TEST BANK for Statistics: THE ART AND SCIENCE OF LEARNING FROM DATA THIRD EDITION

Chapter 1 Exam A Name___________________________________

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

Answer true or false.

1) One method of learning about the impact of randomness and variability from sample to sample is simulation.

A) True B) False Provide an appropriate response.

2) A survey of 1500 American households found that 33% of the respondents own a computer. Is this value a parameter or a statistic?

A) statistic B) parameter

1)

2)

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

Fill in the blank.

3) The three main aspects of statistics are

,

, and

3)

.

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

Answer true or false.

4) A large company would like to know what percentage of itʹs employees would utilize an on -site daycare facility. Rather than asking itʹs 5000 employees, each employee is assigned a number from 1 to 5000 and then a computer program is used to randomly select 100 numbers between 1 and 5000. These employees are then contacted and asked whether they would use an on -site daycare facility. The method used to collect the sample of 100 responses produces a random sample.

B) True A) False

4)

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

Fill in the blank.

5) The basis of ____________________ is that each subject in the population has the same chance of being in the sample.

5)

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

Answer true or false.

6) Descriptive statistics refers to methods of making decisions or predictions about a population, based on data obtained from a sample of that population; while inferential statistics refers to methods for summarizing the data.

A) True B) False

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6)

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

Provide an appropriate response.

7) Drug X, a drug that claims to treat male pattern scalp hair loss, was administered for 12 months to over 1800 men aged 18 to 41 with mild to moderate amounts of ongoing hair loss. Whether they were receiving drug X or a placebo (a pill containing no medication), all men were given a medicated shampoo. In general, men who took drug X maintained or increased the number of visible scalp hairs; while scalp hair counts in men who took the placebo continued to decrease. This concluded that drug X is effective in maintaining or increasing the amount of scalp hair in men. Which statement of this example can be referred to as descriptive statistics?

7)

8) A recent poll asked 1,245 registered voters nationwide, ʺWhich party do you think can do a better job of handling immigration issues?ʺ 31% of the respondents answered ʺRepublicans.ʺ With a margin of error of ±3%, it is estimated that between 28 and 34 percent of registered voters nationwide feel that the Republican party can do a better job of handling immigration issues. Identify which part of this example is inferential.

8)

9) Every year the U.S. Census Bureau releases the Current Population Report based on a survey of 50,000 households within the United States. Identify the population, the sample, and the subjects for this study.

9)

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

Select the most appropriate answer.

10) A short application program for performing a specific task is called a/an A) time series.

B) parameter.

C) applet.

D) None of these.

E) sampling.

10)

Answer true or false.

11) In a recent television survey, participants were asked to answer ʺyesʺ or ʺnoʺ to the question ʺAre you in favor of the death penalty?ʺ. Six thousand five hundred responded ʺyesʺ while 3700 responded ʺnoʺ. There was a fifty-cent charge for the call. The sampling technique used produces a random sample.

B) False A) True SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Fill in the blank.

12) The ____________________ is the set of all subjects of interest; while the ____________________ is a subset of the entire set of interest.

Provide an appropriate response.

13) A radio show host asks listeners whether they believe that human activity is altering the global climate. Of those calling in, only 20% responded by saying yes. Is it safe to infer that only 20% of the general population believes that human activity is altering the global climate?

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12)

13)

11)

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

14) The average salary of all automotive workers is $42,000. Is this value a parameter or a statistic?

A) parameter B) statistic Select the most appropriate answer.

15) The estimation of the population average age of registered voters in the state of Ohio based on the sample average age of 1,000 registered voters in that state and its corresponding margin of error is an example of A) a statistic.

B) deductive statistics.

C) descriptive statistics.

D) inferential statistics.

E) a parameter.

16) The following statement refers to which aspect of a statistical study: ʺA meteorologist constructs a graph showing the total precipitation in Phoenix, Arizona in each of the months of a given yearʺ?

A) Description B) Inference C) Design Answer true or false.

17) Parameter values are usually known.

A) False

14)

15)

16)

17) B) True

Provide an appropriate response.

18) Using an computer to mimic what would actually happen if you selected a sample and used statistics in real life is called A) database B) mini-tab C) time series D) random sampling E) simulation

18)

Answer true or false.

19) Random sampling enables the sample to be a good reflection of the population.

A) True B) False

19)

Determine whether the summary measure is better described as a parameter or a statistic.

20) The average height of horse jockeys A) Statistic B) Parameter

20)

The owners of a coffee shop conducted a taste test to determine whether its customers preferred a new coffee brand to the current one sold by the shop. Customers who were willing to participate were given small samples of each of the two brands in random order and were asked to select which one they preferred without knowing the brand. Of the 100 participating customers, 90% chose the new brand. Based on these results, the owners determined that a majority of their customers preferred the new brand and therefore switched their coffee supplier.

21) Randomizing the order in which the samples of each brand were given to each customer refers to 21) which aspect of statistics?

A) Description B) Investigation C) Inference D) Design E) None of these Copyright © 2013 Pearson Education, Inc. 3

Select the most appropriate answer.

22) The following statement refers to which aspect of a statistical study: ʺThe average age of the students in a statistics class is 25 yearsʺ?

A) Inference B) Description C) Design

22)

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

Fill in the blank.

23) _____________________ is the art and science of learning from data.

23)

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

Select the most appropriate answer.

24) Making decisions and predictions based on the data refers to which aspect of statistics?

A) None of these B) Sampling C) Inference D) Description E) Design Answer true or false.

25) To estimate the percentage of defective items a machine is producing, a quality control analyst inspects the first 100 items produced in a day. This technique produces a random sample.

A) False B) True

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24)

25)

Answer Key Testname: CHAPTER_1_EXAM_A

1) A 2) A 3) design, description, inference 4) B 5) random sampling 6) B 7) Scalp hair counts in the men who took drug X maintained or increased; scalp hair counts in the men who took the placebo decreased 8) It is estimated that between 28 and 34 percent of registered voters nationwide feel that the Republican party can do a better job of handling immigration issues.

9) The population is all U.S. households. The sample is the 50,000 households surveyed within the United States. The subjects are the U.S. households.

10) C 11) B 12) population; sample 13) No. Those who respond to this question are unlikely to be representative of the general population for two reasons.

First, listeners to the show are unlikely to be representative of the general population, as they are likely to share the views of the radio show host, and may not represent a wide spectrum of views. Second, those listeners who respond voluntarily to the question are likely to be those who feel the most strongly about the issue. Their views are unlikely to be representative of all listeners to the show let alone of the general population.

14) A 15) D 16) A 17) A 18) E 19) A 20) B 21) D 22) B 23) Statistics 24) C 25) A

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Chapter 1 Exam B Name___________________________________

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

Provide an appropriate response.

1) A radio show host asks listeners whether they believe that human activity is altering the global climate. Of those calling in, only 20% responded by saying yes. Is it safe to infer that only 20% of the general population believes that human activity is altering the global climate?

1)

2) Define the terms population and sample.

2)

3) Last year, 25% of students at a certain college smoked regularly. A researcher wants to determine whether an anti-smoking campaign was effective in reducing smoking at the college. If the proportion of students smoking regularly were still 25%, would it be surprising to find that only 15% of students smoked in a sample of size 20? in a sample of size 200? In either case would it be reasonable to assume that there had been a decrease in the proportion of students smoking regularly?

3)

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

4) In a survey of students at a certain college, 677 students were asked whether they believed in life after death and whether they believed in reincarnation. The results are summarized in the table below.

Frequency Distribution Reincarnation Life After Death (Column Percent, (Column Percent, Response Number of cases) Number of cases) Yes, Definitely 9.5%, 64 37.7%, 255 Yes, Probably 19.9%, 135 31.0%, 210 No, Probably Not 43.0%, 291 19.2%, 130 No, Definitely Not 27.6%, 187 12.1%, 82 Column Total 100.0%, 677 100.0%, 677 How does the percentage of ʺyes, definitelyʺ responses for life after death compare with the percentage of ʺyes, definitelyʺ responses for reincarnation?

A) The percentage who responded ʺyes, definitelyʺ when asked whether they believed in life after death (37.7%) was slightly higher than the percentage who responded ʺyes, definitelyʺ when asked whether the believed in reincarnation (31.0%).

B) The percentage who responded ʺyes, definitelyʺ when asked whether they believed in life after death (255%) was roughly four times the percentage who responded ʺyes, definitelyʺ when asked whether the believed in reincarnation (64%).

C) The percentage who responded ʺyes, definitelyʺ when asked whether they believed in life after death (19.9%) was roughly twice the percentage who responded ʺyes, definitelyʺ when asked whether the believed in reincarnation (9.5%).

D) The percentage who responded ʺyes, definitelyʺ when asked whether they believed in life after death (37.7%) was roughly four times the percentage who responded ʺyes, definitelyʺ when asked whether the believed in reincarnation (9.5%).

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4)

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

5) What is statistics?

5)

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

6) A recent poll asked 1,245 registered voters, ʺWhich party do you think can do a better job of handling immigration issues?ʺ 31% of the respondents answered ʺRepublicans.ʺ With a margin of error of ±3%, it is estimated that between 28 and 34 percent of registered voters nationwide feel that the Republican party can do a better job of handling immigration issues. Does the proportion of the sample answering ʺRepublicanʺ refer to a statistic or a parameter?

B) parameter A) statistic

6)

7) A study is conducted on a group of 10,000 high school students nationwide. Each week for a period of 13 weeks, participants must take an unannounced urine analysis to screen for illegal drug use. Identify the subjects of the study.

A) the urine analysis test B) researchers C) 13 weeks D) high school students E) illegal drugs detected by urine analysis

7)

Determine whether the summary measure is better described as a parameter or a statistic.

8) The average GPA of a universityʹs graduating class A) Statistic B) Parameter Select the most appropriate answer.

9) In a survey, 71% of 1052 adults polled nationwide answered ʺYesʺ to the question ʺDo you believe the theory that increased carbon dioxide and other gases released into the atmosphere will, if unchecked, lead to global warming and an increase in average temperatures?ʺ The predicted proportion of all American adults who would respond ʺYesʺ to the question is an example of A) a parameter B) the population C) a statistic D) the sample E) random sampling

8)

9)

10) In a survey, 71% of 1052 adults polled answered ʺYesʺ to the question ʺDo you believe the theory that increased carbon dioxide and other gases released into the atmosphere will, if unchecked, lead to global warming and an increase in average temperatures?ʺ The sample consists of A) the proportion of adults polled who responded ʺYesʺ to the question B) the proportion of American adults who are predicted to respond ʺYesʺ to the question C) all American adults D) 71% of American adults E) the 1052 polled adults

10)

11) Making decisions and predictions based on the data refers to which aspect of statistics?

A) None of these B) Inference C) Sampling D) Design E) Description

11)

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12) The following statement refers to which aspect of a statistical study: ʺFrom past figures, it is predicted that 47% of the registered voters in Virginia will vote in the June primaryʺ?

A) Inference B) Description C) Design

12)

13) In a survey, 71% of 1052 adults polled answered ʺYesʺ to the question ʺDo you believe the theory that increased carbon dioxide and other gases released into the atmosphere will, if unchecked, lead to global warming and an increase in average temperatures?ʺ The 71% responding ʺYesʺ to the question is an example of A) a parameter B) a statistic C) the sample D) the population E) random sampling

13)

14) A survey asks ʺwould you like to see more or less government spending on natural disasters?ʺ Of the 1496 respondents, 723 responded ʺmoreʺ or ʺmuch moreʺ. The sample consists of A) the 1496 respondents B) the 723 respondents who responded ʺmoreʺ or ʺmuch moreʺ C) the proportion of American adults estimated to respond ʺmoreʺ or ʺmuch moreʺ D) the proportion of respondents who responded ʺmoreʺ or ʺmuch moreʺ E) all American adults

14)

15) The following statement refers to which aspect of a statistical study: ʺBased on previous clients, a marriage counselor concludes that the majority of marriages that begin with cohabitation before marriage will result in divorceʺ?

A) Design B) Inference C) Description

15)

16) A manufacturer of cellular phones has decided that an assembly line is operating satisfactorily if less than 6% of the phones manufactured per day are defective. To check the quality of a dayʹs production, the company decides to randomly sample 30 phones from a dayʹs production and test for defects. Define the sample of interest to the manufacturer.

A) the 30 cellular phones that were sampled and tested B) all defective cellular phones manufactured by the company C) the 6% of the cellular phones that were defective D) the 30 responses: defective or not defective E) all cellular phones manufactured during the day in question

16)

17) The following statement refers to which aspect of a statistical study: ʺBased on a study of 25 hospitals nationwide, researchers have concluded that there is a relationship between smoking cigarettes and contracting emphysemaʺ?

A) Inference B) Description C) Design

17)

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

Fill in the blank.

18) A ____________________ is a numerical summary of the population; while a ____________________ is a numerical summary of the sample.

19) The basis of ____________________ is that each subject in the population has the same chance of being in the sample.

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18)

19)

20) _____________________ is the art and science of learning from data.

20)

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

Answer true or false.

21) A lobbyist for a major airspace firm assigns a number to each legislator and then uses a computer to randomly generate ten numbers. The lobbyist contacts the legislators corresponding to these numbers. This technique produces a random sample.

B) False A) True

21)

22) Inferential statistics are used when data are available only for a sample; however, descriptive statistics are used when data are available for either a sample or a population.

A) True B) False

22)

23) In a recent television survey, participants were asked to answer ʺyesʺ or ʺnoʺ to the question ʺAre you in favor of the death penalty?ʺ. Six thousand five hundred responded ʺyesʺ while 3700 responded ʺnoʺ. There was a fifty-cent charge for the call. The sampling technique used produces a random sample.

B) False A) True

23)

24) A lobbyist for a major airspace firm wants to get the opinion of state legislators on an issue of importance to his industry. The lobbyist contacts 10 state legislators at a restaurant during a lunch break and each one is polled about the issue. This technique produces a random sample.

A) False B) True

24)

The owners of a coffee shop conducted a taste test to determine whether its customers preferred a new coffee brand to the current one sold by the shop. Customers who were willing to participate were given small samples of each of the two brands in random order and were asked to select which one they preferred without knowing the brand. Of the 100 participating customers, 90% chose the new brand. Based on these results, the owners determined that a majority of their customers preferred the new brand and therefore switched their coffee supplier.

25) Predicting the preference of all of the coffee shop customers based on the taste test results refers to 25) which aspect of statistics?

A) Inference B) Design C) None of these D) Description E) Investigation

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Answer Key Testname: CHAPTER_1_EXAM_B

1) No. Those who respond to this question are unlikely to be representative of the general population for two reasons.

First, listeners to the show are unlikely to be representative of the general population, as they are likely to share the views of the radio show host, and may not represent a wide spectrum of views. Second, those listeners who respond voluntarily to the question are likely to be those who feel the most strongly about the issue. Their views are unlikely to be representative of all listeners to the show let alone of the general population.

2) The population is the total set of subjects in which we are interested. A sample is the subset of the population for whom we have data.

