customers who take a daily vitamin is different then 0.60.

72) C 73) A

74) The calculated p-value is 0.0076 (0.0038*2 for a two-sided test),which is less than 0.05, the stated level of significance.

Therefore, the result is significant. The sample results give evidence that the given proportion of 0.90 is not correct.

75) C 76) D 77) Failing to reject the null hypothesis does not prove that the null hypothesis is true, only that the sample evidence does not show surprising enough results to suggest that the assumption that the null hypothesis is true is incorrect. To say the null hypothesis is proven true means that there is no doubt about it.

This is not possible based on chance processes.

78) B 79) A 80) D 81) Two-proportion z-test. One population is all people in the 20-29 age bracket, the other population is all senior citizens.

82) B 83) C 84) C 85) A 86) C 87) D

88) D 89) C 90) D 91) D 92) C 93) B 94) B 95) B 96) A 97) A 98) D 99) A 100) B 101) z = 2.05; p = 0.04 .

There is sufficient evidence to reject the null hypothesis that the population proportions are equal.

102) The population proportion of single men who attend church regularly is less than the population proportion of single women who attend church regularly. Ha: p men < p women

103) One condition is that the two samples themselves must be independent of each other. The second condition is that the observations within each sample must be independent of each other.

30

Gould/Ryan/Wong Essential Statistics 3e Chapter 9 Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants was taken and the mean finishing time was found to be 1.59 hours with a standard deviation of 0.30 hours. .

1) In this example, the numerical values of 1.67 hours and 0.25 hours are

A) estimates C) unbiased estimators

B) parameters D) statistics

Objective: (1) Distinguish Between Parameters and Statistics

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants in the 40-44 age group was taken and the mean finishing time was found to be 1.62 hours with a standard deviation of 0.40 hours. .

2) In this example, the numerical values of 1.62 hours and 0.40 hours are

A) statistics C) parameters

B) estimates D) unbiased estimators

Objective: (1) Distinguish Between Parameters and Statistics

Feature movie lengths (in hours) were measured for all movies shown in the past year in the U.S. The mean length of all feature length movies shown was 1.80 hours with a standard deviation of 0.15 hours. Suppose the length of a random sample of 20 movies was recorded from all movies released this year. The mean length of the feature length movies was found to be 1.72 hours with a standard deviation of 0.18 hours. .

3) In this example, the numerical values of 1.80 hours and 0.15 hours are

A) estimates C) statistics

B) parameters D) unbiased estimators

Objective: (1) Distinguish Between Parameters and Statistics

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all male participants in a recent large duathlon was 1.54 hours with a standard deviation of 0.22 hours. The distribution of finish times for males is right-skewed. Suppose that a sample of 30 randomly selected male participants is selected.

4) Is the number 1.54 a statistic or parameter? Explain.

Objective: (1) Distinguish Between Parameters and Statistics

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants in the 40-44 age group was taken and the mean finishing time was found to be 1.62 hours with a standard deviation of 0.40 hours.

5) Suppose the process of taking random samples of size 30 from the 40-44 age group is repeated 200 times and a histogram of the 200 sample means is created. Which statement best describes the shape of the histogram?

A) All of these statements are true.

B) The histogram will be roughly bell-shaped.

C) The histogram will be unimodal.

D) The histogram will be roughly symmetrical.

Objective: (2) Sketch Population Distributions and Find Probabilities Using the Empirical Rule

1

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all male participants in a recent large duathlon was 1.54 hours with a standard deviation of 0.22 hours. The distribution of finish times for males is right-skewed. Suppose that a sample of 30 randomly selected male participants is selected.

6) Suppose that the process of drawing samples of size 30 from the population of all male participants is repeated 100 times. If possible, sketch and describe what the sampling distribution of the means will look like and state the approximate mean value of the distribution. Round to the nearest thousandth.

Objective: (2) Sketch Population Distributions and Find Probabilities Using the Empirical Rule

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants was taken and the mean finishing time was found to be 1.59 hours with a standard deviation of 0.30 hours.

7) Suppose we were to make a histogram of the finishing times of all participants in the duathlon. Would the histogram be a display of the population distribution, the distribution of a sample, or the sampling distribution of means?

A) distribution of a sample B) sampling distribution of means C) population distribution Objective: (3) Decide What Type of Distribution is Shown in a Histogram Made from the Data in a Sample

8) Suppose the process of taking random samples of size 30 is repeated 200 times and a histogram of the 200 sample means is created. Would the histogram be an approximate display of the population distribution, the distribution of a sample, or the sampling distribution of means?

A) sampling distribution of means B) distribution of a sample C) population distribution Objective: (3) Decide What Type of Distribution is Shown in a Histogram Made from the Data in a Sample

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants in the 40-44 age group was taken and the mean finishing time was found to be 1.62 hours with a standard deviation of 0.40 hours.

9) Suppose we were to make a histogram of the finishing times of the 30 participants in the 40-44 age group. Would the histogram be a display of the population distribution, the distribution of a sample, or the sampling distribution of means?

A) sampling distribution of means B) population distribution C) distribution of a sample Objective: (3) Decide What Type of Distribution is Shown in a Histogram Made from the Data in a Sample

10) Suppose the process of taking random samples of size 30 from the 40-44 age group is repeated 200 times and a histogram of the 200 sample means is created. Which statement best describes the shape of the histogram?

A) The histogram will be unimodal.

B) The histogram will be roughly symmetrical.

C) The histogram will be roughly bell-shaped.

D) All of these statements are true.

Objective: (3) Decide What Type of Distribution is Shown in a Histogram Made from the Data in a Sample

2

Feature movie lengths (in hours) were measured for all movies shown in the past year in the U.S. The mean length of all feature length movies shown was 1.80 hours with a standard deviation of 0.15 hours. Suppose the length of a random sample of 20 movies was recorded from all movies released this year. The mean length of the feature length movies was found to be 1.72 hours with a standard deviation of 0.18 hours.

11) Suppose we were to make a histogram of the feature length movie times of all movies in the past year. The histogram would be a display of which of the following?

A) distribution of a sample B) sampling distribution of means C) population distribution D) Normal distribution Objective: (3) Decide What Type of Distribution is Shown in a Histogram Made from the Data in a Sample

12) Suppose the process of taking random samples of size 20 is repeated 200 times and a histogram of the 200 sample means is created. The histogram would be a display of which of the following?

A) distribution of a sample B) population distribution C) Normal distribution D) sampling distribution of means Objective: (3) Decide What Type of Distribution is Shown in a Histogram Made from the Data in a Sample

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants was taken and the mean finishing time was found to be 1.59 hours with a standard deviation of 0.30 hours.

13) What is the standard error for the mean finish time of 30 randomly selected participants? Round to the nearest thousandth.

A) 0.055 B) 0.046 C) 0.300 D) 0.250 Objective: (4) Understand and Calculate the Sample Mean and the Standard Error of the Mean

Use the following information to answer the question. A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all participants in a recent large duathlon was 1.67 hours with a standard deviation of 0.25 hours. Suppose a random sample of 30 participants in the 40-44 age group was taken and the mean finishing time was found to be 1.62 hours with a standard deviation of 0.40 hours.

14) What is the standard error for the mean finish time of 30 randomly selected participants in the 40-44 age group?

Round to the nearest thousandth.

A) 0.300 B) 0.250 C) 0.055 D) 0.046 Objective: (4) Understand and Calculate the Sample Mean and the Standard Error of the Mean

Solve the problem.

15) Choose the statement that best describes what is meant when we say that the sample mean is unbiased when estimating the population mean.

A) The standard deviation of the sampling distribution (also called the standard error) and the population standard deviation are equal.

B) The sample mean will always equal the population mean.

C) On average, the sample mean is the same as the population mean.

D) None of these.

Objective: (4) Understand and Calculate the Sample Mean and the Standard Error of the Mean

3

Feature movie lengths (in hours) were measured for all movies shown in the past year in the U.S. The mean length of all feature length movies shown was 1.80 hours with a standard deviation of 0.15 hours. Suppose the length of a random sample of 20 movies was recorded from all movies released this year. The mean length of the feature length movies was found to be 1.72 hours with a standard deviation of 0.18 hours.

16) What is the standard error for the estimated mean feature length movie time of the 20 randomly selected movies?

Round to the nearest thousandth.

A) 0.040 B) 0.034 C) 0.055 D) 0.356 Objective: (4) Understand and Calculate the Sample Mean and the Standard Error of the Mean

17) If we create a sampling distribution of sample means, what would be the mean and standard deviation of that distribution given the sample size of 20?

A) The mean length would be 1.80 hours with a standard deviation of 0.15 hours.

B) The mean length would be 1.80 hours with a standard deviation of 0.034 hours.

C) The mean length would be 1.80 hours with a standard deviation of 0.18 hours.

D) The mean length would be 1.72 hours with a standard deviation of 0.18 hours.

Objective: (4) Understand and Calculate the Sample Mean and the Standard Error of the Mean

Solve the problem.

18) Choose the statement that best describes what is meant when we say that the sample mean is unbiased when estimating the population mean.

A) We cannot say that the sample mean is unbiased.

B) The standard deviation of the sampling distribution (also called the standard error) and the population standard deviation are equal.

C) On average, the sample mean is the same as the population mean.

D) The sample mean will always equal the population mean.

Objective: (4) Understand and Calculate the Sample Mean and the Standard Error of the Mean

19) When the mean of the sampling distribution is the same value as the population parameter, we can say that the statistic is A) unlimited.

B) the standard error.

C) a representation of an unbiased parameter.

D) an unbiased estimator.

Objective: (4) Understand and Calculate the Sample Mean and the Standard Error of the Mean

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

A sprint duathlon consists of a 5 km run, a 20 km bike ride, followed by another 5 km run. The mean finish time of all male participants in a recent large duathlon was 1.54 hours with a standard deviation of 0.22 hours. The distribution of finish times for males is right-skewed. Suppose that a sample of 30 randomly selected male participants is selected.

20) What is the expected finish time for a male participant in the sample of 30? Will the expected mean finish time be the same for any sample of 30 males drawn from the population? Explain.

Objective: (4) Understand and Calculate the Sample Mean and the Standard Error of the Mean

21) Calculate the standard error for the mean finish time of 30 randomly selected male participants. Show all your work and round to the nearest thousandth.

Objective: (4) Understand and Calculate the Sample Mean and the Standard Error of the Mean

Solve the problem.

22) Explain what is meant when we say that the sample mean is an unbiased estimator.

Objective: (4) Understand and Calculate the Sample Mean and the Standard Error of the Mean

4

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

23) Which of the following is not a true statement about the Central Limit Theorem for sample means?

A) If conditions are met, the mean of the sampling distribution is equal to the population mean.

B) The Central Limit Theorem helps us find probabilities for sample means when those means are based on a random sample from a population.

C) If the sample size is large, it doesn't matter what the distribution of the population it was drawn from is, the normal distribution can still be used to perform statistical inference.

D) All of these statements are true about the Central Limit Theorem for sample means.

Objective: (1) Understand and Use the Central Limit Theorem

24) Suppose that the average pop song length in America is 4 minutes with a standard deviation of 1.25 minutes. It is known that song length is not normally distributed. Suppose a sample of 25 songs is taken from the population.

What is the approximate probability that the average song length will be less than 3.5 minutes? Round to the nearest thousandth.

A) 0.155 B) 0.345 C) 0.023 D) 0.477 Objective: (1) Understand and Use the Central Limit Theorem

25) Suppose that the average song length in America is 4 minutes with a standard deviation of 1.25 minutes. It is known that song length is not normally distributed. Find the probability that a single randomly selected song from the population will be longer than 4.25 minutes. Round to the nearest thousandth.

A) 0.079 B) 0.579 C) This probability cannot be determined because we do not know the distribution of the population.