3) No, it would not be surprising to find that only 15% of students smoked in a sample of size 20. When the sample size is small, there is a lot of variability in the sample proportions and a sample proportion can easily lie far from the population proportion. In this case, it would not be reasonable to assume that there had been a decrease in the proportion of students smoking regularly.

Yes, it would be surprising to find that only 15% of students smoked in a sample of size 200. When the sample size is large, the sample proportions tend to lie closer to the population proportion. If the proportion of students smoking regularly were still 25%, it would be surprising to find that only 15% of students smoked in a sample of size 200. In this case, it would be reasonable to assume that there had been a decrease in the proportion of students smoking regularly.

4) D 5) Statistics is the art and science of learning from data.

6) A 7) D 8) B 9) A 10) C 11) B 12) A 13) B 14) A 15) B 16) A 17) A 18) parameter; statistic 19) random sampling 20) Statistics 21) A 22) A 23) B 24) A 25) A

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Chapter 2 Exam A Name___________________________________

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

The heights (in inches) of 30 adult males are listed below. A frequency distribution show the frequency and relative frequency using five classes.

70 72 71 70 69 73 69 68 70 71 67 71 70 74 69 68 71 71 71 72 69 71 68 67 73 74 70 71 69 68 Height (in inches) 67.0-68.4 68.5-69.9 70.0-71.4 71.5-72.9 73.0-74.4

Frequency 6 5 13 2 4

Relative Frequency 0.20 0.167 0.433 0.067 0.133

1) Which category of heights represents the mode?

A) 67.0-68.4 B) 71.5-72.9 C) 73.0-74.4

1) D) 70.0-71.4

2) What proportion of the 30 adult males had heights less than 70 inches?

A) 0.367 B) 0.167 C) 36.7 D) 16.7%

E) 68.5-69.9 2) E) 0.433

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

Provide an appropriate response.

3) A recent survey investigated exposure to tobacco and alcohol use in a series of G-rated animated films. Data on the total tobacco exposure time (in seconds) is below.

223 165

176 74

548 9

37 2

158 6

51 23

299 206

37 9

3)

11

Find the Five-Number Summary of Positions.

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

4) SAT verbal scores are normally distributed with a mean of 433 and a standard deviation of 90. Use the Empirical Rule to determine what percent of the scores lie between 433 and 523.

A) 68% B) 47.5% C) 34% D) 49.9% E) 51%

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4)

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

5) The following data represent the number of grams of fat in various breakfast foods.

5)

Breakfast Food Fat (in grams) Muffin and egg sandwich 12 Muffin, egg, and ham sandwich 22 Muffin, egg, and bacon sandwich 27 Muffin and sausage sandwich 22 25 Bagel, egg, and ham sandwich Bagel, egg, and bacon sandwich 30 Bagel, egg, and sausage sandwich 32 Bagel, egg, sausage, and cheese sandwich 37 Bagel, egg, ham, and cheese sandwich 27 Bagel, egg, bacon, and cheese sandwich 31 Bagel 11 Pancakes platter 16 Pancakes and eggs platter 21 Pancakes, eggs, and bacon platter 32 Yogurt 2 Construct a dot plot for these data.

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

6) Parking at a large university has become a major issue. University administrators would like to determine the average time it takes a student to find a parking spot in a university lot. Students who are willing to participate in the study were asked to record the time between entering campus and pulling into a parking spot. Which of the following would not be appropriate for displaying the parking time data?

A) Box plot B) Stem-and-leaf plot C) None of these should be used.

D) Pie chart E) Histogram

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6)

7) Twenty-four workers were surveyed and asked how long it takes them to travel to work each day.

The data below are given in minutes.

20 35 42 52 65 20 60 49 24 37 23 24 22 20 41 25 28 27 50 47 58 30 32 48 Which of the following shows the data in a stem-and-leaf plot?

A) 2 00002344578 3 0257 4 12789 5 028 6 05 B) 2 0002344578 3 0257 4 12789 5 028 6 05 C) 2 000234457 3 02578 4 12789 5 028 6 05 D) 2 002344578 3 0257 4 12789 5 028 6 05 E) 2 0002344578 3 0257 4 12789 5 028 6 0

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7)

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

8) The following frequency histogram provides average SO 2 (sulfur dioxide) emission rates

8)

from utility and industrial boilers (lb/million Btu) for 47 states (data for Idaho, Alaska, and Hawaii omitted).

a. Identify the intervals of emission rates used for the plot. b. Describe the shape of the distribution. c. What information can you get from the dot plot or stem-and-leaf plot of these data that you cannot get from this plot? d. This histogram shows frequencies. If you were to construct a histogram using the percentages for each interval, how (if at all) would the shape of this histogram change?

9) The table below summarizes total enrollment and female enrollment at a pilot training college for the years 2005 through 2012. The table has been used to construct two different graphs displayed below the table. Summarize the information that is available from each of the graphs and discuss the advantages and disadvantages of each graph.

Enrollment at Pilot Training College Year Total Number Number of of Students Female Students 2005 283 20 2006 275 22 2007 265 22 2008 258 24 2009 252 25 2010 248 25 2011 245 27 2012 242 28 Copyright © 2013 Pearson Education, Inc. 14

9)

Enrollment at Pilot Training College - - - - Total enrollment

300

Female enrollment

Number of Students

250 200 150 100 50

1

2 3 4 5 6 Years Since 2004

7

8

Female Enrollment as Percentage of Total Enrollment at Pilot Training College

Percentage Female Enrollment

12 10 8 6 4 2

1

2

3 4 5 6 Years Since 2004

7

8

10) A sample of 324 randomly selected doctors was asked to indicate the category that best described how often they used the Internet. The results follow.

Internet Usage Pattern Count Never 31 Rarely (about 3 times per year) 15 Occasionally (about once a month) 52 Often (about once a week) 109 Daily 117 a. Construct a pie chart for these data. b. In creating a bar graph of these data, would it be more useful to list the patterns as given in the table above or in the order of a Pareto chart?

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10)

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

11) Brandon kept track of the number of hours he spent exercising each week for four months. The results are shown below. Find the mean number of hours Brandon spent exercising per week.

Round your answer to two decimal places.

11)

7.50 8.20 7.10 7.90 8.00 7.50 7.80 7.10 7.30 7.50 7.90 8.90 7.10 8.20 8.20 8.20 8.00 7.80 A) 7.30

B) 8.25

C) 8.01

D) 7.38

E) 7.79

12) Each year advertisers spend billions of dollars purchasing commercial time on network sports television. A recent article listed the top 10 leading spenders (in millions of dollars) over a 6 month period: Company A Company B Company C Company D Company E

$72.0 63.1 54.7 54.3 29.0

Company F Company G Company H Company I Company J

12)

$26.9 25.0 23.9 23.0 20.0

Which of the following graphs would not be appropriate for displaying this data?

A) Pie chart B) Stem-and-leaf plot C) None of these should be used.

D) Histogram E) Dot plot 13) A safety engineer wishes to use the following data to show the number of deaths in a year from the collision of passenger cars with trucks on a particular highway.

Year 1 2 3 4 5 6 7 8

13)

Number of Deaths 12 17 22 21 16 13 11 12

What is the mode of the number of deaths?

A) 13 B) 12 C) 16

D) 15.5

E) 22

14) Use the following summary information for a data set of 100 observations to determine whether the data set is likely to be bell-shaped, skewed to the right or skewed to the left.

Mean = 120, s=22, Minimum=103, Maximum=170 A) unable to determine from the information given B) skewed to the left C) skewed to the right D) bell-shaped Copyright © 2013 Pearson Education, Inc. 16

14)

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

15) The table below shows the unemployment rate in one city from 2003 to 2012.

15)

Year 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Unemployment Rate (Percent) 5.90 5.78 5.45 5.28 5.06 4.88 4.80 4.63 4.44 4.24 a. b. c.

Construct a time plot for these data.

Is there a trend? If so, what kind?

Would a histogram more clearly describe the above dataset? Explain.

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

16) Use the following summary information for a data set of 100 observations to determine whether the data set is likely to be bell-shaped, skewed to the right or skewed to the left.

Mean = 120, s=22, Minimum=37, Maximum=136 A) skewed to the right B) skewed to the left C) bell-shaped D) unable to determine from the information given

16)

17) The following is a time plot of wine exports (in millions of gallons) in a certain country for the past 15 years. Is there a trend evident in the data?

17)

A) no trend evident

B) yes, decreasing trend

C) yes, increasing trend

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A sample of fifty motorists was taken on a Federal highway where the speed limit was 60 miles per hour. A dot plot of their speeds is shown below.

18) What is the mode for speed?

A) 55 B) 70 C) 60 D) none of these E) 7

18)

19) What proportion of the motorists were speeding?

A) 2 B) 0.72 C) 0.18

19) D) 0.22

E) 0.04

Select the most appropriate answer.

20) Which of the following is a discrete variable?

A) weight of a newborn baby B) number of phones per household C) time it takes to drive to work D) amount of coffee in an 8-ounce cup E) none of these

20)

Answer true or false.

21) Bar graphs and pie charts are graphical methods that are often used in summarizing quantitative data.

A) True B) False SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Fill in the blank.

22) A variable is called ____________________ if each observation belongs to one of a set of categories.

23) The ____________________ is the balance point of the data values; while, the _____________________ is the midpoint of the ordered data values.

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22)

23)

21)

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

A sporting goods retailer conducted a customer survey to determine its customers primary reason for shopping at their store. The results are shown in the graph below.

24) Is the variable ʺreason for shopping at our storeʺ categorical or quantitative?

A) Categorical B) Quantitative

24)

The following data show the number of laps run by each participant in a timed running race: 46 65 55 43 51 48 57 30 43 49 32 56 25) If the stems are 3, 4, 5 and 6, how many leaves are on the ʺ4 stemʺ?

A) 1 B) 0 C) 5

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25) D) 4

Answer Key Testname: CHAPTER_2_EXAM_A

1) D 2) A 3) minimum = 2 seconds, Q1 = 10 seconds, median = 51 seconds, Q3 = 191 seconds, and maximum = 548 seconds 4) C 5)

6) D 7) B 8) a. 0 to 0.49, 0.5 to 0.99, 1.0 to 1.49, 1.5 to 1.99, 2.0 to 2.49, 2.5 to 2.99, 3.0 to 3.49, 3.5 to 3.99, 4.0 to 4.49, 4.5 to 4.99; b. The distribution is skewed to the right. c. You can get the actual data values from a dot plot or stem -and-leaf plot. d. The shape would not change.

9) The first graph shows the total numbers of students for each year as well as the number of female students. We can see the downward trend in overall enrollment, the slight upward trend in female enrollment and that female enrollment is small relative to total enrollment.

However, with both total enrollment and female enrollment on the same graph, since female enrollment is small relative to total enrollment, the scale is not suitable for female enrollment and the upward trend in female enrollment is not very clear.

Since both total enrollment and female enrollment are varying with time, the second graph which shows female enrollment as a percentage of total enrollment may be more useful. It is clear from this graph that as a percentage of total enrollment, female enrollment is increasing significantly. However, this graph gives no indication of the absolute number of students (overall or female) and without reference to the first graph, we cannot know whether the percentage female enrollment is increasing because female enrollment is increasing, because male enrollment is decreasing, or both.

Copyright © 2013 Pearson Education, Inc. 20

Answer Key Testname: CHAPTER_2_EXAM_A

10) a.

b.

Since the categories of Internet usage pattern have a natural order from never to daily, it makes more sense to leave the categories in this natural order rather than ordering them from the tallest bar to the shortest bar.

11) E 12) A 13) B 14) C 15) a.

Unemployment Rate 2003-2012

Unemployment Rate (Percent)

2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Year b. There is a clear decreasing trend over time; c. No, a histogram would not depict the trend in this dataset.

Copyright © 2013 Pearson Education, Inc. 21

Answer Key Testname: CHAPTER_2_EXAM_A

16) B 17) C 18) A 19) C 20) B 21) B 22) categorical 23) mean; median 24) A 25) C

Copyright © 2013 Pearson Education, Inc. 22

Chapter 2 Exam B Name___________________________________

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

Provide an appropriate response.

1) The following frequency histogram provides average SO 2 (sulfur dioxide) emission rates from utility and industrial boilers (lb/million Btu) for 47 states (data for Idaho, Alaska, and Hawaii omitted).

a. Identify the intervals of emission rates used for the plot. b. Describe the shape of the distribution. c. What information can you get from the dot plot or stem-and-leaf plot of these data that you cannot get from this plot? d. This histogram shows frequencies. If you were to construct a histogram using the percentages for each interval, how (if at all) would the shape of this histogram change?

Copyright © 2013 Pearson Education, Inc. 23

1)

2) A sample of 324 randomly selected doctors was asked to indicate the category that best described how often they used the Internet. The results follow.

2)

Internet Usage Pattern Count Never 31 Rarely (about 3 times per year) 15 Occasionally (about once a month) 52 Often (about once a week) 109 Daily 117 a. Construct a pie chart for these data. b. In creating a bar graph of these data, would it be more useful to list the patterns as given in the table above or in the order of a Pareto chart?

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

3) Parking at a large university has become a major issue. University administrators would like to determine the average time it takes a student to find a parking spot in a university lot. Students who are willing to participate in the study were asked to record the time between entering campus and pulling into a parking spot. Which of the following would not be appropriate for displaying the parking time data?

A) Box plot B) Stem-and-leaf plot C) Histogram D) Pie chart E) None of these should be used.

3)

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

4) The table below shows the unemployment rate in one city from 2003 to 2012.

4)

Year 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Unemployment Rate (Percent) 5.90 5.78 5.45 5.28 5.06 4.88 4.80 4.63 4.44 4.24 a. b. c.

Construct a time plot for these data.

Is there a trend? If so, what kind?

Would a histogram more clearly describe the above dataset? Explain.

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

5) Use the following summary information for a data set of 100 observations to determine whether the data set is likely to be bell-shaped, skewed to the right or skewed to the left.

Mean = 120, s=22, Minimum=103, Maximum=170 A) bell-shaped B) unable to determine from the information given C) skewed to the left D) skewed to the right

Copyright © 2013 Pearson Education, Inc. 24

5)

6) Brandon kept track of the number of hours he spent exercising each week for four months. The results are shown below. Find the mean number of hours Brandon spent exercising per week.

Round your answer to two decimal places.

6)

7.50 8.20 7.10 7.90 8.00 7.50 7.80 7.10 7.30 7.50 7.90 8.90 7.10 8.20 8.20 8.20 8.00 7.80 A) 8.25

B) 8.01

C) 7.30

D) 7.79

E) 7.38

7) Use the following summary information for a data set of 100 observations to determine whether the data set is likely to be bell-shaped, skewed to the right or skewed to the left.

Mean = 120, s=22, Minimum=37, Maximum=136 A) unable to determine from the information given B) skewed to the right C) bell-shaped D) skewed to the left

7)

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

8) The following data represent the number of grams of fat in various breakfast foods.

8)

Breakfast Food Fat (in grams) Muffin and egg sandwich 12 Muffin, egg, and ham sandwich 22 Muffin, egg, and bacon sandwich 27 Muffin and sausage sandwich 22 25 Bagel, egg, and ham sandwich Bagel, egg, and bacon sandwich 30 Bagel, egg, and sausage sandwich 32 Bagel, egg, sausage, and cheese sandwich 37 Bagel, egg, ham, and cheese sandwich 27 Bagel, egg, bacon, and cheese sandwich 31 Bagel 11 Pancakes platter 16 Pancakes and eggs platter 21 Pancakes, eggs, and bacon platter 32 Yogurt 2 Construct a dot plot for these data.

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

9) SAT verbal scores are normally distributed with a mean of 433 and a standard deviation of 90. Use the Empirical Rule to determine what percent of the scores lie between 433 and 523.

A) 51% B) 34% C) 47.5% D) 68% E) 49.9% SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Copyright © 2013 Pearson Education, Inc. 25

9)

10) The table below summarizes total enrollment and female enrollment at a pilot training college for the years 2005 through 2012. The table has been used to construct two different graphs displayed below the table. Summarize the information that is available from each of the graphs and discuss the advantages and disadvantages of each graph.

Enrollment at Pilot Training College Year Total Number Number of of Students Female Students 2005 283 20 2006 275 22 2007 265 22 2008 258 24 2009 252 25 2010 248 25 2011 245 27 2012 242 28 Enrollment at Pilot Training College - - - - Total enrollment

300

Female enrollment

Number of Students

250 200 150 100 50

1

2 3 4 5 6 Years Since 2004

7

8

Female Enrollment as Percentage of Total Enrollment at Pilot Training College

Percentage Female Enrollment

12 10 8 6 4 2

1

2

3 4 5 6 Years Since 2004

7

8

Copyright © 2013 Pearson Education, Inc. 26

10)

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

11) Each year advertisers spend billions of dollars purchasing commercial time on network sports television. A recent article listed the top 10 leading spenders (in millions of dollars) over a 6 month period: Company A Company B Company C Company D Company E

$72.0 63.1 54.7 54.3 29.0

Company F Company G Company H Company I Company J

$26.9 25.0 23.9 23.0 20.0

Which of the following graphs would not be appropriate for displaying this data?

A) Stem-and-leaf plot B) Histogram C) Pie chart D) Dot plot E) None of these should be used.

Copyright © 2013 Pearson Education, Inc. 27

11)

12) Twenty-four workers were surveyed and asked how long it takes them to travel to work each day.

The data below are given in minutes.

20 35 42 52 65 20 60 49 24 37 23 24 22 20 41 25 28 27 50 47 58 30 32 48 Which of the following shows the data in a stem-and-leaf plot?

A) 2 0002344578 3 0257 4 12789 5 028 6 0 B) 2 0002344578 3 0257 4 12789 5 028 6 05 C) 2 00002344578 3 0257 4 12789 5 028 6 05 D) 2 000234457 3 02578 4 12789 5 028 6 05 E) 2 002344578 3 0257 4 12789 5 028 6 05 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

13) A recent survey investigated exposure to tobacco and alcohol use in a series of G-rated animated films. Data on the total tobacco exposure time (in seconds) is below.

223 165

176 74

548 9

37 2

158 6

51 23

299 206

37 9

11

Find the Five-Number Summary of Positions.

Copyright © 2013 Pearson Education, Inc. 28

13)

12)

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

14) A safety engineer wishes to use the following data to show the number of deaths in a year from the collision of passenger cars with trucks on a particular highway.

Year 1 2 3 4 5 6 7 8

14)

Number of Deaths 12 17 22 21 16 13 11 12

What is the mode of the number of deaths?

A) 15.5 B) 12 C) 13

D) 16

E) 22

15) The following is a time plot of wine exports (in millions of gallons) in a certain country for the past 15 years. Is there a trend evident in the data?

A) yes, increasing trend

B) no trend evident

15)

C) yes, decreasing trend

The following data show the number of laps run by each participant in a timed running race: 46 65 55 43 51 48 57 30 43 49 32 56 16) If the stems are 3, 4, 5 and 6, how many leaves are on the ʺ4 stemʺ?

A) 1 B) 4 C) 0

Copyright © 2013 Pearson Education, Inc. 29

16) D) 5

Select the most appropriate answer.

17) Which of the following is a discrete variable?

A) amount of coffee in an 8-ounce cup B) none of these C) weight of a newborn baby D) number of phones per household E) time it takes to drive to work

17)

A sample of fifty motorists was taken on a Federal highway where the speed limit was 60 miles per hour. A dot plot of their speeds is shown below.

18) What proportion of the motorists were speeding?

A) 0.18 B) 0.04 C) 2

18) D) 0.72

E) 0.22

19) What is the mode for speed?

A) none of these B) 70 C) 55 D) 60 E) 7

19)

Answer true or false.

20) Bar graphs and pie charts are graphical methods that are often used in summarizing quantitative data.

A) True B) False SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Fill in the blank.

21) A variable is called ____________________ if each observation belongs to one of a set of categories.

22) The ____________________ is the balance point of the data values; while, the _____________________ is the midpoint of the ordered data values.

Copyright © 2013 Pearson Education, Inc. 30

21)

22)

20)

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

A sporting goods retailer conducted a customer survey to determine its customers primary reason for shopping at their store. The results are shown in the graph below.

23) Is the variable ʺreason for shopping at our storeʺ categorical or quantitative?

A) Quantitative B) Categorical

23)

The heights (in inches) of 30 adult males are listed below. A frequency distribution show the frequency and relative frequency using five classes.

70 72 71 70 69 73 69 68 70 71 67 71 70 74 69 68 71 71 71 72 69 71 68 67 73 74 70 71 69 68 Height (in inches) 67.0-68.4 68.5-69.9 70.0-71.4 71.5-72.9 73.0-74.4

Frequency 6 5 13 2 4

Relative Frequency 0.20 0.167 0.433 0.067 0.133

24) What proportion of the 30 adult males had heights less than 70 inches?

A) 0.433 B) 16.7% C) 0.367 D) 36.7

E) 0.167

25) Which category of heights represents the mode?

A) 71.5-72.9 B) 68.5-69.9 C) 67.0-68.4

E) 70.0-71.4

25) D) 73.0-74.4

Copyright © 2013 Pearson Education, Inc. 31

24)

Answer Key Testname: CHAPTER_2_EXAM_B

1) a. 0 to 0.49, 0.5 to 0.99, 1.0 to 1.49, 1.5 to 1.99, 2.0 to 2.49, 2.5 to 2.99, 3.0 to 3.49, 3.5 to 3.99, 4.0 to 4.49, 4.5 to 4.99; b. The distribution is skewed to the right. c. You can get the actual data values from a dot plot or stem -and-leaf plot. d. The shape would not change.

2) a.

b.

Since the categories of Internet usage pattern have a natural order from never to daily, it makes more sense to leave the categories in this natural order rather than ordering them from the tallest bar to the shortest bar.

3) D 4) a.

Unemployment Rate 2003-2012

Unemployment Rate (Percent)

2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Year b. There is a clear decreasing trend over time; c. No, a histogram would not depict the trend in this dataset.

Copyright © 2013 Pearson Education, Inc. 32

Answer Key Testname: CHAPTER_2_EXAM_B

5) D 6) D 7) D 8)

9) B 10) The first graph shows the total numbers of students for each year as well as the number of female students. We can see the downward trend in overall enrollment, the slight upward trend in female enrollment and that female enrollment is small relative to total enrollment.

However, with both total enrollment and female enrollment on the same graph, since female enrollment is small relative to total enrollment, the scale is not suitable for female enrollment and the upward trend in female enrollment is not very clear.

Since both total enrollment and female enrollment are varying with time, the second graph which shows female enrollment as a percentage of total enrollment may be more useful. It is clear from this graph that as a percentage of total enrollment, female enrollment is increasing significantly. However, this graph gives no indication of the absolute number of students (overall or female) and without reference to the first graph, we cannot know whether the percentage female enrollment is increasing because female enrollment is increasing, because male enrollment is decreasing, or both.

11) C 12) B 13) minimum = 2 seconds, Q1 = 10 seconds, median = 51 seconds, Q3 = 191 seconds, and maximum = 548 seconds 14) B 15) A 16) D 17) D 18) A 19) C 20) B 21) categorical 22) mean; median 23) B 24) C 25) E

Copyright © 2013 Pearson Education, Inc. 33

Chapter 3 Exam A Name___________________________________

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

Answer true or false.

1) The value of the correlation is always between 0 and 1.

A) True B) False

1)

Provide an appropriate response.

2) In order for a data point to be considered influential, which of the following must hold?

2)

I) the point has a large residual for the regression line fitted including that point II) its x value must be relatively low or high compared to the rest of the data III) the point has a large residual for the regression line fitted without using that data point B) II only C) II and III D) I only E) III only A) I and II Determine which plot shows the strongest linear correlation.

3) A)

3) B)

y

y

x

C)

x

D) y

y

x

x

Copyright © 2013 Pearson Education, Inc. 34

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

Fill in the blank.

4) When two explanatory variables are both associated with a response variable but are also associated with each other, there is said to be ____________________.

4)

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

Answer true or false.

5) If the absolute value of the correlation is approximately one, then the points lie close to a line that slopes upward or downward.

A) False B) True 6) The advantage of a side-by-side bar graph is that it allows for easy comparison of the explanatory variable groups with respect to values on the response variable.

A) True B) False SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

7) A researcher is investigating the association between blood pressure and ʺworkaholismʺ in a certain population. She classifies someone who works more than 60 hours per week as a workaholic. She records the income level and blood pressure (high or normal) for each participant and whether or not they can be classified as a ʺworkaholic.ʺ The data are summarized in the table below.

Workaholic Yes No

Low HBP NBP 25 75 25 80

Income Group Middle HBP NBP 23 87 18 72

7)

High HBP NBP 26 134 9 51

Consider each income group separately and find the proportion with high blood pressure among the workaholics and the proportion with high blood pressure among the non-workaholics.

Then determine the proportion of workaholics overall who have high blood pressure and the proportion of non-workaholics overall who have high blood pressure (ignoring information about income group). Explain how these data satisfy Simpsonʹs paradox.

How would you explain what is responsible for this result?

8) A large manufacturer hires many handicapped workers and keeps track of both their type of handicap and their level of performance. a. b.

Identify the two variables.

Identify the response variable and the explanatory variable.

Copyright © 2013 Pearson Education, Inc. 35

8)

5)

6)

Solve the problem.

9) Use a scatterplot to display the data below. All measurements are in milligrams per cigarette.

9)

Brand Tar Nicotine A 16 1.2 B 13 1.1 C 16 1.2 D 18 1.4 E 6 0.6

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

Select the most appropriate answer.

10) If a positive association exists between two quantitative variables, A) the movement of x does not affect the movement of y.

B) y tends to decrease as x decreases.

C) none of these.

D) y tends to increase as x decreases.

E) y tends to decrease as x increases.

10)

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

Construct a scatterplot for the data.

11) Below are the gold medal performances in the menʹs high jump at an athletic competition held in one city from 2006 to 2012.

11)

Year High Jump (in.)

2006 85.3 2007 85.8 2008 88.3 2009 87.8 2010 88.5 2011 92.5 92.3 2012

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

Provide an appropriate response.

12) A researcher records for each participant in a clinical trial the amount of alcohol they consume per month and their cholesterol level. Indicate whether each variable is categorical or quantitative.

A) alcohol: categorical; cholesterol level: categorical B) alcohol: quantitative; cholesterol level: categorical C) alcohol: quantitative; cholesterol level: quantitative D) alcohol: categorical; cholesterol level: quantitative Copyright © 2013 Pearson Education, Inc. 36

12)

Select the most appropriate answer.

13) The ____________________ is the outcome variable on which comparisons are made.

A) Both B and C B) lurking variable C) explanatory variable D) response variable E) predictor variable Provide an appropriate response.

14) The relationship between the number of games won by a minor league baseball team and the average attendance at their home games is analyzed. A regression to predict the average attendance from the number of games won has an r = 0.73. Interpret this statistic.

A) Positive, fairly strong linear relationship. 73% of the variation in average attendance is explained by the number of games won.

B) Positive, fairly strong linear relationship. 53.29% of the variation in average attendance is explained by the number of games won.

C) No association D) Negative, fairly strong linear relationship. 53.29% of the variation in average attendance is explained by the number of games won.

E) Positive, weak linear relationship. 7.29% of the variation in average attendance is explained by the number of games won.

15) A researcher recorded for each of a number of recent high school and college graduates the number of years of education and their annual salary when they started their first job. The scatter plot is shown below together with the regression equation. The point (14, 4) was excluded when obtaining the regression equation.

Salary (Thousands of Dollars)

y 48

32

16

4 8 12 16 Years of Education

20

x

Is the point (14, 4) an outlier on x? Is it an outlier on y? Is it a regression outlier?

A) not an outlier on x, outlier on y, regression outlier B) not an outlier on x, not an outlier on y, regression outlier C) not an outlier on x, outlier on y, not a regression outlier D) outlier on x, outlier on y, regression outlier

Copyright © 2013 Pearson Education, Inc. 37

13)

14)

15)

^

16) A regression line for predicting the selling prices of homes in Chicago is y = 168 + 102x, where x is the square footage of the house. Interpret the residual for a house with 1800 square feet that recently sold for $200,000.

A) The house sold for $16,400 less than was to be expected from the regression equation.

B) The house sold for $16,232 less than was to be expected from the regression equation.

C) The house sold for $16,064 more than was to be expected from the regression equation.

D) The house sold for $16,400 more than was to be expected from the regression equation.

E) The house sold for $16,232 more than was to be expected from the regression equation.

Fill in the missing information. _ _ ^ y = a + bx 17) x sx y sy r ?

?

18

16)

17)

^

4 -0.5 y = 30 - 4x

A) x = 12; sx = 1.00 B) x = 3; sx = 1.00 C) x = 48; sx = -18.00 D) x = 12; sx = 2.00 E) x = 3; sx = 0.50 Provide an appropriate response.

18) For 14 baseball teams, the correlation with number of wins in the regular season is 0.51 for shutouts, 0.61 for hits made, -0.70 for runs allowed and -0.56 for homeruns allowed. Which variable has the weakest linear association with number of wins?

A) homeruns allowed B) hits made C) shutouts D) runs allowed 19) Almost all of the acidity of soda pop comes from the phosphoric acid which is added to give them a sharper flavor. Is there an association between the pH of the soda and the amount of phosphoric acid (in grams)? The correlation between pH and phosphoric acid is -0.991. Describe the association.

A) No evidence of association B) Strong linear association in a positive direction C) Weak linear association in a negative direction D) Very strong linear association in a negative direction E) Weak linear association in a positive direction ^

20) A regression line for predicting Internet usage (%) for 39 countries is y = -3.61 + 1.55x, where x is the per capita GDP, in thousands of dollars, and y is Internet usage. Interpret the residual for one of the 39 countries with per capita GDP of $15,000 and actual Internet use of 20 percent.

A) The actual Internet usage for this country is 0.36% higher than expected from the regression equation.