D) 0.421 Objective: (1) Understand and Use the Central Limit Theorem

26) Suppose that the average country song length in America is 4.75 minutes with a standard deviation of 1.10 minutes. It is known that song length is not normally distributed. Suppose a sample of 25 songs is taken from the population. What is the approximate probability that the average song length will last more than 5.25 minutes?

Round to the nearest thousandth.

A) 0.175 B) 0.325 C) 0.488 D) 0.012 Objective: (1) Understand and Use the Central Limit Theorem

27) Suppose that the average country song length in America is 4.75 minutes with a standard deviation of 1.10 minutes. It is known that song length is not normally distributed. Find the probability that a single randomly selected song from the population will be less than 4.20 minutes. Round to the nearest thousandth.

A) 0.006 B) 0.068 C) This probability cannot be determined because we do not know the distribution of the population.

D) 0.494 Objective: (1) Understand and Use the Central Limit Theorem

Use the empirical rule to solve the problem.

28) Some sources report that the systolic blood pressures of 18-year-old women are Normally distributed with a mean of 120 mmHg and a standard deviation of 12 mmHg. What percentage of 18-year-old women have a systolic blood pressure between 96 mmHg and 144 mmHg? A) 95% B) 99.99% C) 68% D) 99.7% Objective: (1) Understand and Use the Central Limit Theorem

5

29) At one college, the GPA's are Normally distributed with a mean of 2.8 and a standard deviation of 0.6. What percentage of students at the college have a GPA between 2.2 and 3.4?

A) 68% B) 84.13% C) 99.7% D) 95% Objective: (1) Understand and Use the Central Limit Theorem

Solve the problem.

30) Which of the following statements is true about the t-distribution?

A) Like the Normal distribution, the t-distribution is symmetric for small n.

B) For small sample sizes, the t-distribution has the same properties as the normal curve.

C) Since population standard deviation is usually unknown, the standard error uses the sample standard deviation to estimate population standard deviation.

D) For large sample sizes, the t-distribution has the same properties as the normal curve.

Objective: (1) Understand and Use the Central Limit Theorem

31) Which of the following is a true statement about the Central Limit Theorem for sample means?

A) If conditions are met, the mean of the sampling distribution is equal to the population mean.

B) If the sample size is large, it doesn't matter what the distribution of the population it was drawn from is, the normal distribution can still be used to perform statistical inference.

C) The Central Limit Theorem helps us find probabilities for sample means when those means are based on a random sample from a population.

D) All of the statements are true about the Central Limit Theorem for sample means.

Objective: (1) Understand and Use the Central Limit Theorem

Suppose that the mean Systolic blood pressure for adults age 50-54 is 125 mmHg with a standard deviation of 5 mmHg. It is known that Systolic blood pressure is not Normally distributed. Suppose a sample of 25 adult Systolic blood pressure measurements is taken from the population.

32) What is the approximate standard error for the sampling distribution of mean blood pressures? Round to the nearest hundredth.

A) 17.00 B) 1.00 C) 5.00 D) 0.20 Objective: (1) Understand and Use the Central Limit Theorem

33) What is the interpretation of the z score used to find the probability that the average Systolic blood pressure will be less than 122 mmHg? Assume technology is not available and so the values must first be converted to standard units. Round to the nearest hundredth.

A) z = 3.00 which is less than or equal to 3 standard deviations above the mean.

B) z = -3.00 which is less than or equal to 3 standard deviations above the mean.

C) z = -3.00 which is less than or equal to 3 standard deviations below the mean.

D) This probability cannot be determined because we do not know the distribution of the population.

Objective: (1) Understand and Use the Central Limit Theorem

6

34) What is the approximate probability with interpretation that the average diastolic blood pressure will be less than 122 mmHg, given the above information? Round to the nearest thousandth.

A) The probability for z = -3.00 or less is less than or equal to 3 standard deviations which is a significant result, using an approximation of 0.5 of (1 – 99.7%) = 0.0015.

B) The probability for z = 3.00 or less is less than or equal to 3 standard deviations which is not a significant result.

C) The probability for z = -3.00 or less is less than or equal to 3 standard deviations which is a significant result, using an approximation of 2*(1 – 99.7%) = 0.0060.

D) None of these statements are correct.

Objective: (1) Understand and Use the Central Limit Theorem

Assume that the average Systolic blood pressure for adults age 50-54 is 125 mmHg with a standard deviation of 5 mmHg. It is known that Systolic blood pressure is not normally distributed. A sample of 25 adult Systolic blood pressure measurements are taken from the population.

35) What type of test would be appropriate for this example to see if the sample results are different from the average diastolic blood pressure measurements?

I. A one-sample t test because the data are not normally distributed.

II. A one-sample z test because the data are not normally distributed.

III. A 95% confidence interval using a critical t statistic.

A) I and III B) I only C) III only D) II only Objective: (1) Understand and Use the Central Limit Theorem

36) What is the approximate z-value with interpretation for the probability that the average Systolic blood pressure will be less than 122 mmHg? Round to the nearest hundredth.

A) z = 3.00 which is greater than or equal to 3 standard deviations which is a significant result.

B) This probability cannot be determined because we do not know the distribution of the population.

C) z = -3.00 which is less than or equal to 3 standard deviations which is not a significant result.

D) z = -3.00 which is less than or equal to 3 standard deviations which is a significant result.

Objective: (1) Understand and Use the Central Limit Theorem

37) What is the approximate z score with interpretation that the average Systolic blood pressure will be greater than 128 mmHg? Round to the nearest thousandth.

A) The probability for z = 3.00 or greater is greater than or equal to 3 standard deviations which is a significant result.

B) The probability for z = -3.00 or less is less than or equal to 3 standard deviations which is a significant result.

C) The probability for z = -3.00 or greater than or equal to 3 standard deviations which is not a significant result.

D) None of these statements are correct.

Objective: (1) Understand and Use the Central Limit Theorem

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Solve the problem.

38) How might the shapes of a population distribution and a sampling distribution look the same? How might they look different?

Objective: (1) Understand and Use the Central Limit Theorem

39) Describe the center and standard deviation of a sampling distribution.

Objective: (1) Understand and Use the Central Limit Theorem

7

40) Suppose that a major league baseball game has an average length of 2.9 hours with a standard deviation of 0.5 hours. It is known that game length is not normally distributed. Suppose a random sample of 36 games is taken from the population. Sketch the probability distribution and shade in the region that corresponds to the probability. What is the approximate probability that average game length will be greater than 3.1 hours? Round to the nearest thousandth.

Objective: (1) Understand and Use the Central Limit Theorem

41) Suppose that a major league baseball game has an average length of 2.9 hours with a standard deviation of 0.5 hours. It is known that game length is not normally distributed. Suppose a random sample of 36 games is taken from the population. What is the approximate probability that average game length will be greater than 3.15 hours or less than 2.75 hours? Round to the nearest thousandth.

Objective: (1) Understand and Use the Central Limit Theorem

42) Compare the normal distribution and the t-distribution. How are they similar? How are they different?

Objective: (1) Understand and Use the Central Limit Theorem

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the following information to answer the question. Many couples believe that it is getting too expensive to host an "average" wedding in the United States. According to the website www.costofwedding.com, the average cost of a wedding in the U.S. in 2009 was $24,066. Recently, in a random sample of 40 weddings in the U.S. it was found that the average cost of a wedding was $23,224, with a standard deviation of $2,903. On the basis of this, a 95% confidence interval for the mean cost of weddings in the U.S. is $22,296 to $24,152.

43) For this description, which of the following does not describe a condition for a valid confidence interval?

A) The description states that the sample was randomly selected, so we can assume that the condition which states that the data must represent a random sample is satisfied.

B) The sample distribution must be normally distributed in order to have a valid confidence interval. The problem does not describe the distribution of the sample, so this condition is not met.

C) The sample observations are independent because knowledge about the cost of any one wedding tells us nothing about the cost of any other wedding in the sample.

D) The sample size of 40 is large enough that knowledge about the population distribution is not necessary and the condition that the population be normally distributed or sample size be larger than 25 is satisfied.

Objective: (1) Find, Interpret, and Use Confidence Levels and Intervals for a Single Population Mean

44) Does the confidence interval provide evidence that the mean cost of a wedding has decreased?

A) No B) Yes Objective: (1) Find, Interpret, and Use Confidence Levels and Intervals for a Single Population Mean

45) Choose the statement that is the best interpretation of the confidence interval.

A) That probability that a U.S. wedding will cost more than $24,152 is less than 3%.

B) In about 95% of all samples of 40 U.S. weddings, the resulting confidence interval will contain the mean cost of all weddings in the U.S. C) We are extremely confident that the mean cost of a U.S. wedding is between $22,296 and $24,152.

Objective: (1) Find, Interpret, and Use Confidence Levels and Intervals for a Single Population Mean

8

Solve the problem.

46) The weights at birth of five randomly chosen baby giraffes were 111, 115, 120, 103, and 106 pounds. Assume the distribution of weights is normally distributed. Find a 95% confidence interval for the mean weight of all baby giraffes. Use technology for your calculations. Give the confidence interval in the form "estimate ± margin of error." Round to the nearest tenth of a pound.

A) 111.0 ± 8.5 pounds B) 110.0 ± 8.5 pounds C) 111.5 ± 9.0 pounds D) There is not enough information given to calculate the confidence interval.

Objective: (1) Find, Interpret, and Use Confidence Levels and Intervals for a Single Population Mean

47) Choose the statement that describes a situation where a confidence interval and a hypothesis test will yield the same results.

A) When the alternative hypothesis is two-tailed.

B) When the null hypothesis contains a population parameter that is equal to zero.

C) Both (a) and (b).

D) Neither (a) nor (b). The confidence interval cannot yield results that are the same as the hypothesis test.

Objective: (1) Find, Interpret, and Use Confidence Levels and Intervals for a Single Population Mean

Use the following information to answer the question. According to the website www.costofwedding.com, the average cost of flowers for a wedding is $698. Recently, in a random sample of 40 weddings in the U.S. it was found that the average cost of the flowers was $734, with a standard deviation of $102. On the basis of this, a 95% confidence interval for the mean cost of flowers for a wedding is $701 to $767.

48) For this description, which of the following does not describe a condition for a valid confidence interval?

A) The description states that the sample was randomly selected, so we can assume that the condition which states that the data must represent a random sample is satisfied.

B) The sample observations are independent because knowledge about the cost of flowers for any one wedding tells us nothing about the cost of flowers for any other wedding in the sample.

C) All of these describe conditions for a valid confidence interval.

D) The sample size of 40 is large enough that knowledge about the population distribution is not necessary and the condition that the population be normally distributed or sample size be larger than 25 is satisfied.

Objective: (1) Find, Interpret, and Use Confidence Levels and Intervals for a Single Population Mean

49) Does the confidence interval provide evidence that the mean cost of flowers for a wedding has increased?

A) No B) Yes Objective: (1) Find, Interpret, and Use Confidence Levels and Intervals for a Single Population Mean

50) Choose the statement that is the best interpretation of the confidence interval.

A) We are extremely confident that the mean cost of flowers at a wedding is between $701 and $767.

B) In about 95% of all samples of size 40, the resulting confidence interval will contain the mean cost of flowers at weddings.

C) That probability that flowers at a wedding will cost less than $767 is nearly 100%.

D) That probability that the flowers at a wedding will cost more than $698 is greater than 5%.

Objective: (1) Find, Interpret, and Use Confidence Levels and Intervals for a Single Population Mean

9

Solve the problem.

51) The weights at birth of five randomly chosen baby Orca whales were 425, 454, 380, 405, and 426 pounds. Assume the distribution of weights is normally distributed. Find a 95% confidence interval for the mean weight of all baby Orca whales. Use technology for your calculations. Give the confidence interval in the form "estimate ± margin of error." Round to the nearest tenth of a pound.