B) The actual Internet usage for this country is 3.6% higher than expected from the regression equation.

C) The actual Internet usage for this country is 3.25% lower than expected from the regression equation.

D) The actual Internet usage for this country is 0.36% lower than expected from the regression equation.

E) The actual Internet usage for this country is 3.25% higher than expected from the regression equation.

Copyright © 2013 Pearson Education, Inc. 38

18)

19)

20)

21) A teacher recorded for each of five students their score on a quiz (x) and their score on a project (y). A scatter plot of the points and the corresponding regression line are shown below.

21

y

Score on Project

18 15 12 9 6 3 2 4 6 8 10 12 14 16 18 20 Score on Quiz

x

Is the point (18, 19) an outlier on x? Is it an outlier on y? Is it a regression outlier?

A) outlier on x, not an outlier on y, not a regression outlier B) outlier on x, outlier on y, regression outlier C) not an outlier on x, not an outlier on y, not a regression outlier D) outlier on x, outlier on y, not a regression outlier SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Fill in the blank.

22) The fact that the direction of an association between two variables can change after we include a third variable and analyze the data at separate levels of that variable is known as ____________________.

Copyright © 2013 Pearson Education, Inc. 39

22)

21)

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

The following scatterplot shows the percentage of the vote a presidential candidate received in an election according to the voterʹs income level based on an exit poll of voters. The income levels 1 -8 correspond to the following income classes: 1=Under $15,000; 2=$15-30,000; 3=$30-50,000; 4=$50-75,000; 5=$75-100,000; 6=$100-150,000; 7=$150-200,000; 8=$200,000 or more.

23) Which of the following describes the linear association between income level and percentage of the vote won by the candidate?

A) weak, positive B) strong, negative C) weak, negative D) strong, positive E) no linear association Determine the type of association apparent in the following scatterplot.

24)

A) Linear association, moderately strong association B) Linear association C) Moderately strong association, negative association D) Little or no association E) Negative association, linear association Copyright © 2013 Pearson Education, Inc. 40

23)

24)

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

Provide an appropriate response.

25) A recent survey polled a sample of male Mexican-American adolescents to determine if there is an association between smoking and unhealthy behaviors. Below is the data. Each boy, age 10-18, was classified according to smoking status and his response to a question asking whether he liked to do risky things.

Likes Risky Things Doesnʹt Like Risky Things

Smoking Status Smoker Nonsmoker 45 46 36 153

a. How does the proportion of sampled smokers that likes risky things compare to the proportion of sampled nonsmokers that likes risky things? b. What proportion of all sampled Mexican-American male adolescents likes risky things?

Copyright © 2013 Pearson Education, Inc. 41

25)

Answer Key Testname: CHAPTER_3_EXAM_A

1) B 2) C 3) B 4) confounding 5) B 6) A 7) For low income: 25% high blood pressure for workaholics versus 23.8% high blood pressure for non -workaholics For middle income: 20.9% high blood pressure for workaholics versus 20% high blood pressure for non -workaholics For high income: 16.3% high blood pressure for workaholics versus 15% high blood pressure for non -workaholics All income groups combined: 20% high blood pressure for workaholics.versus 20.4% for non-workaholics Within each income group, the percentage with high blood pressure is higher for workaholics. However, when income groups are combined the percentage with high blood pressure is higher for non -workaholics.

Answers may vary. Possible explanation: When the income groups are combined, workaholism becomes confounded with income level.

Many of the workaholics are in the high-income group and high incomes bring greater access to other options which tend to lower blood pressure, such as health care, a healthy diet, gym membership, retreats, massage, etc. The large number of high-income people among the workaholics reduces the percentage with high blood pressure in the workaholic group.

8) a. The two variables are type of handicap and level of performance; b. response variable = level of performance, explanatory variable = type of handicap 9)

10) B

Copyright © 2013 Pearson Education, Inc. 42

Answer Key Testname: CHAPTER_3_EXAM_A

11)

2006 2007 2008 2009 2010 2011 2012 Year 12) C 13) D 14) B 15) A 16) E 17) E 18) C 19) D 20) A 21) D 22) Simpsonʹs paradox 23) B 24) C 25) a. The proportion of sampled smokers that likes risky things is 0.5556. The proportion of sampled nonsmokers that likes risky things is 0.2312. The proportion of sampled smokers that likes risky things is almost two and a half times as high as the proportion of sampled nonsmokers that likes risky things; b. 0.325.

Copyright © 2013 Pearson Education, Inc. 43

Chapter 3 Exam B Name___________________________________

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

Provide an appropriate response.

1) A researcher is investigating the association between blood pressure and ʺworkaholismʺ in a certain population. She classifies someone who works more than 60 hours per week as a workaholic. She records the income level and blood pressure (high or normal) for each participant and whether or not they can be classified as a ʺworkaholic.ʺ The data are summarized in the table below.

Workaholic Yes No

Low HBP NBP 25 75 25 80

Income Group Middle HBP NBP 23 87 18 72

1)

High HBP NBP 26 134 9 51

Consider each income group separately and find the proportion with high blood pressure among the workaholics and the proportion with high blood pressure among the non-workaholics.

Then determine the proportion of workaholics overall who have high blood pressure and the proportion of non-workaholics overall who have high blood pressure (ignoring information about income group). Explain how these data satisfy Simpsonʹs paradox.

How would you explain what is responsible for this result?

2) A recent survey polled a sample of male Mexican-American adolescents to determine if there is an association between smoking and unhealthy behaviors. Below is the data. Each boy, age 10-18, was classified according to smoking status and his response to a question asking whether he liked to do risky things.

Likes Risky Things Doesnʹt Like Risky Things

Smoking Status Smoker Nonsmoker 45 46 36 153

a. How does the proportion of sampled smokers that likes risky things compare to the proportion of sampled nonsmokers that likes risky things? b. What proportion of all sampled Mexican-American male adolescents likes risky things?

Copyright © 2013 Pearson Education, Inc. 44

2)

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

3) A regression line for predicting Internet usage (%) for 39 countries is y = -3.61 + 1.55x, where x is the per capita GDP, in thousands of dollars, and y is Internet usage. Interpret the residual for one of the 39 countries with per capita GDP of $15,000 and actual Internet use of 20 percent.

A) The actual Internet usage for this country is 3.6% higher than expected from the regression equation.

B) The actual Internet usage for this country is 0.36% lower than expected from the regression equation.

C) The actual Internet usage for this country is 3.25% higher than expected from the regression equation.

D) The actual Internet usage for this country is 0.36% higher than expected from the regression equation.

E) The actual Internet usage for this country is 3.25% lower than expected from the regression equation.

3)

4) The relationship between the number of games won by a minor league baseball team and the average attendance at their home games is analyzed. A regression to predict the average attendance from the number of games won has an r = 0.73. Interpret this statistic.

A) Positive, fairly strong linear relationship. 53.29% of the variation in average attendance is explained by the number of games won.

B) Negative, fairly strong linear relationship. 53.29% of the variation in average attendance is explained by the number of games won.

C) No association D) Positive, fairly strong linear relationship. 73% of the variation in average attendance is explained by the number of games won.

E) Positive, weak linear relationship. 7.29% of the variation in average attendance is explained by the number of games won.

4)

5) A teacher recorded for each of five students their score on a quiz (x) and their score on a project (y). A scatter plot of the points and the corresponding regression line are shown below.

5)

21

y

Score on Project

18 15 12 9 6 3 2 4 6 8 10 12 14 16 18 20 Score on Quiz

x

Is the point (18, 19) an outlier on x? Is it an outlier on y? Is it a regression outlier?

A) outlier on x, not an outlier on y, not a regression outlier B) not an outlier on x, not an outlier on y, not a regression outlier C) outlier on x, outlier on y, not a regression outlier D) outlier on x, outlier on y, regression outlier

Copyright © 2013 Pearson Education, Inc. 45

^

6) A regression line for predicting the selling prices of homes in Chicago is y = 168 + 102x, where x is the square footage of the house. Interpret the residual for a house with 1800 square feet that recently sold for $200,000.

A) The house sold for $16,064 more than was to be expected from the regression equation.

B) The house sold for $16,232 more than was to be expected from the regression equation.

C) The house sold for $16,400 more than was to be expected from the regression equation.

D) The house sold for $16,232 less than was to be expected from the regression equation.

E) The house sold for $16,400 less than was to be expected from the regression equation.

6)

7) Almost all of the acidity of soda pop comes from the phosphoric acid which is added to give them a sharper flavor. Is there an association between the pH of the soda and the amount of phosphoric acid (in grams)? The correlation between pH and phosphoric acid is -0.991. Describe the association.

A) Very strong linear association in a negative direction B) Weak linear association in a positive direction C) Strong linear association in a positive direction D) No evidence of association E) Weak linear association in a negative direction

7)

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

8) A large manufacturer hires many handicapped workers and keeps track of both their type of handicap and their level of performance. a. b.

8)

Identify the two variables.

Identify the response variable and the explanatory variable.

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

9) A researcher recorded for each of a number of recent high school and college graduates the number of years of education and their annual salary when they started their first job. The scatter plot is shown below together with the regression equation. The point (14, 4) was excluded when obtaining the regression equation.

Salary (Thousands of Dollars)

y 48

32

16

4 8 12 16 Years of Education

20

x

Is the point (14, 4) an outlier on x? Is it an outlier on y? Is it a regression outlier?

A) not an outlier on x, outlier on y, regression outlier B) not an outlier on x, outlier on y, not a regression outlier C) not an outlier on x, not an outlier on y, regression outlier D) outlier on x, outlier on y, regression outlier Copyright © 2013 Pearson Education, Inc. 46

9)

10) For 14 baseball teams, the correlation with number of wins in the regular season is 0.51 for shutouts, 0.61 for hits made, -0.70 for runs allowed and -0.56 for homeruns allowed. Which variable has the weakest linear association with number of wins?

A) homeruns allowed B) shutouts C) hits made D) runs allowed

10)

11) A researcher records for each participant in a clinical trial the amount of alcohol they consume per month and their cholesterol level. Indicate whether each variable is categorical or quantitative.

A) alcohol: categorical; cholesterol level: categorical B) alcohol: quantitative; cholesterol level: categorical C) alcohol: categorical; cholesterol level: quantitative D) alcohol: quantitative; cholesterol level: quantitative

11)

12) In order for a data point to be considered influential, which of the following must hold?

12)

I) the point has a large residual for the regression line fitted including that point II) its x value must be relatively low or high compared to the rest of the data III) the point has a large residual for the regression line fitted without using that data point C) II only D) III only E) I and II A) I only B) II and III SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Fill in the blank.

13) The fact that the direction of an association between two variables can change after we include a third variable and analyze the data at separate levels of that variable is known as ____________________.

14) When two explanatory variables are both associated with a response variable but are also associated with each other, there is said to be ____________________.

13)

14)

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

Answer true or false.

15) If the absolute value of the correlation is approximately one, then the points lie close to a line that slopes upward or downward.

A) False B) True

15)

16) The value of the correlation is always between 0 and 1.

A) True B) False

16)

17) The advantage of a side-by-side bar graph is that it allows for easy comparison of the explanatory variable groups with respect to values on the response variable.

A) True B) False

17)

Select the most appropriate answer.

18) The ____________________ is the outcome variable on which comparisons are made.

A) Both B and C B) predictor variable C) explanatory variable D) lurking variable E) response variable Copyright © 2013 Pearson Education, Inc. 47

18)

19) If a positive association exists between two quantitative variables, A) y tends to decrease as x increases.

B) the movement of x does not affect the movement of y.

C) y tends to decrease as x decreases.

D) none of these.

E) y tends to increase as x decreases.

Determine which plot shows the strongest linear correlation.

20) A)

19)

20) B)

y

y

x

C)

x

D) y

y

x

x

Copyright © 2013 Pearson Education, Inc. 48

Determine the type of association apparent in the following scatterplot.

21)

21)

A) Little or no association B) Negative association, linear association C) Moderately strong association, negative association D) Linear association E) Linear association, moderately strong association SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Construct a scatterplot for the data.

22) Below are the gold medal performances in the menʹs high jump at an athletic competition held in one city from 2006 to 2012.

Year High Jump (in.)

2006 85.3 2007 85.8 2008 88.3 2009 87.8 2010 88.5 2011 92.5 92.3 2012

Copyright © 2013 Pearson Education, Inc. 49

22)

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

The following scatterplot shows the percentage of the vote a presidential candidate received in an election according to the voterʹs income level based on an exit poll of voters. The income levels 1 -8 correspond to the following income classes: 1=Under $15,000; 2=$15-30,000; 3=$30-50,000; 4=$50-75,000; 5=$75-100,000; 6=$100-150,000; 7=$150-200,000; 8=$200,000 or more.

23) Which of the following describes the linear association between income level and percentage of the vote won by the candidate?

A) weak, positive B) strong, positive C) strong, negative D) weak, negative E) no linear association Fill in the missing information. _ _ ^ y = a + bx 24) x sx y sy r ?

?

18

23)

24)

^

4 -0.5 y = 30 - 4x

A) x = 3; sx = 1.00 B) x = 12; sx = 2.00 C) x = 48; sx = -18.00 D) x = 12; sx = 1.00 E) x = 3; sx = 0.50

Copyright © 2013 Pearson Education, Inc. 50

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

Solve the problem.

25) Use a scatterplot to display the data below. All measurements are in milligrams per cigarette.

Brand Tar Nicotine A 16 1.2 B 13 1.1 C 16 1.2 D 18 1.4 E 6 0.6

Copyright © 2013 Pearson Education, Inc. 51

25)

Answer Key Testname: CHAPTER_3_EXAM_B 1) For low income: 25% high blood pressure for workaholics versus 23.8% high blood pressure for non -workaholics For middle income: 20.9% high blood pressure for workaholics versus 20% high blood pressure for non -workaholics For high income: 16.3% high blood pressure for workaholics versus 15% high blood pressure for non -workaholics All income groups combined: 20% high blood pressure for workaholics.versus 20.4% for non-workaholics Within each income group, the percentage with high blood pressure is higher for workaholics. However, when income groups are combined the percentage with high blood pressure is higher for non -workaholics.

Answers may vary. Possible explanation: When the income groups are combined, workaholism becomes confounded with income level.

Many of the workaholics are in the high-income group and high incomes bring greater access to other options which tend to lower blood pressure, such as health care, a healthy diet, gym membership, retreats, massage, etc. The large number of high-income people among the workaholics reduces the percentage with high blood pressure in the workaholic group.

2) a. The proportion of sampled smokers that likes risky things is 0.5556. The proportion of sampled nonsmokers that likes risky things is 0.2312. The proportion of sampled smokers that likes risky things is almost two and a half times as high as the proportion of sampled nonsmokers that likes risky things; b. 0.325.