A) 384.0 ± 68.0 pounds B) 418.0 ± 34.5 pounds C) There is not enough information given to calculate the confidence interval.

D) 418.0 ± 34.0 pounds Objective: (1) Find, Interpret, and Use Confidence Levels and Intervals for a Single Population Mean

Many couples believe that it is getting too expensive to host an "average" wedding in the United States. According to a statistics study in the U.S., the average cost of a wedding in the U.S. in 2014 was $25,200. Recently, in a random sample of 35 weddings in the U.S. it was found that the average cost of a wedding was $24,224 with a standard deviation of $2,210.

52) For this description, which of the following does not describe a required condition for a valid confidence interval based on the sample results?

A) The description states that the sample was randomly selected, so we can assume that the condition which states that the data must represent a random sample is satisfied.

B) The sample size of 35 is large enough that knowledge about the population distribution is not necessary and the condition that the population be normally distributed or sample size be larger than 25 is satisfied.

C) The sample observations are independent because knowledge about the cost of any one wedding tells us nothing about the cost of any other wedding in the sample.

D) The sample distribution must be normally distributed in order to have a valid confidence interval. The problem does not describe the distribution of the sample, so this condition is not met.

Objective: (1) Find, Interpret, and Use Confidence Levels and Intervals for a Single Population Mean

53) Which method should be used for finding a 95% margin of error for the sample mean for this example?

A) Find the critical t value for the given level of confidence and multiply by the standard error using the formula / n.

B) Find the critical z value for the given level of confidence and multiply by the standard error using the formula s/ n .

C) Find the critical z value for the given level of confidence and multiply by the standard error using the formula z/ n .

D) Find the critical t value for the given level of confidence and multiply by the standard error using the formula s/ n .

Objective: (1) Find, Interpret, and Use Confidence Levels and Intervals for a Single Population Mean

54) Which is the best interpretation of a 95% confidence interval for the sample mean?

A) The 95% confidence interval means that we are 95% confident that the population mean is between the low and high interval values.

B) The 95% confidence interval means that there is a 95% probability that the sample mean is between the low and high interval values.

C) The 95% confidence interval means that there is a 95% probability that the population mean is between the low and high interval values.

D) The 95% confidence interval means that we are 95% confident that the sample mean is between the low and high interval values.

Objective: (1) Find, Interpret, and Use Confidence Levels and Intervals for a Single Population Mean

10

55) If a 95% confidence interval for the mean for the wedding sample is ($23465, $24983), does this mean that the sample results are significantly different from the claimed value for the mean of $25,200?

A) Since the claimed population mean is outside of the 95% confidence interval, we conclude that there is a 95% chance that the sample results are significantly different.

B) Since the accepted population average is outside of the 95% confidence interval, we conclude that the sample results are not significantly different.

C) Since the accepted population average is outside of the 95% confidence interval, we conclude that there is a 5% chance that the sample results are significantly different.

D) Since the claimed population mean is outside of the 95% confidence interval, we conclude that the sample results are significantly different.

Objective: (1) Find, Interpret, and Use Confidence Levels and Intervals for a Single Population Mean

According to the website www.costofwedding.com, the average cost of flowers for a wedding is $698. Recently, in a random sample of 40 weddings in the U. S. it was found that the average cost of the flowers was $734, with a standard deviation of $102. On the basis of this, a 95% confidence interval for the mean cost of flowers for a wedding is $701 to $767.

56) For this description, which of the following does not describe a condition for a valid confidence interval?

A) The sample size of 40 is large enough that knowledge about the population distribution is not necessary and the condition that the population be normally distributed or sample size be larger than 25 is satisfied.

B) The sample observations are independent because knowledge about the cost of flowers for any one wedding tells us nothing about the cost of flowers for any other wedding in the sample.

C) The description states that the sample was randomly selected, so we can assume that the condition which states that the data must represent a random sample is satisfied.

D) All of these describe conditions for a valid confidence interval.

Objective: (1) Find, Interpret, and Use Confidence Levels and Intervals for a Single Population Mean

57) Choose the statement that is the best interpretation of the confidence interval.

I. That probability that the flowers at a wedding will cost more than $698 is greater than 5%.

II. In about 95% of all samples of size 40, the resulting confidence interval will contain the mean cost of flowers at weddings.

III. We are extremely confident that the mean cost of flowers at a wedding is between $701 and $767.

A) II only B) I only C) III only D) II and III are both correct.

Objective: (1) Find, Interpret, and Use Confidence Levels and Intervals for a Single Population Mean

Solve the problem.

58) The weights at birth of five randomly chosen baby Orca whales were 425, 454, 380, 405, and 426 pounds. Assume the distribution of weights is normally distributed. Find a 95% confidence interval for the mean weight of all baby Orca whales. Use technology for your calculations. Give the confidence interval in the form "estimate ± margin of error". Round to the nearest tenth of a pound.

A) 418.0 ± 34.1 pounds B) 418.0 ± 34.5 pounds C) There is not enough information given to calculate the confidence interval.

D) 384.0 ± 68.0 pounds Objective: (1) Find, Interpret, and Use Confidence Levels and Intervals for a Single Population Mean

11

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

According to the website www.costofwedding.com, the average cost of catering a wedding (with an open bar) is $100 per person. Recently, in a random sample of 40 weddings in the U. S. it was found that the average catering cost was $110, with a standard deviation of $12. On the basis of this, a 95% confidence interval for the mean catering cost for a wedding is $106 to $114.

59) Verify that the conditions for a valid confidence interval are met.

Objective: (1) Find, Interpret, and Use Confidence Levels and Intervals for a Single Population Mean

60) Explain whether the confidence interval provides evidence that the mean catering cost of a wedding has increased.

Be specific about the reasoning of using the confidence interval.

Objective: (1) Find, Interpret, and Use Confidence Levels and Intervals for a Single Population Mean

61) A popular wedding magazine states in an article on catering costs that "There is a 95% chance that the catering cost of your wedding will be between $106 and $114 per person." Explain what is wrong with this statement and write a better statement that correctly interprets the confidence interval.

Objective: (1) Find, Interpret, and Use Confidence Levels and Intervals for a Single Population Mean

Solve the problem.

62) The weights at birth of five randomly chosen baby hippopotamuses were 75, 99, 107, 82, and 63 pounds. Assume the distribution of weights is normally distributed. Find a 95% confidence interval for the mean weight of all baby hippopotamuses. Use technology for your calculations. Give the confidence interval in the form "estimate ± margin of error". Round to the nearest pound.

Objective: (1) Find, Interpret, and Use Confidence Levels and Intervals for a Single Population Mean

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

63) Suppose a consumer product researcher wanted to find out whether a highlighter lasted longer than the manufacturer's claim that their highlighters could write continuously for 14 hours. The researcher tested 40 highlighters and recorded the number of continuous hours each highlighter wrote before drying up. Test the hypothesis that the highlighters wrote for more than 14 continuous hours. Following are the summary statistics: x =14.5 hours, s =1.2 hours Report the test statistic, p-value, your decision regarding the null hypothesis. At the 5% significance level, state your conclusion about the original claim. Round all values to the nearest thousandth.

A) t = 2.635; p = 0.006; Fail to reject the null hypothesis; there is not strong evidence to suggest that the highlighters last longer than 14 hours.

B) t = 2.635; p = 0.006; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last longer than 14 hours.

C) z = 9.583; p = 0.000+ ; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last

longer than 14 hours.

D) z = 9.583; p = 0.000+ ; Fail to reject the null hypothesis; there is not strong evidence to suggest that the highlighters last longer than 14 hours.

Objective: (1) Test Hypotheses Concerning a Population Mean

12

64) Suppose a consumer product researcher wanted to find out whether a highlighter lasted less than the manufacturer's claim that their highlighters could write continuously for 14 hours. The researcher tested 40 highlighters and recorded the number of continuous hours each highlighter wrote before drying up. Test the hypothesis that the highlighters wrote for less than 14 continuous hours. Following are the summary statistics: x =13.6 hours, s =1.3 hours Report the test statistic, p-value, your decision regarding the null hypothesis, and your conclusion about the original claim. Round all values to the nearest thousandth.

A) z = 1.946; p = 0.974; Fail to reject the null hypothesis; there is not strong evidence to suggest that the highlighters last less than 14 hours.

B) z = 1.946; p = 0.029; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last less than 14 hours.

C) t = -1.946; p = 0.029; Fail to reject the null hypothesis; there is not strong evidence to suggest that the highlighters last less than 14 hours.

D) t = -1.946; p = 0.029; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last less than 14 hours.

Objective: (1) Test Hypotheses Concerning a Population Mean

65) An economist conducted a hypothesis test to test the claim that the average cost of eating a meal at home increased from 2009 to 2010. The average cost of eating a meal at home in 2009 was $5.25 per person per meal. Assume that all conditions for testing have been met. He used technology to complete the hypothesis test. Following is his null and alternative hypothesis and the output from his graphing calculator.

H0 : µ = $5.25 Ha : µ > $5.25

At the 5% significance level, choose the statement that contains the correct conclusion regarding the hypothesis and the original claim.

A) Reject the null hypothesis; there is not sufficient evidence to support the claim that the average cost of eating at home has increased since 2009.

B) Reject the null hypothesis; there is sufficient evidence to support the claim that the average cost of eating at home has increased since 2009.

C) Fail to reject the null hypothesis; there is sufficient evidence to support the claim that the average cost of eating at home has increased since 2009.

D) Fail to reject the null hypothesis; there is not sufficient evidence to support the claim that the average cost of eating at home has increased since 2009.

Objective: (1) Test Hypotheses Concerning a Population Mean

13

66) An economist conducted a hypothesis test to test the claim that the average cost of eating a meal away from home decreased from 2009 to 2010. The average cost of eating a meal away from home in 2009 was $7.15 per person per meal. Assume that all conditions for testing have been met. He used technology to complete the hypothesis test.

Following is his null and alternative hypothesis and the output from his graphing calculator.

H0 : µ = $7.15 Ha : µ < $7.15

Choose the statement that contains the correct conclusion regarding the hypothesis and the original claim.

A) Reject the null hypothesis; there is not sufficient evidence to support the claim that the average cost of eating away from home has decreased since 2009.

B) Reject the null hypothesis; there is sufficient evidence to support the claim that the average cost of eating away from home has decreased since 2009.

C) Fail to reject the null hypothesis; there is sufficient evidence to support the claim that the average cost of eating away from home has decreased since 2009.

D) Fail to reject the null hypothesis; there is not sufficient evidence to support the claim that the average cost of eating away from home has decreased since 2009.

Objective: (1) Test Hypotheses Concerning a Population Mean

67) Suppose a consumer product researcher wanted to find out whether a Sharpie lasted longer than the manufacturer's claim that their Sharpies could write continuously for a mean of 14 hours. The researcher tested 40 Sharpies and recorded the number of continuous hours each Sharpie wrote before drying up. Test the hypothesis that Sharpies can write for more than a mean of 14 continuous hours. Following are the summary statistics: x 14.5 hours, s 1.2 hours At the 5% significance level, t = 2.635; p = 0.006. State your conclusion about the original claim.

A) There needs to be more data to determine if the Sharpies last longer than a mean of 14 hours.

B) Do not reject the null hypothesis; there is not strong enough evidence to suggest that the Sharpies last longer than a mean of 14 hours.

C) Reject the alternative hypothesis; there is strong evidence to suggest that the Sharpies last longer than a mean of 14 hours.

D) Reject the null hypothesis; there is strong evidence to suggest that the Sharpies last longer than a mean of 14 hours.