3) D 4) A 5) C 6) B 7) A 8) a. The two variables are type of handicap and level of performance; b. response variable = level of performance, explanatory variable = type of handicap 9) A 10) B 11) D 12) B 13) Simpsonʹs paradox 14) confounding 15) B 16) B 17) A 18) E 19) C 20) B 21) C

Copyright © 2013 Pearson Education, Inc. 52

Answer Key Testname: CHAPTER_3_EXAM_B

22)

2006 2007 2008 2009 2010 2011 2012 Year 23) C 24) E 25)

Copyright © 2013 Pearson Education, Inc. 53

Chapter 4 Exam A Name___________________________________

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

Provide an appropriate response.

1) Explain whether an experiment or an observational study would be more appropriate to investigate whether meditation is effective in lowering blood pressure.

A) Experiment; it would be easier to control for the effects of lurking variables such as diet and exercise.

B) Experiment; an observational study would take too long.

C) Experiment; it would be unethical to deprive people of a potentially beneficial treatment over a long period of time.

D) Experiment; in an observational study it would be too difficult to monitor participantsʹ behavior.

E) Observational study; it would be easier to control for the effects of lurking variables such as diet and exercise.

2) 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 4 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 population of interest?

A) The one box that was chosen at random from the 4 boxes B) The 6 cables chosen randomly for testing C) The 4 boxes D) 60 cables E) 120 cables

1)

2)

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

Identify the flaw(s) in the experiment or study described.

3) At one hospital, 674 women were diagnosed with breast cancer. Five years later, 88% of the Caucasian women and 83% of the African American women were still alive. A researcher concludes that being Caucasian causes women with breast cancer to have an increased chance of surviving five years. Why is this conclusion not justified?

3)

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

Provide an appropriate response.

4) Of the 5000 outpatients released from a local hospital in the past year, one hundred were contacted and asked their opinion on the care they received. Select the first five patients who belong to the simple random sample.

16348

76938

90169

51392

55887

71015

09209

79157

A) 163, 169, 15, 92, 97 B) 1634, 3890, 1695, 1392, 1509 C) 1, 6, 3, 4, 8 D) 16, 34, 69, 38, 13 E) 163, 487, 693, 169, 513 Copyright © 2013 Pearson Education, Inc. 54

4)

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

5) What is the difference between a retrospective study and a prospective study?

5)

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

Identify the specified elements of the experiment.

6) In a clinical trial, 780 participants suffering from high blood pressure were randomly assigned to one of three groups. Over a one-month period, the first group received a low dosage of an experimental drug, the second group received a high dosage of the drug, and the third group received a placebo. The diastolic blood pressure of each participant was measured at the beginning and at the end of the period and the change in blood pressure was recorded. Identify the explanatory variable.

A) Diastolic blood pressure at the start, diastolic blood pressure at the end B) Placebo, low drug dosage, high drug dosage C) The experimental drug D) High blood pressure, low blood pressure E) The one-month period of the experiment Identify the bias.

7) A magazine publisher mails a survey to every subscriber asking about the quality of its subscription service. From which of the following is this study most likely to suffer?

A) Sampling bias B) Nonresponse bias C) Both undercoverage and sampling bias D) Undercoverage E) Both nonresponse bias and undercoverage Provide an appropriate response.

8) Explain whether an experiment or an observational study would be more appropriate to investigate whether acupuncture can help people to heal from sports-related injuries.

A) Experiment; it would be easier to control for the effects of lurking variables such as exercise.

B) Experiment; it would be unethical to subject people to a potentially harmful treatment over a long period of time.

C) Observational study; an experiment would take too long.

D) Experiment; an observational study would take too long.

E) Observational study; it would be easier to control for the effects of lurking variables such as exercise.

Copyright © 2013 Pearson Education, Inc. 55

6)

7)

8)

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

Identify the flaw(s) in the experiment or study described.

9) A pharmaceutical company has developed a medication that they believe will help to reduce the pain of arthritis. They would like to test the medication at two different dosage levels. They design an experiment as follows to test the medication. They will obtain a group of volunteers who suffer from arthritis. A doctor from the pharmaceutical company will evaluate each patientʹs condition at the start of the experiment. Volunteers will be randomly assigned to one of three groups. Each day for the duration of the experiment, patients in group 1 will receive a low dose of the medication, patients in group 2 will receive a higher dose of the medication, and patients in group 3 will receive a placebo.

After a suitable amount of time (two months, for example), the same doctor will evaluate each patientʹs progress. Based on the amount of inflammation and the patientʹs report on the amount of pain, the doctor will give each patient a numerical score to represent their improvement. The amount of improvement for the three groups would then be compared.

They will also ensure that the technicians administering the supplements are unaware of which patients receive a low dose, a high dose, or a placebo. Identify the flaw(s) in this experiment.

9)

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

Provide an appropriate response.

10) An educational researcher used school records to determine that, in one school district, 84% of children living in two-parent homes graduated high school while 75% of children living in single-parent homes graduated high school. What is the explanatory variable?

A) Whether the child lived with two parents or with a single parent B) Graduation rate C) Whether the child lived with one or two parents and whether or not they graduated high school D) Whether the child graduated from high school

Copyright © 2013 Pearson Education, Inc. 56

10)

Answer the question.

11) A clothing manufacturer would like to determine whether celebrity endorsements influence a customerʹs decision to buy its products. In order to estimate this potential influence, the manufacturer premieres its latest series of commercials privately to two separate groups of potential buyers. One group will see a series of commercials without celebrities, and one group will view a series of commercials with celebrities. The potential buyers are further divided by gender.

11)

Who is in the control group?

A) The men and women who see the commercials without celebrities.

B) The men and women who see the commercials with celebrities.

C) The women who see the commercials without celebrities.

D) The men who see the commercials without celebrities.

E) The 100 potential buyers.

Select the most appropriate answer.

12) Experiments where two observations (one for each treatment) are recorded for each subject are called A) Stratified Designs B) Completely Randomized Designs C) Randomized Block Designs D) Cluster Designs E) Matched Pair Designs List all possible samples from the specified population.

13) Given a group of students: Allen (A), Brenda (B), Chad (C), Dorothy (D), and Eric (E), list all of the possible samples (without replacement) of size four that can be obtained from the group.

A) ABCD, ABCE, ACDE, ADEB, BCDE, BCEA, BDEA, CABD, CEDB, DACE B) ABCD, ABCE, ACDE, ADEB, BCDE C) ABCD, ABCE, ACDE, ADEB D) ABCD E) ABCD, ABCE, ABDE Select the most appropriate answer.

14) The most common type of convenience sample is A) a systematic sample.

B) a simple random sample.

C) a cluster sample.

D) a volunteer sample.

E) a stratified sample.

12)

13)

14)

Copyright © 2013 Pearson Education, Inc. 57

Identify the type of observational study.

15) A statistical analyst obtains data concerning ankle injuries by examining hospital records from the past 3 years.

A) Retrospective B) Prospective C) Cross-sectional D) Census E) Case-control Provide an appropriate response.

16) A magazine publisher mails a survey to every subscriber asking about the quality of its subscription service. Describe the population of interest.

A) the respondents to the survey B) all subscribers to the magazine C) all American adults D) all American adults who read the magazine

15)

16)

Answer true or false.

17) Nonresponse bias occurs when the subject gives an incorrect response.

A) False B) True

17)

18) Sampling bias occurs when some sampled subjects cannot be reached or refuse to participate or fail to answer some questions.

A) False B) True Identify which type of sampling is used.

19) A lobbyist for a major airspace firm assigns a number to each legislator and then uses a computer to randomly generate ten numbers. The lobbyist contacts the legislators corresponding to these numbers. What sampling technique was used?

A) Matched pair sample B) Convenience sample C) Simple random sample D) Cluster random sample E) Stratified random sample

18)

19)

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

Fill in the blank.

20) Bias that results from the sampling method, such as nonrandom sampling or undercoverage, is called ____________________.

20)

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

Identify the study as observational or experimental.

21) To determine whether children born with fetal alcohol syndrome have a less than average IQ, 200 children between the ages of 8 and 10 who were born with the syndrome were given an IQ test and their scores were compared to the average IQ of children aged 8 to 10 who were born healthy.

B) Observational A) Experimental

Copyright © 2013 Pearson Education, Inc. 58

21)

Select the most appropriate answer.

22) A method of sampling which divides the population into separate groups and then selects a simple random sample from each group is called ____________________.

A) systematic random sampling B) convenience sampling C) simple random sampling D) cluster random sampling E) stratified random sampling Identify which type of sampling is used.

23) The student dean of a university uses a computer to randomly select 500 student identification numbers then interviews the students corresponding to those identification numbers.

A) Convenience sample B) Simple random sample C) Matched pair sample D) Stratified random sample E) Cluster random sample

22)

23)

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

Fill in the blank.

24) When the difference between the results for the two treatments in an experimental study is so large that it would be rare to see such a difference by ordinary random variation among the experimental units, the results are said to be ____________________.

24)

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

Provide an appropriate response.

25) Explain whether an experiment or an observational study would be more appropriate to investigate whether women are more likely than men to suffer from anxiety.

A) Observational study; it is unethical to subject study participants to anxiety over a long period of time.

B) Observational study; it would be easier to control for lurking variables such as number of hours worked per week.

C) Experiment; it would be easier to control for lurking variables such as number of hours worked per week.

D) Observational study; gender cannot be assigned as a treatment.

E) Experiment; an observational study would take too long.

Copyright © 2013 Pearson Education, Inc. 59

25)

Answer Key Testname: CHAPTER_4_EXAM_A

1) A 2) E 3) Since there is no random assignment, there is no way to know that being Caucasian causes women with breast cancer to have an increased chance of surviving five years; there may have been lurking variables. For example, Caucasian women may be more affluent and able to afford better health care or better nutrition. They may have a less stressful lifestyle, or maybe they donʹt have to work as much. They may live in more affluent areas where there is less pollution and less noise.

4) B 5) A retrospective study looks into the past, while a prospective study follows its subjects into the future.

6) B 7) B 8) A 9) The doctor evaluating the patientsʹ progress is still aware of which treatment patients received. The doctor may be biased and influenced by his or her knowledge of whether the patient received the medication or a placebo. This is especially important because the doctor works for the pharmaceutical company and has a vested interest in finding that the medication is effective.

10) A 11) A 12) E 13) B 14) D 15) A 16) B 17) A 18) A 19) C 20) sampling bias 21) B 22) E 23) B 24) statistically significant 25) D

Copyright © 2013 Pearson Education, Inc. 60

Chapter 4 Exam B Name___________________________________

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

Provide an appropriate response.

1) Explain whether an experiment or an observational study would be more appropriate to investigate whether acupuncture can help people to heal from sports-related injuries.

A) Experiment; an observational study would take too long.

B) Observational study; it would be easier to control for the effects of lurking variables such as exercise.

C) Observational study; an experiment would take too long.

D) Experiment; it would be unethical to subject people to a potentially harmful treatment over a long period of time.

E) Experiment; it would be easier to control for the effects of lurking variables such as exercise.

2) Of the 5000 outpatients released from a local hospital in the past year, one hundred were contacted and asked their opinion on the care they received. Select the first five patients who belong to the simple random sample.

16348

76938

90169

51392

55887

71015

09209

1)

2)

79157

A) 163, 169, 15, 92, 97 B) 1634, 3890, 1695, 1392, 1509 C) 163, 487, 693, 169, 513 D) 16, 34, 69, 38, 13 E) 1, 6, 3, 4, 8 3) A magazine publisher mails a survey to every subscriber asking about the quality of its subscription service. Describe the population of interest.

A) all American adults who read the magazine B) all subscribers to the magazine C) the respondents to the survey D) all American adults

3)

4) Explain whether an experiment or an observational study would be more appropriate to investigate whether women are more likely than men to suffer from anxiety.

A) Observational study; it would be easier to control for lurking variables such as number of hours worked per week.

B) Experiment; it would be easier to control for lurking variables such as number of hours worked per week.

C) Observational study; gender cannot be assigned as a treatment.

D) Observational study; it is unethical to subject study participants to anxiety over a long period of time.

E) Experiment; an observational study would take too long.

4)

Copyright © 2013 Pearson Education, Inc. 61

5) An educational researcher used school records to determine that, in one school district, 84% of children living in two-parent homes graduated high school while 75% of children living in single-parent homes graduated high school. What is the explanatory variable?

A) Graduation rate B) Whether the child lived with one or two parents and whether or not they graduated high school C) Whether the child lived with two parents or with a single parent D) Whether the child graduated from high school

5)

6) 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 4 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 population of interest?

A) 60 cables B) The 6 cables chosen randomly for testing C) 120 cables D) The one box that was chosen at random from the 4 boxes E) The 4 boxes

6)

7) Explain whether an experiment or an observational study would be more appropriate to investigate whether meditation is effective in lowering blood pressure.

A) Experiment; in an observational study it would be too difficult to monitor participantsʹ behavior.

B) Observational study; it would be easier to control for the effects of lurking variables such as diet and exercise.

C) Experiment; it would be easier to control for the effects of lurking variables such as diet and exercise.

D) Experiment; it would be unethical to deprive people of a potentially beneficial treatment over a long period of time.

E) Experiment; an observational study would take too long.

7)

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

8) What is the difference between a retrospective study and a prospective study?

8)

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

Answer true or false.

9) Sampling bias occurs when some sampled subjects cannot be reached or refuse to participate or fail to answer some questions.

A) True B) False 10) Nonresponse bias occurs when the subject gives an incorrect response.

A) True B) False

Copyright © 2013 Pearson Education, Inc. 62

9)

10)

Select the most appropriate answer.

11) The most common type of convenience sample is A) a systematic sample.

B) a volunteer sample.

C) a stratified sample.

D) a cluster sample.

E) a simple random sample.

11)

12) Experiments where two observations (one for each treatment) are recorded for each subject are called A) Stratified Designs B) Matched Pair Designs C) Cluster Designs D) Completely Randomized Designs E) Randomized Block Designs

12)

13) A method of sampling which divides the population into separate groups and then selects a simple random sample from each group is called ____________________.

A) cluster random sampling B) stratified random sampling C) simple random sampling D) convenience sampling E) systematic random sampling

13)

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

Fill in the blank.

14) When the difference between the results for the two treatments in an experimental study is so large that it would be rare to see such a difference by ordinary random variation among the experimental units, the results are said to be ____________________.

15) Bias that results from the sampling method, such as nonrandom sampling or undercoverage, is called ____________________.

14)

15)

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

Identify the bias.

16) A magazine publisher mails a survey to every subscriber asking about the quality of its subscription service. From which of the following is this study most likely to suffer?

A) Both undercoverage and sampling bias B) Both nonresponse bias and undercoverage C) Nonresponse bias D) Undercoverage E) Sampling bias

Copyright © 2013 Pearson Education, Inc. 63

16)

Identify which type of sampling is used.

17) The student dean of a university uses a computer to randomly select 500 student identification numbers then interviews the students corresponding to those identification numbers.

A) Cluster random sample B) Simple random sample C) Matched pair sample D) Convenience sample E) Stratified random sample 18) A lobbyist for a major airspace firm assigns a number to each legislator and then uses a computer to randomly generate ten numbers. The lobbyist contacts the legislators corresponding to these numbers. What sampling technique was used?

A) Simple random sample B) Cluster random sample C) Matched pair sample D) Convenience sample E) Stratified random sample Answer the question.

19) A clothing manufacturer would like to determine whether celebrity endorsements influence a customerʹs decision to buy its products. In order to estimate this potential influence, the manufacturer premieres its latest series of commercials privately to two separate groups of potential buyers. One group will see a series of commercials without celebrities, and one group will view a series of commercials with celebrities. The potential buyers are further divided by gender.

17)

18)

19)

Who is in the control group?

A) The men and women who see the commercials without celebrities.

B) The men who see the commercials without celebrities.

C) The women who see the commercials without celebrities.

D) The men and women who see the commercials with celebrities.

E) The 100 potential buyers.

List all possible samples from the specified population.

20) Given a group of students: Allen (A), Brenda (B), Chad (C), Dorothy (D), and Eric (E), list all of the possible samples (without replacement) of size four that can be obtained from the group.

A) ABCD B) ABCD, ABCE, ACDE, ADEB C) ABCD, ABCE, ACDE, ADEB, BCDE D) ABCD, ABCE, ACDE, ADEB, BCDE, BCEA, BDEA, CABD, CEDB, DACE E) ABCD, ABCE, ABDE

Copyright © 2013 Pearson Education, Inc. 64

20)

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

Identify the flaw(s) in the experiment or study described.

21) At one hospital, 674 women were diagnosed with breast cancer. Five years later, 88% of the Caucasian women and 83% of the African American women were still alive. A researcher concludes that being Caucasian causes women with breast cancer to have an increased chance of surviving five years. Why is this conclusion not justified?

22) A pharmaceutical company has developed a medication that they believe will help to reduce the pain of arthritis. They would like to test the medication at two different dosage levels. They design an experiment as follows to test the medication. They will obtain a group of volunteers who suffer from arthritis. A doctor from the pharmaceutical company will evaluate each patientʹs condition at the start of the experiment. Volunteers will be randomly assigned to one of three groups. Each day for the duration of the experiment, patients in group 1 will receive a low dose of the medication, patients in group 2 will receive a higher dose of the medication, and patients in group 3 will receive a placebo.

After a suitable amount of time (two months, for example), the same doctor will evaluate each patientʹs progress. Based on the amount of inflammation and the patientʹs report on the amount of pain, the doctor will give each patient a numerical score to represent their improvement. The amount of improvement for the three groups would then be compared.

They will also ensure that the technicians administering the supplements are unaware of which patients receive a low dose, a high dose, or a placebo. Identify the flaw(s) in this experiment.

21)

22)

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

Identify the specified elements of the experiment.

23) In a clinical trial, 780 participants suffering from high blood pressure were randomly assigned to one of three groups. Over a one-month period, the first group received a low dosage of an experimental drug, the second group received a high dosage of the drug, and the third group received a placebo. The diastolic blood pressure of each participant was measured at the beginning and at the end of the period and the change in blood pressure was recorded. Identify the explanatory variable.

A) The one-month period of the experiment B) High blood pressure, low blood pressure C) Diastolic blood pressure at the start, diastolic blood pressure at the end D) Placebo, low drug dosage, high drug dosage E) The experimental drug Identify the study as observational or experimental.

24) To determine whether children born with fetal alcohol syndrome have a less than average IQ, 200 children between the ages of 8 and 10 who were born with the syndrome were given an IQ test and their scores were compared to the average IQ of children aged 8 to 10 who were born healthy.

A) Experimental B) Observational Identify the type of observational study.

25) A statistical analyst obtains data concerning ankle injuries by examining hospital records from the past 3 years.

A) Cross-sectional B) Prospective C) Census D) Case-control E) Retrospective Copyright © 2013 Pearson Education, Inc. 65

23)

24)

25)

Answer Key Testname: CHAPTER_4_EXAM_B

1) E 2) B 3) B 4) C 5) C 6) C 7) C 8) A retrospective study looks into the past, while a prospective study follows its subjects into the future.

9) B 10) B 11) B 12) B 13) B 14) statistically significant 15) sampling bias 16) C 17) B 18) A 19) A 20) C 21) Since there is no random assignment, there is no way to know that being Caucasian causes women with breast cancer to have an increased chance of surviving five years; there may have been lurking variables. For example, Caucasian women may be more affluent and able to afford better health care or better nutrition. They may have a less stressful lifestyle, or maybe they donʹt have to work as much. They may live in more affluent areas where there is less pollution and less noise.

22) The doctor evaluating the patientsʹ progress is still aware of which treatment patients received. The doctor may be biased and influenced by his or her knowledge of whether the patient received the medication or a placebo. This is especially important because the doctor works for the pharmaceutical company and has a vested interest in finding that the medication is effective.

23) D 24) B 25) E

Copyright © 2013 Pearson Education, Inc. 66

Chapter 5 Exam A Name___________________________________

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

List the outcomes comprising the specified event.

1) When a quarter is tossed four times, 16 outcomes are possible.

HHHH HTHH THHH TTHH

HHHT HTHT THHT TTHT

HHTH HTTH THTH TTTH

1)

HHTT HTTT THTT TTTT

Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth toss is heads. List the outcomes that comprise the event of obtaining the same face on the first three tosses.

A) HHHT, TTTH B) HHH, TTT C) HHHH, HHHT, TTTH, TTTT D) HHHH, TTTT E) HHHT, TTTH, HTTT, THHH SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

2) The census reported the frequencies in the following table for occupations of Americans 16 years and older.

2)

a. Find the probability that a randomly selected worker is in an occupation other than farming, fishing, or forestry. b. Given that a randomly selected worker is in service or in sales and office, find the probability they are in sales and office.

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

Select the most appropriate answer.

3) For two events A and B, P(A) = 0.4, P(B) = 0.3, and P(A and B) = 0. It follows that A and B are A) both disjoint and independent.

B) neither disjoint nor independent.

C) complementary.

D) disjoint but not independent.

E) independent but not disjoint.

Copyright © 2013 Pearson Education, Inc. 67

3)

Provide an appropriate response.

4) You flip a coin x number of times and calculate the probability of heads as (number of heads)/x.

What happens to this probability as x gets larger?

A) It gets smaller B) It stays the same, 0.50 C) It gets closer and closer to 0.50 D) It gets larger Find the indicated probability.

5) If two balanced die are rolled, the possible outcomes can be represented as follows.

(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)

(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)

(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

5)

(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

Determine the probability that the sum of the dice is 7.

2 7 5 A) B) C) 9 18 36

D)

7 36

E)

1 6

Provide an appropriate response.

6) Mr. Smithʹs gardener is not dependable; the probability that he will forget to water the rosebush during Smithʹs absence is 2/3. The rosebush is in questionable condition anyhow; if watered, the probability of its withering is 1/2, but if it is not watered, the probability of its withering is 3/4.

Upon returning, Smith finds that the rosebush has withered. What is the probability that the gardener did not water the rosebush?

1 A) 3 B)

2 3

C)

3 4

4)

D) None of these.

1 E) 2

Copyright © 2013 Pearson Education, Inc. 68

6)

List the outcomes comprising the specified event.

7) Three board members for a nonprofit organization will be selected from a group of five people.

The board members will be selected by drawing names from a hat. The names of the five possible board members are Allison, Betty, Charlie, Dave, and Emily. The possible outcomes can be represented as follows.

ABC ADE

ABD BCD

ABE BCE

ACD BDE

7)

ACE CDE

Here, for example, ABC represents the outcome that Allison, Betty, and Charlie are selected to be on the board. List the outcomes that comprise the event that Betty and Emily are selected.

A) ABE, BCE, BDE B) BE C) ABC, ABD, ABE, ACE, ADE, BCD, BCE, BDE, CDE D) ABE, BDE E) ABE, BCE Draw a Venn diagram and shade the described events.

8) From a finite sample, events A, B, and C are disjoint. Shade the collection A or B or C. A) B)

C)

8)

D)

Find the probability of the given event.

9) A random spinner has equal-sized regions numbered 1 through 18. The spinner stops on an even number or a multiple of 3.

1 1 2 B) C) 1 D) 15 E) A) 2 3 3

Copyright © 2013 Pearson Education, Inc. 69

9)

Determine whether the events are disjoint.

10) A card is selected randomly from a deck of 52. The events A, B, and C are defined as follows.

10)

A = event the card selected is a heart B = event the card selected is a club C = event the card selected is an ace Are the events A, B, and C disjoint?

A) Yes

B) No

Provide an appropriate response.

11) If A and B are independent events, with P(A) = A) equals

3 .

25

B) equals

3 .

10

1 2 , P(B) = , then P(A or B) 5 5

11)

C) cannot be determined from the given information.

3 D) equals .

5 E) equals

13 .

25

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

12) A production process of computer parts uses two machines, one old machine and one new machine. If the old machine is used, the probability that a defective part is produced is 0.13. If the new machine is used, the probability that a defective part is produced is 0.04.

Moreover, the new machine produces parts 4 times as fast as the old machine does. What is the probability that a randomly selected part produced by this process is defective?

12)

13) Among the 12 applicants for managerial positions at a chain of movie theaters, 8 are college graduates and 4 are high school graduates. If three of the applicants are randomly selected,

13)

a. Identify the possible outcomes in terms of whether a selected applicant is a college graduate (C) or a high school graduate (H). b. Find the probability for each possible outcome and verify that these probabilities follow the two basic rules of the probabilities for the outcomes in a sample space.

Copyright © 2013 Pearson Education, Inc. 70

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

Draw a Venn diagram and shade the described events.

14) From a finite sample, events A, B, and C are not disjoint. Shade the collection A and B and C. A) B)

C)

14)

D)

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

Provide an appropriate response.

15) How does one determine whether or not two events, say A and B, are independent?

15)

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

Suppose P(C) =0 .048, P(M and C) = 0.044, and P(M or C) = 0.524. Find the indicated probability.

16) P(M) A) 0.480 B) 0.524 C) 0.472 D) 0.528 E) 0.520

16)

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

Provide an appropriate response.

17) When entering data into a computer, the probability that a student will make at most three mistakes per 1,000 keystrokes is 0.71, and the probability of making anywhere from 4 to 6 mistakes per 1,000 keystrokes is 0.22. Find the probabilities that in 1,000 keystrokes the student will make a. b.

at most 6 mistakes more than 3 mistakes

Copyright © 2013 Pearson Education, Inc. 71

17)

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

18) According to a survey, 41.5% of babies born in the U.S. were still being breastfed at 6 months of age. If 4 children who are born in the U.S. are randomly selected, what is the probability that none of them are breastfed for at least 6 months?

A) 0.03 B) 1 C) 0.12 D) none of these E) 0.585 Solve the problem.

19) Find the probability that in a class of 31 students, at least two have the same birthday. Express the probability as a decimal rounded to four decimal places.

A) 0.7305 B) 0.7063 C) 0.2695 D) 0.7533 20) A patient is told that a test for a certain disease is 92% accurate. The way this is worded, this could mean that (a) 92% of those with the disease test positive, (b) 92% of those without the disease test negative, (c) 92% of those who test positive have the disease, or (d) 92% of those who test negative do not have the disease. Let D denote {person has the disease}, and let P denote {person tests positive}. Using these events and their complements, express as a conditional probability the event that a person who tests positive does not have the disease.

B) P(Pc D) C) P(Dc Pc) D) P(Dc P) E) P(P Dc) A) P(D Pc) Provide an appropriate response.

21) A prix fixed menu offers a choice of 2 appetizers, 4 main courses and 3 desserts. If a tree diagram is used to list all possible meal combinations from the prix fixed menu, how many branches will there be?

A) 9 B) none of these C) 24 D) 12 E) 8 List the outcomes comprising the specified event.

22) When a quarter is tossed four times, 16 outcomes are possible.

HHHH HTHH THHH TTHH

HHHT HTHT THHT TTHT

HHTH HTTH THTH TTTH

HHTT HTTT THTT TTTT

Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth toss is heads. List the outcomes that comprise the event of tossing exactly three tails.

A) HTTT, THTT, TTHT, TTTH, TTTT B) HTTT, THTT, TTHT, TTTH C) THTT, TTHT, TTTH D) TTTH E) HTTT, THTT, TTTH

Copyright © 2013 Pearson Education, Inc. 72

18)

19)

20)

21)

22)

Provide an appropriate response.

23) Ten white balls, 20 blue balls and 20 red balls are placed in an urn. If two balls are drawn, with replacement, what is the probability of drawing two white balls?

A) 0.04 B) 0.36 C) 0.037 D) 0.01

23)

Draw a tree diagram to represent the problem. At the end of each branch use symbols to represent the event that the branch corresponds to and give the probability of the event.

24) 24) Two cards are selected randomly without replacement from a standard deck of 52 cards. The color of each card (red or black) is recorded. Draw a tree diagram showing the possible outcomes and their probabilities for this problem.

A)

B) None of these C)

Copyright © 2013 Pearson Education, Inc. 73

D)

Find the probability using complements.

25) Suppose that on a particular multiple choice question, 96% of the students answered correctly.

What is the probability that a randomly selected student answered the question incorrectly?

A) 1.04 B) 0.04 C) 0.96 D) 24.00 E) 0.48

Copyright © 2013 Pearson Education, Inc. 74

25)

Answer Key Testname: CHAPTER_5_EXAM_A

1) C 2) a. 0.9927; b. 0.6423 3) D 4) C 5) E 6) C 7) A 8) A 9) A 10) B 11) E 12) P(D) = P(N and D) + P(O and D) = 0.032 + 0.026 = 0.058 13) a. {CCC, CCH, CHC, CHH, HCC, HCH, HHC, HHH}; b. P(CCC) = 336/1320, P(CCH) = P(CHC) = P(HCC) = 224/1320, P(CHH) = P(HCH) = P(HHC) = 96/1320, P(HHH) =24/1320; The probability of each individual outcome is between 0 and 1. The total of the probabilities of all of the individual outcomes is 1.

14) A 15) A and B are independent events if P(A|B) = P(A), P(B|A) = P(B), or P(A and B) = P(A) × P(B). If one equation holds, all 3 equations hold. If one equation does not hold, none of the equations hold. Therefore, only one of the equations must be checked.

16) E 17) a. 0.93; b. 0.29 18) C 19) A 20) D 21) C 22) B 23) A 24) A 25) B

Copyright © 2013 Pearson Education, Inc. 75

Chapter 5 Exam B Name___________________________________

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

Provide an appropriate response.

1) The census reported the frequencies in the following table for occupations of Americans 16 years and older.

1)

a. Find the probability that a randomly selected worker is in an occupation other than farming, fishing, or forestry. b. Given that a randomly selected worker is in service or in sales and office, find the probability they are in sales and office.

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

2) You flip a coin x number of times and calculate the probability of heads as (number of heads)/x.

What happens to this probability as x gets larger?

A) It gets larger B) It gets closer and closer to 0.50 C) It stays the same, 0.50 D) It gets smaller

2)

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

3) A production process of computer parts uses two machines, one old machine and one new machine. If the old machine is used, the probability that a defective part is produced is 0.13. If the new machine is used, the probability that a defective part is produced is 0.04.