Objective: (1) Test Hypotheses Concerning a Population Mean

14

68) Understand the hypothesis test of the mean] An economist conducted a hypothesis test to test the claim that the average cost of eating a meal away from home decreased from 2012 to 2013. The average cost of eating a meal away from home in 2012 was $7.15 per person per meal. Assume that all conditions for testing have been met. He used technology to complete the hypothesis test. Following is his null and alternative hypothesis and the output from his graphing calculator.

H0 : µ = $7.15 Ha: µ < $7.15

Choose the statement that contains the correct conclusion regarding the hypothesis and the original claim.

A) Reject the null hypothesis; there is not sufficient evidence to support the claim that the average cost of eating away from home has decreased since 2012.

B) Fail to reject the null hypothesis; there is sufficient evidence to support the claim that the average cost of eating away from home has decreased since 2012.

C) Fail to reject the null hypothesis; there is not sufficient evidence to support the claim that the average cost of eating away from home has decreased since 2012.

D) Reject the null hypothesis; there is sufficient evidence to support the claim that the average cost of eating away from home has decreased since 2012.

Objective: (1) Test Hypotheses Concerning a Population Mean

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

69) Suppose a consumer product researcher wanted to find out whether a printer ink cartridge lasted longer than the manufacturer"s claim that their ink cartridges could print 400 pages. The researcher tested 40 ink cartridges and recorded the number of pages that were printed before the ink started to fade. Test the hypothesis that the ink cartridges lasted for more than 400 pages. Following are the summary statistics: x = 415 pages, s = 30 pages Report the null and alternative hypothesis, test statistic, p-value, your decision regarding the null hypothesis, and your conclusion about the original claim. Round all values to the nearest thousandth.

Objective: (1) Test Hypotheses Concerning a Population Mean

15

70) The quality engineer at a paint manufacturer conducted a hypothesis test to test the claim that the mean volume of paint cans had changed after an adjustment in the manufacturing process. Mean volume in paint cans before the adjustment was 1.02 gallons. Assume that all conditions for testing have been met. She used technology to complete the hypothesis test. Following is the null and alternative hypothesis and the output from her graphing calculator.

H0 : µ = 1.02 gallons Ha: µ 1.02 gallons

Write a statement explaining what her decision regarding the null hypothesis should be and a statement summarizing her conclusion regarding the claim that average volume of paint cans had changed. Has the adjustment in the manufacturing process changed the average volume of paint cans?

Objective: (1) Test Hypotheses Concerning a Population Mean

ESSAY. Write your answer in the space provided or on a separate sheet of paper.

71) no exercises available Objective: (2) Find and Interpret Confidence Intervals for a Population Mean (no exercises available)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

72) The reading level of a random sample of men and a random sample of women are measured. Researchers want know whether women typically read at a higher level than men.

A) Independent B) Dependent Objective: (1) Distinguish Between Independent and Paired (Dependent) Samples

73) The college GPA's of identical twins are compared to see whether the means are different.

A) Independent B) Dependent Objective: (1) Distinguish Between Independent and Paired (Dependent) Samples

74) The productivity of manufacturing plant workers is compared before and after the installation of air conditioning.

A) Independent B) Dependent Objective: (1) Distinguish Between Independent and Paired (Dependent) Samples

75) The weight of King Salmon from Lake Michigan and Lake Superior are measured. Researchers want to know whether Lake Michigan King Salmon weigh less than those from Lake Superior.

A) Dependent B) Independent Objective: (1) Distinguish Between Independent and Paired (Dependent) Samples

16

76) The reading level of a random sample of men and a random sample of women is measured. Researchers want to know whether women typically read at a higher level than men. The samples A) are independent B) are not a type that can be determined C) are dependent D) follow a normal distribution Objective: (1) Distinguish Between Independent and Paired (Dependent) Samples

77) The weight of King Salmon from Lake Michigan and Lake Superior are measured. Researchers want to know whether Lake Michigan King Salmon weigh less than those from Lake Superior. The samples A) follow a normal distribution B) are dependent C) are independent D) are not a type that can be determined Objective: (1) Distinguish Between Independent and Paired (Dependent) Samples

78) The productivity of manufacturing plant workers is compared before and after the installation of air conditioning.

The samples A) are dependent B) are independent C) are not a type that can be determined D) follow a normal distribution Objective: (1) Distinguish Between Independent and Paired (Dependent) Samples

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

79) State whether the situation has dependent or independent samples. A researcher wants to know if reaction time is affected by body type of the vehicle being driven. He measures the reaction time of 40 drivers while they drive a compact car then he measures the reaction time while they drive an SUV. Objective: (1) Distinguish Between Independent and Paired (Dependent) Samples

80) State whether the situation has dependent or independent samples. A researcher wants to know if reaction time is affected by the gender of the driver. He measures the reaction time of 30 female drivers while they drive a compact car, then he measures the reaction time of 30 male drivers while they drive a compact car.

Objective: (1) Distinguish Between Independent and Paired (Dependent) Samples

17

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

81) A researcher wants to know whether athletic women are more flexible than non-athletic women. For this experiment, a woman who exercised vigorously at least four times per week was considered "athletic." Flexibility is measured in inches on a sit & reach box. Test the researcher's claim using the following summary statistics:

Assume that all conditions for testing have been met. Report the test statistic and p-value. At the 1% significance level, state your decision regarding the null hypothesis and your conclusion about the original claim. Round all values to the nearest thousandth.

A) t = -1.623; p = 0.054; Reject the null hypothesis; there is strong evidence to suggest that athletic women are more flexible than non-athletic women.

B) t =1.623; p = 0.108; Reject the null hypothesis; there is not strong evidence to suggest that athletic women are more flexible than non-athletic women.

C) t = -1.623; p = 0.108; Reject the null hypothesis; there is strong evidence to suggest that athletic women are more flexible than non-athletic women.

D) t =1.623; p = 0.054; Fail to reject the null hypothesis; there is not strong evidence to suggest that athletic women are more flexible than non-athletic women.

Objective: (2) Test Hypotheses Concerning the Comparison of Two Population Means

82) A researcher wants to know whether athletic men are more flexible than non-athletic men. For this experiment, a man who exercised vigorously at least four times per week was considered "athletic." Flexibility is measured in inches on a sit & reach box. Test the researcher's claim using the following summary statistics:

Assume that all conditions for testing have been met. Report the test statistic and p-value. At the 5% significance level, state your decision regarding the null hypothesis and your conclusion about the original claim. Round all values to the nearest thousandth.

A) t = 3.270; p = 0.001; Reject the null hypothesis; there is strong evidence to suggest that athletic men are more flexible than non-athletic men.

B) t = -3.270; p = 0.002; Reject the null hypothesis; there is not strong evidence to suggest that athletic men are more flexible than non-athletic men.

C) t = 3.270; p = 0.001; Fail to reject the null hypothesis; there is not strong evidence to suggest that athletic men are more flexible than non-athletic men.

D) t = -3.270; p = 0.002; Reject the null hypothesis; there is strong evidence to suggest that athletic men are more flexible than non-athletic men.

Objective: (2) Test Hypotheses Concerning the Comparison of Two Population Means

18

83) A researcher wants to know if mood is affected by music. She conducts a test on a sample of 4 randomly selected adults and measures mood rating before and after being exposed to classical music. Test the hypothesis that mood rating improved after being exposed to classical music. Following are the mood ratings for the four participants:

Assume that all conditions for testing have been met. Report the null and alternative hypothesis and p-value. At the 5% significance level, state your decision regarding the null hypothesis and your conclusion about the original claim. Round all values to the nearest thousandth.

A) H0 : µ1 = µ2 , Ha : µ1 µ2 ; p = 0.008; Fail to reject the null hypothesis; there is not strong evidence to suggest

that exposure to classical music improved mood rating.

B) H0 : µdifference = 0, Ha : µdifference > 0; p = 0.922; Fail to reject the null hypothesis; there is not strong evidence to suggest that exposure to classical music improved mood rating.

C) H0 : µ1 = µ2 , Ha : µ1 < µ2 ; p = 0.077; Fail to reject the null hypothesis; there is not strong evidence to suggest that exposure to classical music improved mood rating.

D) H0 : µdifference = 0, Ha : µdifference < 0; p = 0.008; Reject the null hypothesis; there is strong evidence to suggest that exposure to classical music improved mood rating.

Objective: (2) Test Hypotheses Concerning the Comparison of Two Population Means

84) A researcher wants to know if mood is affected by music. She conducts a test on a sample of 4 randomly selected adults and measures mood rating before and after being exposed to classic rock music. Test the hypothesis that mood rating decreased after being exposed to classic rock music. Following are the mood ratings for the four participants:

Assume that all conditions for testing have been met. Report the null and alternative hypothesis and p-value. At the 5% significance level, state your decision regarding the null hypothesis and your conclusion about the original claim. Round all values to the nearest thousandth.

A) H0 : µdifference = 0, Ha : µdifference > 0; p = 0.154; Fail to reject the null hypothesis; there is not strong

evidence to suggest that exposure to classic rock music decreased mood rating.

B) H0 : µdifference = 0, Ha : µdifference > 0; p = 0.015; Fail to reject the null hypothesis; there is not strong evidence to suggest that exposure to classic rock music decreased mood rating.

C) H0 : µdifference = 0, Ha : µdifference 0; p = 0.309; Reject the null hypothesis; there is strong evidence to suggest that exposure to classic rock music decreased mood rating.

D) H0 : µdifference = 0, Ha : µdifference > 0; p = 0.154; Reject the null hypothesis; there is strong evidence o suggest that exposure to classic rock music decreased mood rating.

Objective: (2) Test Hypotheses Concerning the Comparison of Two Population Means

19

85) A researcher wants to know whether athletic women are more flexible than non-athletic women. For this experiment, a woman who exercised vigorously at least four times per week was considered "athletic". Flexibility is measured in inches on a sit & reach box. A researcher tested his claim using the following summary statistics:

Assume that all conditions for testing have been met. t = 1.626; p = 0.057 ; At the 1% significance level, state your decision regarding the null hypothesis and your conclusion about the original claim.

A) Fail to reject the null hypothesis; there is not strong enough evidence to suggest that athletic women are more flexible, on average, than non-athletic women.

B) Reject the null hypothesis; there is strong evidence to suggest that non-athletic women are more flexible, on average, than athletic women.

C) Fail to reject the null hypothesis; there is strong evidence to suggest that non-athletic women are more flexible, on average, than athletic women.

D) Reject the null hypothesis; there is strong evidence to suggest that athletic women are more flexible, on average, than non-athletic women.

Objective: (2) Test Hypotheses Concerning the Comparison of Two Population Means

86) A researcher wants to know whether athletic men are more flexible than non-athletic men. For this experiment, a man who exercised vigorously at least four times per week was considered "athletic". Flexibility is measured in inches on a sit & reach box. Test the researcher's claim using the following summary statistics:

Assume that all conditions for testing have been met. Report the test statistic and p-value. At the 5% significance level, state your decision regarding the null hypothesis and your conclusion about the original claim. Round all values to the nearest thousandth.

A) t = 3.270; p = 0.002 ; Reject the null hypothesis; there is strong evidence to suggest that athletic men are more flexible than non-athletic men.

B) t = 3.270; p = 0.001 ; Fail to reject the null hypothesis; there is not strong evidence to suggest that athletic men are more flexible than non-athletic men.

C) t = 3.270; p = 0.002 ; Reject the null hypothesis; there is not strong evidence to suggest that athletic men are more flexible than non-athletic men.

D) t = 3.270; p = 0.001 ; Reject the null hypothesis; there is strong evidence to suggest that athletic men are more flexible than non-athletic men.

Objective: (2) Test Hypotheses Concerning the Comparison of Two Population Means

20

87) A researcher wants to know if mood is affected by music. She conducts a test on a sample of 4 randomly selected adults and measures mood rating before and after being exposed to classical music. She is interested in testing whether the mean mood rating improves after an adult is exposed to classical music. Assume that all conditions for testing have been met. The resulting p-value is 0.008. Following are the mood ratings for the four participants:

A) H0 = µdifference = 0, Ha: µdifference > 0; Fail to reject the null hypothesis; there is not strong evidence to suggest that exposure to classical music improves mean mood rating.