Moreover, the new machine produces parts 4 times as fast as the old machine does. What is the probability that a randomly selected part produced by this process is defective?

3)

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

4) According to a survey, 41.5% of babies born in the U.S. were still being breastfed at 6 months of age. If 4 children who are born in the U.S. are randomly selected, what is the probability that none of them are breastfed for at least 6 months?

A) 0.03 B) 0.12 C) 0.585 D) none of these E) 1 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

5) How does one determine whether or not two events, say A and B, are independent?

Copyright © 2013 Pearson Education, Inc. 76

5)

4)

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

6) If A and B are independent events, with P(A) = A) equals

3 .

25

B) equals

3 .

5

1 2 , P(B) = , then P(A or B) 5 5

6)

C) cannot be determined from the given information.

3 .

D) equals 10 E) equals

13 .

25

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

7) Among the 12 applicants for managerial positions at a chain of movie theaters, 8 are college graduates and 4 are high school graduates. If three of the applicants are randomly selected,

7)

a. Identify the possible outcomes in terms of whether a selected applicant is a college graduate (C) or a high school graduate (H). b. Find the probability for each possible outcome and verify that these probabilities follow the two basic rules of the probabilities for the outcomes in a sample space.

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

8) Mr. Smithʹs gardener is not dependable; the probability that he will forget to water the rosebush during Smithʹs absence is 2/3. The rosebush is in questionable condition anyhow; if watered, the probability of its withering is 1/2, but if it is not watered, the probability of its withering is 3/4.

Upon returning, Smith finds that the rosebush has withered. What is the probability that the gardener did not water the rosebush?

1 A) 2 B)

1 3

C)

2 3

8)

D) None of these.

3 E) 4 9) A prix fixed menu offers a choice of 2 appetizers, 4 main courses and 3 desserts. If a tree diagram is used to list all possible meal combinations from the prix fixed menu, how many branches will there be?

A) 12 B) 24 C) none of these D) 8 E) 9

Copyright © 2013 Pearson Education, Inc. 77

9)

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

10) When entering data into a computer, the probability that a student will make at most three mistakes per 1,000 keystrokes is 0.71, and the probability of making anywhere from 4 to 6 mistakes per 1,000 keystrokes is 0.22. Find the probabilities that in 1,000 keystrokes the student will make a. b.

10)

at most 6 mistakes more than 3 mistakes

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

11) Ten white balls, 20 blue balls and 20 red balls are placed in an urn. If two balls are drawn, with replacement, what is the probability of drawing two white balls?

A) 0.01 B) 0.04 C) 0.36 D) 0.037 Solve the problem.

12) Find the probability that in a class of 31 students, at least two have the same birthday. Express the probability as a decimal rounded to four decimal places.

A) 0.2695 B) 0.7063 C) 0.7305 D) 0.7533 13) A patient is told that a test for a certain disease is 92% accurate. The way this is worded, this could mean that (a) 92% of those with the disease test positive, (b) 92% of those without the disease test negative, (c) 92% of those who test positive have the disease, or (d) 92% of those who test negative do not have the disease. Let D denote {person has the disease}, and let P denote {person tests positive}. Using these events and their complements, express as a conditional probability the event that a person who tests positive does not have the disease.

B) P(P Dc) C) P(Pc D) D) P(Dc Pc) E) P(Dc P) A) P(D Pc) Find the probability of the given event.

14) A random spinner has equal-sized regions numbered 1 through 18. The spinner stops on an even number or a multiple of 3.

1 1 2 B) 15 C) D) E) 1 A) 2 3 3 Find the indicated probability.

15) If two balanced die are rolled, the possible outcomes can be represented as follows.

(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)

(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)

(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

11)

12)

13)

14)

15)

(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

Determine the probability that the sum of the dice is 7.

7 7 1 A) B) C) 18 36 6

D)

2 9

E)

5 36

Draw a tree diagram to represent the problem. At the end of each branch use symbols to represent the event that the branch corresponds to and give the probability of the event.

Copyright © 2013 Pearson Education, Inc. 78

16) Two cards are selected randomly without replacement from a standard deck of 52 cards. The color of each card (red or black) is recorded. Draw a tree diagram showing the possible outcomes and their probabilities for this problem.

A)

B) None of these C)

D)

Copyright © 2013 Pearson Education, Inc. 79

16)

Draw a Venn diagram and shade the described events.

17) From a finite sample, events A, B, and C are disjoint. Shade the collection A or B or C. B) A)

C)

D)

18) From a finite sample, events A, B, and C are not disjoint. Shade the collection A and B and C. B) A)

C)

17)

D)

Copyright © 2013 Pearson Education, Inc. 80

18)

List the outcomes comprising the specified event.

19) When a quarter is tossed four times, 16 outcomes are possible.

HHHH HTHH THHH TTHH

HHHT HTHT THHT TTHT

HHTH HTTH THTH TTTH

19)

HHTT HTTT THTT TTTT

Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth toss is heads. List the outcomes that comprise the event of tossing exactly three tails.

A) THTT, TTHT, TTTH B) HTTT, THTT, TTHT, TTTH C) HTTT, THTT, TTHT, TTTH, TTTT D) HTTT, THTT, TTTH E) TTTH 20) Three board members for a nonprofit organization will be selected from a group of five people.

The board members will be selected by drawing names from a hat. The names of the five possible board members are Allison, Betty, Charlie, Dave, and Emily. The possible outcomes can be represented as follows.

ABC ADE

ABD BCD

ABE BCE

ACD BDE

20)

ACE CDE

Here, for example, ABC represents the outcome that Allison, Betty, and Charlie are selected to be on the board. List the outcomes that comprise the event that Betty and Emily are selected.

A) ABC, ABD, ABE, ACE, ADE, BCD, BCE, BDE, CDE B) ABE, BCE C) ABE, BDE D) BE E) ABE, BCE, BDE 21) When a quarter is tossed four times, 16 outcomes are possible.

HHHH HTHH THHH TTHH

HHHT HTHT THHT TTHT

HHTH HTTH THTH TTTH

HHTT HTTT THTT TTTT

Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth toss is heads. List the outcomes that comprise the event of obtaining the same face on the first three tosses.

A) HHHT, TTTH, HTTT, THHH B) HHHT, TTTH C) HHHH, HHHT, TTTH, TTTT D) HHHH, TTTT E) HHH, TTT

Copyright © 2013 Pearson Education, Inc. 81

21)

Select the most appropriate answer.

22) For two events A and B, P(A) = 0.4, P(B) = 0.3, and P(A and B) = 0. It follows that A and B are A) disjoint but not independent.

B) both disjoint and independent.

C) independent but not disjoint.

D) neither disjoint nor independent.

E) complementary.

Find the probability using complements.

23) Suppose that on a particular multiple choice question, 96% of the students answered correctly.

What is the probability that a randomly selected student answered the question incorrectly?

A) 0.96 B) 1.04 C) 0.48 D) 24.00 E) 0.04 Determine whether the events are disjoint.

24) A card is selected randomly from a deck of 52. The events A, B, and C are defined as follows.

22)

23)

24)

A = event the card selected is a heart B = event the card selected is a club C = event the card selected is an ace Are the events A, B, and C disjoint?

A) No

B) Yes

Suppose P(C) =0 .048, P(M and C) = 0.044, and P(M or C) = 0.524. Find the indicated probability.

25) P(M) A) 0.524 B) 0.528 C) 0.472 D) 0.480 E) 0.520

Copyright © 2013 Pearson Education, Inc. 82

25)

Answer Key Testname: CHAPTER_5_EXAM_B

1) a. 0.9927; b. 0.6423 2) B 3) P(D) = P(N and D) + P(O and D) = 0.032 + 0.026 = 0.058 4) B 5) A and B are independent events if P(A|B) = P(A), P(B|A) = P(B), or P(A and B) = P(A) × P(B). If one equation holds, all 3 equations hold. If one equation does not hold, none of the equations hold. Therefore, only one of the equations must be checked.

6) E 7) a. {CCC, CCH, CHC, CHH, HCC, HCH, HHC, HHH}; b. P(CCC) = 336/1320, P(CCH) = P(CHC) = P(HCC) = 224/1320, P(CHH) = P(HCH) = P(HHC) = 96/1320, P(HHH) =24/1320; The probability of each individual outcome is between 0 and 1. The total of the probabilities of all of the individual outcomes is 1.

8) E 9) B 10) a. 0.93; b. 0.29 11) B 12) C 13) E 14) A 15) C 16) A 17) B 18) A 19) B 20) E 21) C 22) A 23) E 24) A 25) E

Copyright © 2013 Pearson Education, Inc. 83

Chapter 6 Exam A Name___________________________________

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

Find the indicated probability.

1) Suppose that 11% of people are left handed. If 6 people are selected at random, what is the probability that exactly 2 of them are left handed?

A) 0.1139 B) 0.2278 C) 0.0076 D) 0.0566 E) 0.0121 Find the standard deviation of the binomial random variable.

2) The probability of winning a certain lottery is 1/51,949. For people who play 560 times, find the standard deviation for the random variable X, the number of wins.

A) 2.4569 B) 0.0108 C) 0.1223 D) 0.1137 E) 0.1038 Find the specified probability distribution of the binomial random variable.

3) In one city, 21% of the population is under 25 years of age. Three people are selected at random from the city. Find the probability distribution of X, the number among the three that are under 25 years of age. x P(X = x) 0 0.4930 A) 1 0.1311 2 0.0348 3 0.0093 x P(X = x) 0 0.4930 B) 1 0.3932 2 0.0925 3 0.0213 x P(X = x) 0 0.4930 C) 1 0.3932 2 0.1045 3 0.0093 x P(X = x) 0.21 D) 1 2 0.0441 3 0.0213 x P(X = x) 0.21 E) 1 2 0.0441 3 0.0093 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

4) Serum cholesterol is an important risk factor for coronary disease. The level of serum cholesterol is approximately normally distributed with a mean of 219 mg/dL and a standard deviation of 50 mg/dL. If the clinically desirable range for serum cholesterol is < 200 mg/dL, what is the probability that a randomly selected person will have a clinically desirable level of serum cholesterol?

Copyright © 2013 Pearson Education, Inc. 84

4)

1)

2)

3)

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

Find the indicated probability for the normally distributed variable.

5) The weekly salaries of elementary school teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. What is the probability that a randomly selected elementary school teacher earns more than $525 a week?

B) 0.1003 C) 0.2177 D) 0.7823 E) 0.4354 A) 0.2823 Find the mean of the binomial random variable.

6) The probability is 0.7 that a person shopping at a certain store will spend less than $20. For random samples of 28 customers, find the mean number of shoppers who spend less than $20.

A) 14.0 B) 18.2 C) 8.4 D) 19.6 E) 6.0 Obtain the probability distribution of the random variable.

7) When a coin is tossed four times, sixteen equally likely outcomes are possible as shown below: HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHH TTHT TTTH TTTT Let X denote the total number of tails obtained in the four tosses. Find the probability distribution of the random variable X. Leave your probabilities in fraction form.

A) x P(X = x) 0 1/16 1 3/16 2 1/2 3 3/16 4 1/16 B) x P(X = x) 0 0 1 1/4 2 3/8 3 1/4 4 1/16 C) x P(X = x) 1 1/4 2 7/16 3 1/4 4 1/16 D) x P(X = x) 0 1/16 1 1/4 2 3/8 3 1/4 4 1/16

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5)

6)

7)

E) x P(X = x) 0 1/16 1 1/8 2 3/8 3 1/8 4 1/16 Find the mean of the given probability distribution.

8) The random variable X is the number of houses sold by a realtor in a single month at a particular real estate office. Its probability distribution is given in the table below. x P(X = x) 0 0.24 1 0.01 2 0.12 3 0.16 4 0.01 5 0.14 6 0.11 7 0.21 A) 3.40 B) 3.60 C) 3.35 D) 3.50 Use a table of areas to find the specified area under the standard normal curve.

9) The area that lies to the right of -1.82 A) 0.4656 B) -0.0344 C) 0.4828 D) 0.0344

9) E) 0.9656

Find the indicated probability.

10) An archer is able to hit the bullʹs-eye 55% of the time. If she shoots 8 arrows, what is the probability that she gets exactly 4 bullʹs-eyes? Assume each shot is independent of the others.

A) 0.1719 B) 0.5254 C) 0.2627 D) 0.0915 E) 0.0038 Obtain the probability distribution of the random variable.

11) When two balanced dice are rolled, 36 equally likely outcomes are possible as shown below.

(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) Let X denote the smaller of the two numbers or the common value if doubles are thrown. Find the probability distribution of X. Leave your probabilities in fraction form.

A) x P(X = x) 1 11/36 2 1/8 3 7/36 4 5/36 5 1/18 6 1/36

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8)

10)

11)

B) x P(X = x) 1 5/18 2 2/9 3 1/6 4 1/9 5 1/18 6 0 C) x P(X = x) 1 5/18 2 1/4 3 7/36 4 5/36 5 1/9 6 1/36 D) x P(X = x) 1 11/36 2 1/4 3 7/36 4 5/36 5 1/12 6 1/36 E) x P(X = x) 1 1/6 2 1/6 3 1/6 4 1/6 5 1/6 6 1/6 Find the indicated probability.

12) A multiple choice test has 10 questions each of which has 4 possible answers, only one of which is correct. If Judy, who forgot to study for the test, guesses on all questions, what is the probability that she will answer exactly 3 questions correctly?

A) 0.0156 B) 0.2503 C) 0.0021 D) 0.5006 E) 0.2816 Determine whether the conditions for the normal approximation to the binomial are satisfied.

13) In one town, 2% of adults are HIV positive. A researcher selects a random sample of 400 adults from a population of 23,250. X = number of people in the sample who are HIV positive. In this scenario, the conditions for the binomial distribution are satisfied. Is it reasonable to use the normal approximation to determine an interval within which X will almost certainly fall? Explain why or why not.

A) No, np is less than 15.

B) Yes, as n is large.

C) Yes, sampling is without replacement but the sample size is less than 10% of population.

D) No, the trials are not independent as sampling is without replacement.

Copyright © 2013 Pearson Education, Inc. 87

12)

13)

Find the mean of the binomial random variable.

14) According to a survey on drug use, 54.3% of males have never used marijuana. Based on this percentage, what is the expected number of males who have used marijuana for samples of size 100?

A) 5 B) 24.8 C) 54.3 D) 50 E) 45.7 Find the mean of the given probability distribution.

15) The percentage of families by size in the U.S. is given in the table below.

14)

15)

(note: the category ʺ7ʺ actually represents 7 or more but ʺ7ʺ will be used for calculation purposed) A) 2.5 B) 3.1 C) 0.17 D) 2 E) 4.5 Find the mean of the binomial random variable.

16) According to a poll taken in February of 2008, 67% of respondents disapproved of the overall job that the President was doing. Based on this poll, for samples of size 200, what is the mean number of adults who disapprove of the overall job that the President is doing?

A) 6.65 B) 100 C) 44.22 D) 67 E) 134 17) A die is rolled 10 times and the number of times that two shows on the up face is counted. If this experiment is repeated many times, find the mean for the random variable X, the number of twos thrown out of ten tosses.