B) H0 : µ1 = µ2 , Ha: µ1 < µ2 ; Fail to reject the null hypothesis; there is not strong evidence to suggest that exposure to classical music improves mean mood rating.

C) H0 : µ1 = µ2 , Ha: µ1 µ2 ; Fail to reject the null hypothesis; there is not strong evidence to suggest that exposure to classical music improves mean mood rating.

D) H0 = µdifference = 0, Ha: µdifference < 0; Reject the null hypothesis; there is strong evidence to suggest that exposure to classical music improves mean mood rating.

Objective: (2) Test Hypotheses Concerning the Comparison of Two Population Means

88) A researcher wants to know if mood is affected by music. She conducts a test on a sample of 4 randomly selected adults and measures mood rating before and after being exposed to classic rock music. Test the hypothesis that mood rating decreased after being exposed to classic rock music. Following are the mood ratings for the four participants:

Assume that all conditions for testing have been met. Report the null and alternative hypothesis and p-value. At the 5% significance level, state your decision regarding the null hypothesis and your conclusion about the original claim. Round all values to the nearest thousandth.

A) H0 = µdifference = 0, Ha: µdifference > 0; p = 0.015; Fail to reject the null hypothesis; there is not strong

evidence to suggest that exposure to classic rock music decreased mood rating.

B) H0 = µdifference = 0, Ha: µdifference 0; p = 0.309; Reject the null hypothesis; there is strong evidence to suggest that exposure to classic rock music decreased mood rating.

C) H0 = µdifference = 0, Ha: µdifference > 0; p = 0.154; Reject the null hypothesis; there is strong evidence to suggest that exposure to classic rock music decreased mood rating.

D) H0 = µdifference = 0, Ha: µdifference > 0; p = 0.154; Fail to reject the null hypothesis; there is not strong evidence to suggest that exposure to classic rock music decreased mood rating.

Objective: (2) Test Hypotheses Concerning the Comparison of Two Population Means

21

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

89) A sociologist wants to know whether there is a difference in the mean number of times that men and women in the U. S. check their Smartphone during the day. Test the hypothesis that the mean number of times that men and women in the U. S. check their Smartphone during the day is different. Following are the summary statistics:

Assume that all conditions for testing have been met. Be sure to report the null and alternative hypothesis, test statistic, p-value, your decision regarding the null hypothesis, and your conclusion about the original claim.

Round all values to the nearest thousandth.

Objective: (2) Test Hypotheses Concerning the Comparison of Two Population Means

ESSAY. Write your answer in the space provided or on a separate sheet of paper.

90) no exercises available Objective: (3) Find, Interpret, and Use Confidence Intervals for the Difference of Two Sample Means (no exercises available)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

91) Choose the statement that describes a situation where a confidence interval and a hypothesis test would yield the same results.

I. When the null hypothesis contains a population parameter that is equal to zero.

II. When the alternative hypothesis is two-tailed.

A) I and II B) Neither I nor II. The confidence interval cannot yield results that are the same as the hypothesis test.

C) I only D) II only Objective: (1) Compare Hypothesis Tests and Confidence Intervals

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

92) Describe the circumstances under which a confidence interval and hypothesis test yield the same results?

Objective: (1) Compare Hypothesis Tests and Confidence Intervals

22

Answer Key Testname: GOULDCH9TESTGEN

1) B 2) A 3) B 4) This is a parameter. It is calculated using data from every member of the population. The population it was drawn from is small enough in scope that the population mean can be calculated.

5) A 6) The distribution will be approximately bell-shaped (normally distributed). The mean will be 1.54 hours (the same as the population mean).

7) C 8) A 9) C 10) D 11) C 12) D 13) B 14) D 15) C 16) B 17) B 18) C 19) D 20) The sample mean can vary from sample to sample, but the expected value of any sample of 30 drawn from the population will typically be the same as the population mean of 1.54 hours.

21) SE = / n 0.22/5.477 0.040

22) When many samples of size n are taken from a population, the mean of the sampling distribution of sample means is equal to the population mean.

Since sample mean is an accurate estimate of the population parameter, it is called an unbiased estimator.

23) D 24) C 25) C 26) D 27) C 28) A 29) A 30) D 31) D 32) B 33) C 34) A 35) A 36) D 37) A 38) A population distribution and sampling distribution might both be normally distributed, but not necessarily.

The population distribution histogram can have any distribution, but if the sample size is large, the sampling distribution will always be approximately normal.

39) The mean of this Normal distribution will be the same as the population mean.

The standard deviation of this distribution is the standard error.

40) 0.008 41) 0.037 42) Both distributions are symmetrical and unimodal, but the t-distribution takes on a slightly different shape depending on sample size. The t-distribution will have thicker tails for smaller samples, but as sample size increases, the shape will more closely resemble the bell-shaped normal distribution.

43) B 44) A 45) B 46) A 47) A 48) C 49) B 50) B 51) D 52) D 53) D 54) A 55) D 56) D 57) D 58) A

23

59) All conditions are met. The sample is randomly selected, the sample observations are independent, and the sample size is large enough that population distribution does not matter.

60) The confidence interval provides strong evidence that the catering cost of a wedding has increased because the 95% confidence interval is above $100 and there is no overlap. If the value is not included in the interval, the result is significant.

61) A confidence interval does not describe a probability. The correct statement should be similar to the following: "We are 95% confident that the mean catering cost of a wedding will be between $106 and $114 per person."

62) 85 + 22 pounds 63) B 64) D 65) B 66) D 67) D 68) C

Answer Key Testname: GOULDCH9TESTGEN

69) H0 : µ = 400 and Ha: µ > 400; t = 3.162; p = 0.002; Reject the null hypothesis; there is strong evidence to suggest the ink cartridges last for more than 400 pages (the claim is supported).

70) Reject the null hypothesis; there is strong evidence to suggest that average volume of paint cans is different than 1.02 gallons. The adjustment in the manufacturing process has affected volume of paint cans.

71) 72) A 73) B 74) B 75) B 76) A 77) C 78) A 79) The samples are dependent 80) The samples are independent 81) D 82) A 83) D 84) A 85) A 86) D 87) D 88) D

89) H0 : µ1 = µ2 and Ha: µ1 µ2 ; t = 3.063; p = 0.003; Reject the null hypothesis; there is strong evidence to suggest that there is a difference in the mean number of times that men and women check their Smartphone during the day.

90) 91) D 92) When the alternative hypothesis is two-tailed the confidence interval and hypothesis will yield the same results.

24

Gould/Ryan/Wong Essentials Statistics 3e Chapter 10 Test

ESSAY. Write your answer in the space provided or on a separate sheet of paper.

1) no exercises available Objective: (1) Classify Tests as Using Categorical or Numerical Data (no exercises available)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the following table to answer the question. The following table summarizes the outcomes of a study that researchers carried out to determine if females expressed a greater fear of flying than males.

2) How many categorical variables are summarized in the table?

A) Zero B) Three C) Four

D) Two

Objective: (2) Create Two-Way Tables

3) What fraction represents the proportion of people in the study who did not express a fear of flying?

154 100 210 156 A) B) C) D) 310 310 310 310 Objective: (2) Create Two-Way Tables

Use the following table to answer the question. The following table summarizes the outcomes of a study that researchers carried out to determine if females expressed a greater fear of heights than males.

4) How many categorical variables are summarized in the table?

A) Zero B) Three C) Two

D) Four

Objective: (2) Create Two-Way Tables

5) What fraction represents the proportion of people in the study who expressed a fear of heights?

177 198 183 162 A) B) C) D) 360 360 360 360 Objective: (2) Create Two-Way Tables

1

The following table summarizes the results of a study to determine if job satisfaction is related to pay category.

6) How many categorical variables are summarized in the table?

A) Four B) Two C) One

D) Three

Objective: (2) Create Two-Way Tables

7) What fraction represents the fraction of people in the study who were satisfied with their jobs?

350 194 605 381 A) B) C) D) 1310 1310 1310 1310 Objective: (2) Create Two-Way Tables

8) What fraction of salaried employees are satisfied with their jobs?

605 200 200 A) B) C) 1310 350 605

D)

200 1310

Objective: (2) Create Two-Way Tables

The following table summarizes the outcomes of a study that researchers carried out to determine if females expressed a greater fear of heights than males.

9) What fraction represents the proportion of people in the study who expressed a fear of heights?

198 183 162 177 A) B) C) D) 360 360 360 360 Objective: (2) Create Two-Way Tables

10) How many categorical variables are summarized in the table?

A) Zero B) Four C) Two

D) Three

Objective: (2) Create Two-Way Tables

11) What fraction of women expressed a fear of heights?

109 177 A) B) 177 360 Objective: (2) Create Two-Way Tables

2

C)

109 198

D)

109 360

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

The following table summarizes the results of a study to determine if job satisfaction is related to pay category.

12) Describe the categorical variables that are summarized in the table. Describe an association that could be tested based on the information from the table.

Objective: (2) Create Two-Way Tables

13) Calculate the percentage of people in the study who were dissatisfied with their job. Round your answer to the nearest tenth of a percent.

Objective: (2) Create Two-Way Tables

ESSAY. Write your answer in the space provided or on a separate sheet of paper.

14) no exercises available Objective: (3) Classify Variables as Numeric or Categorical (no exercises available)

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the following table to answer the question. The following table summarizes the outcomes of a study that researchers carried out to determine if females expressed a greater fear of flying than males.

15) Find the expected number of women who should express a fear of flying, if the variables are independent. Round to the nearest whole number.

A) 104 B) 81 C) 11 D) 50 Objective: (4) Calculate Expected Values

Use the following table to answer the question. The following table summarizes the outcomes of a study that researchers carried out to determine if females expressed a greater fear of heights than males.

16) Find the expected number of men who should express a fear of heights, if the variables are independent. Round to the nearest whole number.

A) 93 B) 80 C) 87 D) 97 Objective: (4) Calculate Expected Values

3

Use the following information to answer the question. Lambda olive oil is touted as the "World's most expensive olive oil." A twelve ounce bottle typically costs fifty dollars or more. In a blind taste test, a group of food experts tasted three premium olive oils, one of which was Lambda olive oil. When asked to pick the Lambda olive oil, 84 got it right and 87 got it wrong.

17) If this group were just guessing, how many people (out of 171) would be expected to guess correctly?

A) 86 B) 114 C) Not enough information given to calculate expected value.

D) 57 Objective: (4) Calculate Expected Values

Use the following information to answer the question. Bellei Extravecchio Balsamico Tradizionale is a very expensive brand of balsamic vinegar. A twelve ounce bottle typically costs two-hundred dollars or more. In a blind taste test, a group of food experts tasted three premium balsamic vinegars, with the most expensive one being Bellei Extravecchio Balsamico Tradizionale. When asked to pick the most expensive balsamic vinegar, 92 got it right and 76 got it wrong.

18) If this group were just guessing, how many people (out of 168) would be expected to guess correctly?

A) 84 B) Not enough information given to calculate expected value.

C) 56 D) 70 Objective: (4) Calculate Expected Values

The following table summarizes the results of a study to determine if job satisfaction is related to pay category.

19) The proportion of hourly employees is about 0.733. If the variables are independent, what is the expected number of hourly employees who are dissatisfied with their jobs.

A) 0.733(174) B) 0.733(194) C) 0.733(1310) D) 0.733(20) Objective: (4) Calculate Expected Values

The following table summarizes the outcomes of a study that researchers carried out to determine if females expressed a greater fear of heights than males.

20) The proportion of those who expressed a fear of heights is about 0.492. If the variables are independent, what is the expected number of men who expressed a fear of heights?

A) 0.492(162) B) 0.492(360) C) 0.492(94) D) 0.492(68) Objective: (4) Calculate Expected Values

4

Solve the problem.

21) Package design is an important marketing tool, especially when marketing to children. The same food was presented to children using three different packaging designs. Each child was asked to select his or her favorite. In a taste test among 243 children, 55 selected package A as tasting best, 112 selected package B as tasting best, and 76 selected package C as tasting best. If there is no difference in the products in the 3 package designs, how many children out of the 243 would you expect to pick package B as tasting best?

A) 81 B) 121 C) 61 D) 112 Objective: (4) Calculate Expected Values

22) Package design is important marketing tool, especially when marketing to children. The same food was presented to children using three different packaging designs. Each child was asked to select his or her favorite. In a taste test among 267 children, 68 selected package A as tasting best, 105 selected package B as tasting best, and 94 selected package C as tasting best. If there is no difference in the products in the 3 package designs, how many children out of the 267 would you expect to pick package B as tasting best?

A) 89 B) 128 C) 133 D) 105 Objective: (4) Calculate Expected Values

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

The following table summarizes the results of a study to determine if job satisfaction is related to pay category.

23) Find the expected number of salaried workers who should be satisfied with their jobs if the variables are independent. Round to the nearest hundredth.

Objective: (4) Calculate Expected Values

Almas caviar is a very expensive Iranian brand of Beluga sturgeon caviar. A one pound gold-plated tin typically costs $12,000 or more. In a blind taste test, a group of food experts tasted four premium Beluga sturgeon caviars, with the most expensive one being Almas caviar. When asked to pick the most expensive caviar, 141 got it right and 79 got it wrong.

24) If this group were just guessing, how many people (out of 220) would be expected to guess correctly?

Objective: (4) Calculate Expected Values

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the following information to answer the question. Lambda olive oil is touted as the "World's most expensive olive oil." A twelve ounce bottle typically costs fifty dollars or more. In a blind taste test, a group of food experts tasted three premium olive oils, one of which was Lambda olive oil. When asked to pick the Lambda olive oil, 84 got it right and 87 got it wrong.

25) Calculate the observed value of the chi-square statistic. Round to the nearest hundredth.

A) 19.18 B) 6.39 C) 12.79 D) 23.68 Objective: (5) Calculate Chi-Square Statistics

Use the following information to answer the question. Bellei Extravecchio Balsamico Tradizionale is a very expensive brand of balsamic vinegar. A twelve ounce bottle typically costs two-hundred dollars or more. In a blind taste test, a group of food experts tasted three premium balsamic vinegars, with the most expensive one being Bellei Extravecchio Balsamico Tradizionale. When asked to pick the most expensive balsamic vinegar, 92 got it right and 76 got it wrong.

26) Calculate the observed value of the chi-square statistic. Round to the nearest hundredth.

A) 11.57 B) 34.71 C) 41.21 D) 23.14 Objective: (5) Calculate Chi-Square Statistics

5

Solve the problem.

27) Typically the percentage of women in an engineering class at a particular university has been 15%. A new recruiting plan was implemented in the past year to increase the proportion of women in the incoming class. This year, there were 49 women and 208 men in the incoming class. The data are summarized below.

Calculate the observed value of the chi-square statistic. Round to the nearest hundredth.

A) 218.41 B) 3.33 C) 2.75

D) 98.37

Objective: (5) Calculate Chi-Square Statistics

28) Typically the percentage of women in an engineering class at a particular university has been 18%. A new recruiting plan was implemented in the past year to increase the proportion of women in the incoming class. This year, there were 57 women and 201 men in the incoming class. The data are summarized below.

Calculate the observed value of the chi-square statistic. Round to the nearest hundredth.

A) 2.93 B) 0.86 C) 223.03

D) 2.51

Objective: (5) Calculate Chi-Square Statistics

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Almas caviar is a very expensive Iranian brand of Beluga sturgeon caviar. A one pound gold-plated tin typically costs $12,000 or more. In a blind taste test, a group of food experts tasted four premium Beluga sturgeon caviars, with the most expensive one being Almas caviar. When asked to pick the most expensive caviar, 141 got it right and 79 got it wrong.

29) Calculate the observed value of the chi-square statistic to test whether the proportion of people selecting the correct brand as most expensive differs from chance. Show all your work. Round to the nearest hundredth.

Objective: (5) Calculate Chi-Square Statistics

Solve the problem.

30) Compare the sampling distributions of the normally distributed test statistic z and the chi-square test statistic.

Specifically, how do the sampling distributions differ in shape and range of values?

Objective: (5) Calculate Chi-Square Statistics

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

31) Suppose a random sample of 1,220 U.S. adults were asked about their opinion regarding federal spending on public education. Respondents were asked whether federal spending on public education was (a) too low, (b) adequate, or (c) too high. Respondents were classified by income level. If we wanted to test whether there was an association between the response to the question and income level, would this be a test of homogeneity or of independence?

A) Independence B) Homogeneity Objective: (1) Determine Whether a Test is a Test of Independence or Homogeneity

6

32) Suppose a random sample of 1,220 U.S. adults were asked about their opinion regarding federal spending on infrastructure (i.e. roads and bridges). Respondents were asked whether federal spending on infrastructure was (a) too low, (b) adequate, or (c) too high. Respondents were classified by income level. If we wanted to test whether there was an association between the response to the question and income level, would this be a test of homogeneity or of independence?

A) Independence B) Homogeneity Objective: (1) Determine Whether a Test is a Test of Independence or Homogeneity

33) Suppose a researcher was interested in learning more about parents' concerns when their children start elementary school. The researcher asks the parents of 800 randomly selected first graders in rural school district and the parents of 950 randomly selected first graders in an urban school district to rate their level of concern with the following statement: We are (a) not at all concerned (b) somewhat concerned or (c) very concerned about the nutrition level of school lunches. If we wanted to test whether there was an association between the response to the question and the type of school district that the first grader was attending, would this be a test of homogeneity or of independence?

A) Independence B) Homogeneity Objective: (1) Determine Whether a Test is a Test of Independence or Homogeneity

34) Suppose a researcher was interested in learning more about parents' concerns when their children go away to college. The researcher asks the parents of 900 randomly selected freshman at a private college and the parents of 1,020 randomly selected freshman at a public college to rate their level of concern with the following statement: We are (a) not at all concerned (b) somewhat concerned or (c) very concerned about the potential pressure to drink alcohol that our child will be exposed to while at college. If we wanted to test whether there was an association between the response to the question and the type of college that the freshman was attending, would this be a test of homogeneity or of independence?

A) Independence B) Homogeneity Objective: (1) Determine Whether a Test is a Test of Independence or Homogeneity

The roads in a particular state are in very poor condition, but the state claims that it does not have enough money to repair the roads. A proposal is on the ballot to raise the sales tax in the state from 6% to 7% to pay for repairing the roads.

A month before the election, a survey of likely voters is taken. A random sample of 500 likely voters under the age of 30 is selected, a random sample of 500 likely voters aged 30-49 is selected, and a random sample of 500 likely voters aged 50 or more is selected. Each likely voter is asked whether he/she is in favor of the increase in the sales tax or not.

35) Differentiate between a test for homogeneity and a test for independence] If we want to test whether there is an association between the response to the tax increase and age, would this be a test of homogeneity or of independence?

A) Homogeneity B) Independence Objective: (1) Determine Whether a Test is a Test of Independence or Homogeneity

Solve the problem.

36) In 2004, voters in the state of Michigan approved a constitutional amendment that banned same-sex marriage and civil unions in the state. To see if voter sentiment has changed over the years, a survey of 500 registered Michigan voters was taken. Each voter was asked his/her opinion on same-sex relationships with the following options: (a) same-sex marriage should be legalized, (b) same-sex unions should be legalized, (c) no same-sex relationships should be legalized, or (d) no opinion. Each voter was also classified by sex. If we wanted to test whether there was an association between the response to the question and sex, would this be a test of homogeneity or of independence?

A) Homogeneity B) Independence Objective: (1) Determine Whether a Test is a Test of Independence or Homogeneity

7

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

37) Suppose a researcher was interested in learning more about high school seniors' concerns about the future. The researcher asks the 750 randomly selected female high school seniors and the 800 randomly selected male high school seniors to rate their level of concern with the following statement: I am (a) not at all concerned (b) somewhat concerned or (c) very concerned about getting accepted into a two or four year college. If we wanted to test whether there was an association between the response to the question and the gender of the high school senior, would this be a test of homogeneity or independence?

Objective: (1) Determine Whether a Test is a Test of Independence or Homogeneity

38) Suppose a random sample of 1,105 adults were asked about their opinion regarding salaries of full-time employees at a local state funded university. Respondents were asked whether salaries at the university were (a) too low, (b) adequate, or (c) too high. Respondents were also classified by income level. If we wanted to test whether there was an association between the response to the question and income level, would this be a test of homogeneity or of independence?

Objective: (1) Determine Whether a Test is a Test of Independence or Homogeneity

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

39) Choose the statement that is not true about the chi-square test or choose (d) if all the statements are true.

A) The test statistic is the same for a test of homogeneity or a test for independence, it is chi-square ( 2 ).

B) To conduct a chi-square test you must have a large enough sample. This condition is met if each expected value is 5 or more.

C) The conclusion of a chi-square test tells whether the variables under study are associated and how they are associated.

D) All of these statements are true.

Objective: (2) Give Reasons not to do a Chi-Square Test for Given Data

40) Choose the statement that is not true about the chi-square test or choose (d) if all the statements are true.

A) The conclusion of a chi-square test tells only whether the variables under study are associated, not how they are associated.

B) To conduct a chi-square test you must have a large enough sample. This condition is met if each expected value is 5 or more.

C) The test statistic is the same for a test of homogeneity or a test for independence, it is chi-square ( 2 ).

D) All of these statements are true.

Objective: (2) Give Reasons not to do a Chi-Square Test for Given Data

41) The table below shows the gender and the percentage of each gender that spent different amounts at a local toy store. The data was taken from a random sample of single shoppers collected over five consecutive Saturdays at the toy store. Choose the reason(s) why you cannot do a chi-square test with this data.

A) The data are from the entire population, not a sample, so inference is unnecessary.

B) The samples were not collected randomly.

C) There is not enough information to convert the percentages to counts.

D) All of these.

Objective: (2) Give Reasons not to do a Chi-Square Test for Given Data

8

42) The table below shows the gender and the percentage of each gender that spent different amounts at a local hardware store. The data was taken from a random sample of single shoppers collected over five consecutive Saturdays at the hardware store. Choose the reason(s) why you cannot do a chi-square test with this data.

A) There is not enough information to convert the percentages to counts.

B) The data are from the entire population, not a sample, so inference is unnecessary.

C) The samples were not collected randomly.

D) All of these.

Objective: (2) Give Reasons not to do a Chi-Square Test for Given Data

43) Suppose a random sample of 1,220 U.S. adults were asked about their opinion regarding federal spending on public education. Respondents were asked whether federal spending on public education was (a) too low, (b) adequate, or (c) too high. Respondents were classified by income level. Choose the correct hypotheses to test whether there is an association between the response to the question and income level.

A) H0 : There is no difference between the proportions of U.S. adults who responded (a), (b) or (c) to the opinion question.

Ha : There is a difference between the proportions of U.S. adults who responded (a), (b) or (c) to the opinion question.

B) H0 : Among U.S. adults, opinions about federal spending on education and income level are independent.

Ha : Among U.S. adults, opinions about federal spending on education and income level are associated.

C) H0 : Among U.S. adults, opinions about federal spending on education and income level are associated.

Ha : Among U.S. adults, opinions about federal spending on education and income level are independent.

D) None of these Objective: (3) Perform Chi-Square Tests of Independence and Homogeneity

9

44) Suppose a random sample of 1,220 U.S. adults were asked about their opinion regarding federal spending on infrastructure (i.e. roads and bridges). Respondents were asked whether federal spending on infrastructure was (a) too low, (b) adequate, or (c) too high. Respondents were classified by income level. Choose the correct hypotheses to test whether there is an association between the response to the question and income level.

A) H0 : Among U.S. adults, opinions about federal spending on infrastructure and income level are associated.

Ha : Among U.S. adults, opinions about federal spending on infrastructure and income level are independent.

B) H0 : Among U.S. adults, opinions about federal spending on infrastructure and income level are independent.

Ha : Among U.S. adults, opinions about federal spending on infrastructure and income level are associated.

C) H0 : There is no difference between the proportions of U.S. adults who responded (a), (b) or (c) to the opinion question.

Ha : There is a difference between the proportions of U.S. adults who responded (a), (b) or (c) to the opinion question.

D) None of these Objective: (3) Perform Chi-Square Tests of Independence and Homogeneity

45) A health foods store owner is thinking about carrying some new products and is interested in her customer's opinions. The shop owner decides to randomly sample 202 customers and ask them whether they have (a) heard about the health benefits of coconut milk and (b) whether they have heard of the health benefits of Quinoa flour.

She also asked each respondent how often they typically make purchases during a month. The table below shows the results from the study. Assume all conditions for testing have been met.

Test the hypothesis that how the respondents answered the questions is associated with number of monthly purchases, using a significance level of 0.05. Choose the correct decision regarding the null hypothesis and conclusion. Refer to the computer output below.

A) Fail to reject the null hypothesis; how the respondents answered the questions and number of monthly purchases are associated.

B) Reject the null hypothesis; how the respondents answered the questions and number of monthly purchases are associated.

C) Reject the null hypothesis; how the respondents answered the questions and number of monthly purchases are not associated.

D) Fail to reject the null hypothesis; how the respondents answered the questions and number of monthly purchases are not associated.

Objective: (3) Perform Chi-Square Tests of Independence and Homogeneity

10

46) Suppose a study was conducted to see whether there is an association between marital status and breast cancer remission. The table below shows the results from the study. Assume all conditions for testing have been met.

This was an observational study of randomly chosen patients who had received similar chemotherapy treatments.

Test the hypothesis that marital status and remission from breast cancer are associated, using a significance level of 0.05. Choose the correct decision regarding the null hypothesis and conclusion. Refer to the computer output below.

A) Fail to reject the null hypothesis; marital status and cancer remission are not associated.

B) Reject the null hypothesis; marital status and cancer remission are not associated.

C) Fail to reject the null hypothesis; marital status and cancer remission are associated.

D) Reject the null hypothesis; marital status and cancer remission are associated.

Objective: (3) Perform Chi-Square Tests of Independence and Homogeneity

47) Suppose a study was conducted to see whether there is an association between marital status and vehicle color.

The table below shows the results from the study. Assume all conditions for testing have been met.

This was an observational study of randomly chosen vehicle owners. Test the hypothesis that marital status and vehicle color are associated, using a significance level of 0.05. Choose the correct decision regarding the null hypothesis and conclusion. Refer to the computer output below.

A) Reject the null hypothesis; marital status and vehicle color are not associated.

B) Reject the null hypothesis; marital status and vehicle color are associated.

C) Fail to reject the null hypothesis; marital status and vehicle color are not associated.

D) Fail to reject the null hypothesis; marital status and vehicle color are associated.

Objective: (3) Perform Chi-Square Tests of Independence and Homogeneity

11

The roads in a particular state are in very poor condition, but the state claims that it does not have enough money to repair the roads. A proposal is on the ballot to raise the sales tax in the state from 6% to 7% to pay for repairing the roads.

A month before the election, a survey of likely voters is taken. A random sample of 500 likely voters under the age of 30 is selected, a random sample of 500 likely voters aged 30-49 is selected, and a random sample of 500 likely voters aged 50 or more is selected. Each likely voter is asked whether he/she is in favor of the increase in the sales tax or not.

48) Choose the correct hypotheses to test whether there is an association between the response to whether to increase the sales tax or not and age.

A) H0 : Among likely voters, opinions on the sales tax increase and age are independent

Ha: Among likely voters, opinions on the sales tax increase and age are associated B) H0 : Among likely voters, opinions on the sales tax increase and age are associated Ha: Among likely voters, opinions on the sales tax increase and age are independent C) H0 : There is no difference in the proportions of likely voters who favor and who do not favor the increase in sales tax Ha: There is a difference in the proportions of likely voters who favor and who do not favor the increase in sales tax D) H0 : There is a difference in the proportions of likely voters who favor and who do not favor the increase in sales tax Ha: There is no difference in the proportions of likely voters who favor and who do not favor the increase in sales tax Objective: (3) Perform Chi-Square Tests of Independence and Homogeneity

Solve the problem.

49) Recently, many states have been considering legalizing the use of marijuana. A survey was taken last year where adults in one state were asked if they favored legalizing the use of marijuana. The following table displays the percentage of adults in the state who favor and who do not favor the legalization of marijuana for both males and females:

Choose the reason(s) why you cannot perform a chi-square test on the data.

I. The percentages do not add up to 100%.

II. There is not enough information to convert the percentages to counts.

III. The samples were not randomly selected A) II only B) I, II, and III C) III only Objective: (3) Perform Chi-Square Tests of Independence and Homogeneity

12

D) I only

50) Recently, many states have been considering legalizing the use of marijuana. A survey was taken last year where adults in one state were asked if they favored legalizing the use of marijuana. The following table displays the percentage of adults in the state who favor and who do not favor the legalization of marijuana for both males and females:

What additional information would be necessary to be able to perform a chi-square test on the data.

A) We would just need to know the total number of people in the sample.

B) None of these C) We would have to know the total number of those favoring legalizing marijuana in the sample and the total number of those not favoring legalizing marijuana in the sample.

D) We would have to know the total number of men in the sample and the total number of women in the sample.

Objective: (3) Perform Chi-Square Tests of Independence and Homogeneity

51) The American Academy of Pediatrics recommends breast milk as the best nutrition for infants. A survey was conducted to see if pregnant women in their last trimester of pregnancy planned to breast feed their babies. It was thought that the income level of the women might be related to whether they planned to breast feed or not. The table below shows the results of the study:

Assume that all conditions for testing have been met. This was an observational study of randomly selected pregnant women in their last trimester of pregnancy. Test whether there is an association between whether a woman plans to breast feed her baby or not and her income level, using a significance level of 0.05. Choose the correct decision and conclusion regarding the null hypothesis that no association exists. Refer to the computer output above.

A) Fail to reject the null hypothesis; income level and plan to breast feed are associated.

B) Reject the null hypothesis; income level and plan to breast feed are not associated.

C) Fail to reject the null hypothesis; income level and plan to breast feed are not associated.

D) Reject the null hypothesis; income level and plan to breast feed are associated.

Objective: (3) Perform Chi-Square Tests of Independence and Homogeneity

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52) A study of middle school and high school students was conducted to examine the ethnic/racial self-classification of adolescents. A group of 500 students in the eighth grade were randomly selected and followed for 4 years. At the beginning of each year, the students were asked among many questions to classify themselves as White, Black, Hispanic, or Multiracial (additional classifications were eliminated because of small frequencies). At the end of the study, the number of times each student changed his/her classification was recorded. The table below shows the results from the study.

Test the hypothesis that the number of changes in racial classification is associated with students' racial classification in eighth grade, using a significance level of 0.05. Choose the correct decision regarding the null hypothesis and decision. Refer to the computer output above.

A) Reject the null hypothesis; racial classification in 8th grade is associated with number of changes in racial classification B) Reject the null hypothesis; racial classification in 8th grade is not associated with number of changes in racial classification C) Fail to reject the null hypothesis; racial classification in 8th grade is associated with number of changes in racial classification D) Fail to reject the null hypothesis; racial classification in 8th grade is not associated with number of changes in racial classification Objective: (3) Perform Chi-Square Tests of Independence and Homogeneity

53) Suppose a study was conducted to see whether there is an association between marital status and vehicle color.

The table below shows the results from the study. Assume all conditions for testing have been met.

This was an observational study of randomly chosen vehicle owners. Test the hypothesis that marital status and vehicle color are associated, using a significance of 0.05. Choose the correct decision regarding the null hypothesis and conclusions. Refer to the computer output above.

A) Fail to reject the null hypothesis; marital status and vehicle color are associated.

B) Reject the null hypothesis; marital status and vehicle color are not associated.

C) Reject the null hypothesis; marital status and vehicle color are associated.

D) Fail to reject the null hypothesis; marital status and vehicle color are not associated.

Objective: (3) Perform Chi-Square Tests of Independence and Homogeneity

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54) A study was conducted to see if teenagers work longer hours to pay for newer cars. A random sample of teenagers was taken and the number of hours each worked was recorded along with the age of the car that each usually drove. The table below shows the results from the study.

Test the hypothesis that the age of the car driven is associated with the number of hours worked per week, using a significance level of 0.10. Choose the correct decision regarding the null hypothesis and decision. Refer to the computer output above.

A) Fail to reject the null hypothesis; age of car usually driven is associated with number of hours worked per week B) Reject the null hypothesis; age of car usually driven is associated with number of hours worked per week C) Fail to reject the null hypothesis; age of car usually driven is not associated with number of hours worked per week D) Reject the null hypothesis; age of car usually driven is not associated with number of hours worked per week Objective: (3) Perform Chi-Square Tests of Independence and Homogeneity

55) Choose the statement that is not true about the chi-square test or state that none of the statements is true.

A) The conclusion of a chi-square test tells us whether the variables are associated as well as how they are associated.

B) To conduct a chi-square test you must have a large enough sample. This condition is met if the sample size is at least 40.

C) None of these statements are true.

D) To conduct a chi-square test you must have a large enough sample. This condition is met if each of the observed cells is 5 or more.

Objective: (3) Perform Chi-Square Tests of Independence and Homogeneity

56) Choose the statement that is not true about the chi-square test or state that all the statements are true.

A) To conduct a chi-square test you must have a large enough sample. This condition is met if each expected value is 5 or more.

B) The test statistic is the same for a test of homogeneity or a test for independence, it is chi-square ( 2 ).

C) All of these statements are true.

D) The conclusion of a chi-square test tells whether the variables under study are associated and how they are associated.

Objective: (3) Perform Chi-Square Tests of Independence and Homogeneity

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

57) Suppose a random sample of 1,105 adults were asked about their opinion regarding salaries of full-time employees at a local state funded university. Respondents were asked whether salaries at the university were (a) too low, (b) adequate, or (c) too high. Respondents were also classified by income level. State the correct hypothesis to test whether there is an association between the response to the questions and income level.

Objective: (3) Perform Chi-Square Tests of Independence and Homogeneity

15

58) Recently, many states have been considering legalizing the use of marijuana. A survey was taken in 2014 where adults in one state were asked if they favored legalizing the use of marijuana. The following table displays the percentage of adults in the state who favor and who do not favor the legalization of marijuana for both males and females. Can a chi-square test be done with these data? Explain why or why not.

Objective: (3) Perform Chi-Square Tests of Independence and Homogeneity

Suppose that you are a researcher and that you want to research whether a home remedy that recommends applying a salve of tobacco and saliva to cuts or scrapes to absorb toxins really works. You decide to conduct a study to see whether there is an association between the treatment and the outcome. A positive outcome means that the patient reported lower pain levels and the wound had healed without infection in less than 14 days. The table below shows the results from your study. Assume all conditions for testing have been met.

59) Test the hypothesis that the treatment is associated with the outcome, using a significance level of 0.05. State the correct decision regarding the null hypothesis and write a conclusion using a full sentence. Refer to the computer output above.

Objective: (3) Perform Chi-Square Tests of Independence and Homogeneity

60) From a purely scientific point-of-view, would you suggest the tobacco and saliva salve to a co-worker who expressed an interest in home remedies? Explain why or why not.

Objective: (3) Perform Chi-Square Tests of Independence and Homogeneity

16

Solve the problem.

61) A study of middle school and high school students was conducted to examine the ethnic/racial self-classification of adolescents. A group of 500 students in the eighth grade were randomly selected and followed for 4 years. At the beginning of each year, the students were asked among many questions to classify themselves as White, Black, Hispanic, or Multiracial (additional classifications were eliminated because of small frequencies). At the end of the study, the number of times each student changed his/her classification was recorded. The table below shows the results from the study. Assume all conditions for testing have been met.

Test the hypothesis that the number of changes in racial classification is not associated to students' racial classification in eighth grade, using a significance level of 0.05. State the correct decision regarding the null hypothesis and write a conclusion using a full sentence. Refer to the output above.

Objective: (3) Perform Chi-Square Tests of Independence and Homogeneity

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the following information to answer the question. A researcher wonders whether receiving a job offer is effected by whether an interviewee wears a red tie. The researcher used the following study design to collect data: The researcher chose five large companies in a large city and observed the tie color of all interviewees during a two week period. He also records whether the person was hired by the company. He finds that interviewees who wear red ties are more likely to be hired than interviewees who do not wear red ties.

62) Choose the statement that correctly explains why we can or cannot generalize these results to a larger population.

A) The interviewees were randomly selected to participate in the study so the results can be generalized to the larger population.

B) This was an observational study so results can be generalized to a larger population.

C) The interviewees were not randomly assigned to wear a red tie to the interview so the results cannot be generalized to beyond the sample.

D) The interviewees (and companies where they interviewed) were not selected from a larger population, so the results cannot be generalized beyond the sample.

Objective: (1) Decide Whether the Results of a Study can be Generalized to a Larger Group, or if Causality can be Inferred

63) Choose the statement that correctly explains why we can or cannot make a cause-and-effect conclusion.

A) This was an experimental study so we conclude that wearing a red tie caused an interviewee to be hired.

B) Since this was a controlled observational study we can conclude that there was a cause-and-effect relationship.

C) This was an observational study. Since random assignment was not used, we cannot conclude that getting hired was caused by wearing a red tie.

D) The interviewees (and companies where they were interviewed) were not selected from a larger population, so we cannot conclude that there was a cause-and-effect relationship.

Objective: (1) Decide Whether the Results of a Study can be Generalized to a Larger Group, or if Causality can be Inferred

17

Often college students taking an introductory course in psychology are required to participate in research experiments.

One experiment was performed to see if using colored paper increased reading comprehension. One hundred students enrolled in an introductory college psychology course volunteered to participate in the study. Fifty of the students were randomly chosen to read a chapter in a psychology test that was printed on yellow paper and the remaining fifty students were given the same chapter to read printed on white paper. After reading the chapter, each student was asked to answer a series of questions to test his/her comprehension. The results indicated that those students reading the chapter printed on yellow paper tended to have higher comprehension scores than those students reading the chapter printed on white paper.

64) Choose the statement that correctly explains why we can or cannot generalize these results to a larger population.

A) The participants were not selected from a larger population so the results cannot be generalized beyond the sample.

B) The participants were randomly selected, so the results can be generalized to a large population.

C) The participants were randomly assigned to a paper color, so the results can be generalized to a larger population.

D) This was an observational study so the results can be generalized to a larger population.

Objective: (1) Decide Whether the Results of a Study can be Generalized to a Larger Group, or if Causality can be Inferred

65) Choose the statement that correctly explains why we can or cannot make a cause-and-effect conclusion.

A) The participants were not selected from a larger population so we cannot conclude a cause-and effect relationship.

B) This was an observational study so we cannot conclude that reading comprehension increases when reading text printed on yellow paper.

C) Since this was a controlled observational study, we can conclude there was a cause-and-effect relationship.

D) This was an experimental study so we conclude that reading comprehension increases when reading from text printed on yellow paper, but the results cannot be generalized beyond the sample.

Objective: (1) Decide Whether the Results of a Study can be Generalized to a Larger Group, or if Causality can be Inferred

A researcher wonders whether speed of service at a diner is affected by whether a male customer is wearing a suit jacket.

The researcher used the following study design to collect data: The researcher chose five diners in a large city and recorded the number of male customers who wore a suit jacket during a two week period. He also records how long it took a waiter or waitress to address the customer. He finds that male customers who wear suit jackets were addressed by the wait staff faster than male customers who did not wear a suit jacket.

66) Choose the statement that correctly explains why we can or cannot generalize these results to a larger population.

A) The male customers were randomly selected to participate in the study so the results can be generalized to the larger population.

B) This was an observational study so results can be generalized to a larger population.

C) The male customers (and diners) were not selected from a larger population, so the results cannot be generalized beyond the sample.

D) The male customers were randomly assigned to wear a suit jacket so the results cannot be generalized to beyond the sample.

Objective: (1) Decide Whether the Results of a Study can be Generalized to a Larger Group, or if Causality can be Inferred

18

67) Choose the statement that correctly explains why we can or cannot make a cause-and-effect conclusion.

A) This was an experimental study so we conclude that wearing a suit jacket caused a male customer to be addressed faster.

B) Since this was a controlled observational study we can conclude that there was a cause-and-effect relationship.

C) This was an observational study. Since random assignment was not used, we cannot conclude that getting addressed faster was caused by wearing a suit jacket.

D) The male customers (and diners) were not selected from a larger population, so we cannot conclude that there was a cause-and-effect relationship.

Objective: (1) Decide Whether the Results of a Study can be Generalized to a Larger Group, or if Causality can be Inferred

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

A researcher wonders whether length of time that it takes to hail a taxi is affected by the gender of the person hailing the taxi. The researcher used the following study design to collect data: The researcher chose five busy intersections in a large city and recorded the number of males and females who hailed a taxi. He also records how long it took to get a taxi to stop. He finds that male customers waited a shorter period of time than females waited for a taxi.

68) Explain why we can or cannot generalize these results to a larger population.

Objective: (1) Decide Whether the Results of a Study can be Generalized to a Larger Group, or if Causality can be Inferred

69) Restate the conclusion of the study in terms of a cause-and-effect conclusion. Explain why we can or cannot make a cause-and-effect conclusion.

Objective: (1) Decide Whether the Results of a Study can be Generalized to a Larger Group, or if Causality can be Inferred

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

70) A small study was conducted on a new procedure for treating atrial fibrillation. The study involved a new way to perform ablation surgery. One method currently being used had a success rate of only 50% in preventing additional episodes of atrial fibrillation within one year. The new method of performing ablation surgery was performed on 8 patients and 6 of the 8 patients did not suffer additional episodes of atrial fibrillation within one year. Choose the statement that best summarizes the significance of this result.

A) Although this result may have clinical significance, it does not have statistical significance because the sample size is so small.

B) Although this result may have statistical significance, it does not have clinical significance because the sample was not randomly selected.

C) Many people would say that this result has both clinical and statistical significance because the probability of success increases from 50% to 75% and the result could have significant impact on lives.

D) Although this result may have statistical significance, it does not have clinical significance because the sample size is so small.

Objective: (2) Interpret the Results of Studies

71) Which of the following statements are true concerning meta-analysis?

A) Meta-analysis is used to prove statistical significance but not clinical significance.

B) Meta-analysis is the practice of stating hypotheses after first looking at the data.

C) A meta-analysis considers all studies done to test a particular treatment and tries to reconcile different conclusions, attempting to determine whether other factors played a role in the reported outcomes.

D) Meta-analysis is used to prove clinical significance but not statistical significance.

Objective: (2) Interpret the Results of Studies

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72) Which of the following is not an important principle that should always be kept in mind when reading research articles containing statistical research results?

A) All of these are important principles.

B) Stick to peer-reviewed journals.

C) Don't rely solely on the conclusions of any single paper.

D) Be wary of conclusions based on very complex statistical or mathematical models.

Objective: (2) Interpret the Results of Studies

73) Suppose it was reported on the news that a recent study concluded that the probability that you will get brain cancer if you use a cell phone doubled from 1 in 460,000 to 1 in 230,000. Choose the statement that best summarizes the significance of this result.

A) Many would say that this result does not have clinical or statistical significance because the probabilities are so small that they are meaningless.

B) Although this result may have clinical significance, it does not have statistical significance since the probability that you will get brain cancer if you use a cell phone is still so small that it is unlikely to have a meaningful effect on lives.

C) Many would say that this result has both clinical and statistical significance because the probability more than doubled and this result could have a significant impact on lives.

D) Although this result may have statistical significance, it does not have clinical significance since the probability that you will get brain cancer if you use cell phone is still so small that it is unlikely to have a meaningful effect on lives.

Objective: (2) Interpret the Results of Studies

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

74) Write at least two questions that you should ask yourself when reading articles containing statistical research results. Explain why these questions are important.

Objective: (2) Interpret the Results of Studies

75) Suppose it was reported on the news that a recent study concluded that pollutants in the air have dramatically increased our chances of getting a rare form of skin cancer from 1 in 250,000 to 1 in 150,000. Compare the clinical and statistical significance of this result.

Objective: (2) Interpret the Results of Studies

20

Answer Key Testname:

1) 2) D 3) D 4) C 5) A 6) B 7) C 8) B 9) D 10) C 11) C 12) Pay category and job satisfaction are the categorical variables.

One association that could be tested is whether there is an association between pay category and job satisfaction.

194 = 0.148 or 13) 1310 14.8% 14) 15) A 16) B 17) D 18) C 19) B 20) A 21) A 22) A 23) 161.64 24) 55 25) A 26) B 27) B 28) A 29) 2 = 179.30

30) The sampling distribution of z is bell-shaped and values can be any real number. The sampling distribution of 2 is usually not

57) H0 : Among adults, opinions about state-funded university salaries for full-time employees and income level are independent.

Ha: Among adults,

symmetric and is often right skewed.

The values of 2

opinions about state-funded university salaries for full-time employees and income level are associated.

58) The data are given as percentages, not frequencies, and there is not enough information given to convert the percentages to counts.

59) Reject the null hypothesis. There is enough evidence to conclude that the treatment and the outcome are associated.

60) Yes, they should try the home remedy because the study showed that the treatment and the positive outcome were associated.

61) Reject the null hypothesis. The number of changes in racial classification and students' classification in the eighth grade are associated.

62) D 63) C 64) A 65) D 66) C

must be positive.

31) A 32) A 33) B 34) B 35) A 36) B 37) Homogeneity 38) Independence 39) C 40) D 41) C 42) A 43) B 44) B 45) B 46) A 47) C 48) A 49) A 50) D 51) C 52) A 53) D 54) B 55) C 56) D

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67) C 68) The male and female customers (and intersections) were not selected from a larger population, so the results cannot be generalized beyond the sample.

69) Possible cause-and-effect conclusion: Being male leads to shorter wait times for a taxi, a new study finds.

This was an observational study.

Since random assignment was not used, we cannot conclude that being male caused the taxis to stop faster.

70) A 71) C 72) A 73) D

Answer Key Testname:

74) Possible questions: Did the study use random sampling and random assignment? Is the conclusion supported by other similar studies? Are the conclusions based on complex statistical or mathematical models? Is the journal containing the article peer-reviewed? Is the evidence compelling enough to support the conclusion? These questions encourage critical evaluation of published research or televised new reports that could affect our lives.

75) Although this result may have statistical significance, it does not have clinical significance since the probability that you will get the rare form of skin cancer is still so small that it is unlikely to have a meaningful effect on lives.

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