A) 3.33 B) 8.33 C) 1.67 D) 2.98 E) 2.5 Find the mean of the given probability distribution.

18) According to a survey, the percentage of households by number of vehicles is given in the following table:

(note, the category ʺ5ʺ actually represents 5 or more, but we will use ʺ5ʺ for ease of calculation) A) 2 B) 1.5 C) 1.88 D) 2.5 E) 188.2

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16)

17)

18)

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

Provide an appropriate response.

19) Serum cholesterol is an important risk factor for coronary disease. The level of serum cholesterol is approximately normally distributed with a mean of 219 mg/dL and a standard deviation of 50 mg/dL. If the clinically desirable range for serum cholesterol is < 200 mg/dL and serum cholesterol levels of over 250 mg/dL indicate a high-enough risk for heart disease to warrant treatment, what is the probability that a randomly selected person will have a borderline high serum cholesterol level (that is, > 200, but < 250 mg/dL)?

19)

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

Determine whether the conditions for the binomial distribution are satisfied. If the conditions are not satisfied, state why not.

20) X = number of Democrats in a sample of 500 voters selected randomly from a total of 2560 20) registered voters in one town. 42% of the 2560 registered voters are Democrats.

A) Conditions for binomial distribution are not satisfied. Trials are not independent. Sampling is without replacement and the sample size is less than 20% of the population.

B) Conditions for binomial distribution are not satisfied. np is larger than 15.

C) Conditions for binomial distribution are satisfied.

D) Conditions for binomial distribution are not satisfied. Trials are not independent. Sampling is without replacement and sample size is more than 10% of the population.

Find the standard deviation of the binomial random variable.

21) According to a college survey, 22% of all students work full time. Find the standard deviation for the random variable X, the number of students who work full time in samples of size 16.

A) 1.88 B) 2.75 C) 3.52 D) 1.66 E) 1.98

21)

Determine whether the conditions for the binomial distribution are satisfied. If the conditions are not satisfied, state why not.

22) A polling agency in one city randomly selects 1000 registered voters from a pool of 385,600 22) registered voters of whom 17% are African American. X = number of African Americans in the sample.

A) Conditions for binomial distribution are not satisfied. Trials are not independent. Sampling is without replacement and sample size is less than 10% of population.

B) Conditions for binomial distribution are not satisfied. There are more than two possible outcomes per trial.

C) Conditions for binomial distribution are satisfied.

D) Conditions for binomial distribution are not satisfied. The probability of success is not the same on each trial.

Use a table of areas for the standard normal curve to find the required z -score.

23) Find the z-score for which the area under the standard normal curve to its left is 0.96 A) 1.82 B) 1.03 C) -1.38 D) 1.75 E) -1.75 24) Find the z-score having area 0.86 to its right under the standard normal curve.

A) 1.08 B) 0.8051 C) -1.08 D) 0.5557

24) E) -0.5557

Find the standard deviation of the binomial random variable.

25) A die is rolled 18 times and the number of twos that come up is tallied. If this experiment is repeated many times, find the standard deviation for the random variable X, the number of twos.

A) 1.581 B) 1.537 C) 1.622 D) 1.73 E) 2.5 Copyright © 2013 Pearson Education, Inc. 89

23)

25)

Answer Key Testname: CHAPTER_6_EXAM_A

1) A 2) E 3) C 4) 0.3520 5) C 6) D 7) D 8) B 9) E 10) C 11) D 12) B 13) A 14) E 15) B 16) E 17) C 18) C 19) 0.3804 20) D 21) D 22) C 23) D 24) C 25) A

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Chapter 6 Exam B Name___________________________________

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

Provide an appropriate response.

1) Serum cholesterol is an important risk factor for coronary disease. The level of serum cholesterol is approximately normally distributed with a mean of 219 mg/dL and a standard deviation of 50 mg/dL. If the clinically desirable range for serum cholesterol is < 200 mg/dL and serum cholesterol levels of over 250 mg/dL indicate a high-enough risk for heart disease to warrant treatment, what is the probability that a randomly selected person will have a borderline high serum cholesterol level (that is, > 200, but < 250 mg/dL)?

2) Serum cholesterol is an important risk factor for coronary disease. The level of serum cholesterol is approximately normally distributed with a mean of 219 mg/dL and a standard deviation of 50 mg/dL. If the clinically desirable range for serum cholesterol is < 200 mg/dL, what is the probability that a randomly selected person will have a clinically desirable level of serum cholesterol?

1)

2)

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

Use a table of areas to find the specified area under the standard normal curve.

3) The area that lies to the right of -1.82 A) 0.4656 B) 0.4828 C) 0.0344 D) -0.0344

3) E) 0.9656

Find the indicated probability.

4) A multiple choice test has 10 questions each of which has 4 possible answers, only one of which is correct. If Judy, who forgot to study for the test, guesses on all questions, what is the probability that she will answer exactly 3 questions correctly?

A) 0.2816 B) 0.5006 C) 0.0021 D) 0.0156 E) 0.2503

4)

5) Suppose that 11% of people are left handed. If 6 people are selected at random, what is the probability that exactly 2 of them are left handed?

A) 0.0076 B) 0.0566 C) 0.2278 D) 0.0121 E) 0.1139

5)

6) An archer is able to hit the bullʹs-eye 55% of the time. If she shoots 8 arrows, what is the probability that she gets exactly 4 bullʹs-eyes? Assume each shot is independent of the others.

A) 0.0915 B) 0.5254 C) 0.1719 D) 0.2627 E) 0.0038

6)

Find the mean of the binomial random variable.

7) According to a poll taken in February of 2008, 67% of respondents disapproved of the overall job that the President was doing. Based on this poll, for samples of size 200, what is the mean number of adults who disapprove of the overall job that the President is doing?

A) 6.65 B) 44.22 C) 67 D) 100 E) 134 8) A die is rolled 10 times and the number of times that two shows on the up face is counted. If this experiment is repeated many times, find the mean for the random variable X, the number of twos thrown out of ten tosses.

A) 1.67 B) 2.5 C) 2.98 D) 8.33 E) 3.33

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7)

8)

9) According to a survey on drug use, 54.3% of males have never used marijuana. Based on this percentage, what is the expected number of males who have used marijuana for samples of size 100?

A) 24.8 B) 5 C) 54.3 D) 45.7 E) 50

9)

10) The probability is 0.7 that a person shopping at a certain store will spend less than $20. For random samples of 28 customers, find the mean number of shoppers who spend less than $20.

A) 19.6 B) 6.0 C) 14.0 D) 18.2 E) 8.4

10)

Find the indicated probability for the normally distributed variable.

11) The weekly salaries of elementary school teachers in one state are normally distributed with a mean of $490 and a standard deviation of $45. What is the probability that a randomly selected elementary school teacher earns more than $525 a week?

A) 0.1003 B) 0.2177 C) 0.2823 D) 0.7823 E) 0.4354 Obtain the probability distribution of the random variable.

12) When two balanced dice are rolled, 36 equally likely outcomes are possible as shown below.

(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) Let X denote the smaller of the two numbers or the common value if doubles are thrown. Find the probability distribution of X. Leave your probabilities in fraction form.

A) x P(X = x) 1 1/6 2 1/6 3 1/6 4 1/6 5 1/6 6 1/6 B) x P(X = x) 1 5/18 2 1/4 3 7/36 4 5/36 5 1/9 6 1/36 C) x P(X = x) 1 11/36 2 1/4 3 7/36 4 5/36 5 1/12 6 1/36

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11)

12)

D) x P(X = x) 1 5/18 2 2/9 3 1/6 4 1/9 5 1/18 6 0 E) x P(X = x) 1 11/36 2 1/8 3 7/36 4 5/36 5 1/18 6 1/36 13) When a coin is tossed four times, sixteen equally likely outcomes are possible as shown below: HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT THHH THHT THTH THTT TTHH TTHT TTTH TTTT Let X denote the total number of tails obtained in the four tosses. Find the probability distribution of the random variable X. Leave your probabilities in fraction form.

A) x P(X = x) 1/16 0 1 3/16 2 1/2 3 3/16 1/16 4 B) x P(X = x) 0 1/16 1 1/8 2 3/8 3 1/8 4 1/16 C) x P(X = x) 1 1/4 2 7/16 3 1/4 4 1/16 D) x P(X = x) 0 0 1 1/4 2 3/8 3 1/4 4 1/16 Copyright © 2013 Pearson Education, Inc. 93

13)

E) x P(X = x) 0 1/16 1 1/4 2 3/8 3 1/4 4 1/16 Determine whether the conditions for the binomial distribution are satisfied. If the conditions are not satisfied, state why not.

14) X = number of Democrats in a sample of 500 voters selected randomly from a total of 2560 14) registered voters in one town. 42% of the 2560 registered voters are Democrats.

A) Conditions for binomial distribution are satisfied.

B) Conditions for binomial distribution are not satisfied. Trials are not independent. Sampling is without replacement and sample size is more than 10% of the population.

C) Conditions for binomial distribution are not satisfied. np is larger than 15.

D) Conditions for binomial distribution are not satisfied. Trials are not independent. Sampling is without replacement and the sample size is less than 20% of the population.

15) A polling agency in one city randomly selects 1000 registered voters from a pool of 385,600 registered voters of whom 17% are African American. X = number of African Americans in the sample.

A) Conditions for binomial distribution are not satisfied. Trials are not independent. Sampling is without replacement and sample size is less than 10% of population.

B) Conditions for binomial distribution are not satisfied. The probability of success is not the same on each trial.

C) Conditions for binomial distribution are not satisfied. There are more than two possible outcomes per trial.

D) Conditions for binomial distribution are satisfied.

Copyright © 2013 Pearson Education, Inc. 94

15)

Find the specified probability distribution of the binomial random variable.

16) In one city, 21% of the population is under 25 years of age. Three people are selected at random from the city. Find the probability distribution of X, the number among the three that are under 25 years of age. x P(X = x) 0.21 A) 1 2 0.0441 3 0.0213 x P(X = x) 0 0.4930 B) 1 0.3932 2 0.0925 3 0.0213 x P(X = x) 0 0.4930 C) 1 0.3932 2 0.1045 3 0.0093 x P(X = x) 0 0.4930 D) 1 0.1311 2 0.0348 3 0.0093 x P(X = x) 0.21 E) 1 2 0.0441 3 0.0093 Use a table of areas for the standard normal curve to find the required z -score.

17) Find the z-score for which the area under the standard normal curve to its left is 0.96 A) 1.03 B) -1.38 C) 1.75 D) 1.82 E) -1.75 18) Find the z-score having area 0.86 to its right under the standard normal curve.

A) -1.08 B) 0.8051 C) 0.5557 D) 1.08

16)

17)

18) E) -0.5557

Find the standard deviation of the binomial random variable.

19) A die is rolled 18 times and the number of twos that come up is tallied. If this experiment is repeated many times, find the standard deviation for the random variable X, the number of twos.

A) 1.537 B) 1.622 C) 2.5 D) 1.581 E) 1.73

19)

20) According to a college survey, 22% of all students work full time. Find the standard deviation for the random variable X, the number of students who work full time in samples of size 16.

A) 1.88 B) 1.98 C) 2.75 D) 3.52 E) 1.66

20)

21) The probability of winning a certain lottery is 1/51,949. For people who play 560 times, find the standard deviation for the random variable X, the number of wins.

A) 0.0108 B) 0.1038 C) 2.4569 D) 0.1137 E) 0.1223

21)

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Determine whether the conditions for the normal approximation to the binomial are satisfied.

22) In one town, 2% of adults are HIV positive. A researcher selects a random sample of 400 adults from a population of 23,250. X = number of people in the sample who are HIV positive. In this scenario, the conditions for the binomial distribution are satisfied. Is it reasonable to use the normal approximation to determine an interval within which X will almost certainly fall? Explain why or why not.

A) Yes, sampling is without replacement but the sample size is less than 10% of population.

B) No, np is less than 15.

C) Yes, as n is large.

D) No, the trials are not independent as sampling is without replacement.

Find the mean of the given probability distribution.

23) According to a survey, the percentage of households by number of vehicles is given in the following table:

22)

23)

(note, the category ʺ5ʺ actually represents 5 or more, but we will use ʺ5ʺ for ease of calculation) A) 188.2 B) 2 C) 2.5 D) 1.88 E) 1.5 24) The random variable X is the number of houses sold by a realtor in a single month at a particular real estate office. Its probability distribution is given in the table below. x P(X = x) 0 0.24 1 0.01 2 0.12 3 0.16 4 0.01 5 0.14 6 0.11 7 0.21 A) 3.35 B) 3.40 C) 3.50 D) 3.60

24)

25) The percentage of families by size in the U.S. is given in the table below.

25)

(note: the category ʺ7ʺ actually represents 7 or more but ʺ7ʺ will be used for calculation purposed) A) 3.1 B) 2.5 C) 2 D) 0.17 E) 4.5

Copyright © 2013 Pearson Education, Inc. 96

Answer Key Testname: CHAPTER_6_EXAM_B

1) 0.3804 2) 0.3520 3) E 4) E 5) E 6) D 7) E 8) A 9) D 10) A 11) B 12) C 13) E 14) B 15) D 16) C 17) C 18) A 19) D 20) E 21) B 22) B 23) D 24) D 25) A

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Chapter 7 Exam A Name___________________________________

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

Provide an appropriate response.

1) Which of the following sampling distributions of x has the least amount of variability?

I) μ = 50, σ = 10, n = 100 II) μ = 50, σ = 5, n = 30 III) μ = 50, σ = 10, n = 30 A) II B) not enough information because the variability depends upon the shape of the population distribution C) I D) not enough information because the variability depends upon the shape of the sampling distribution E) III

1)

2) Assume that the heights of adult Caucasian women have a mean of 63.6 inches and a standard deviation of 2.5 inches. If 100 women are randomly selected, find the probability that they have a mean height greater than 63.0 inches.

A) 0.0082 B) not enough information to determine C) 0.2881 D) 0.9918 E) 0.8989

2)

For samples of the specified size from the population described, find the mean and standard deviation of the sampling distribution of the sample mean x.

3) The mean and the standard deviation of the sampled population are, respectively, 77.4 and 4.0. n = 225 A) mean = 20.6; standard deviation = 0.8 B) mean = 20.6; standard deviation = 0.3 C) mean =0.3; standard deviation =77.4 D) mean = 77.4; standard deviation = 0.02 E) mean = 77.4; standard deviation = 0.3

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3)

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

Provide an appropriate response.

4) A recent poll of 1000 British adults asked, ʺIf there were a referendum on the issue, would you favor Britain becoming a republic or remaining a monarchy?ʺ Suppose that the population proportion favoring the monarchy equals 0.70. (This was, in fact, the value for the sample proportion.) For a random sample of 1000 residents, let X denote the number in this category.

4)

a. Find the mean of the probability distribution of X. b. Find the standard deviation of the probability distribution of X. Round to four decimal places. c. What range of values falls within 3 standard deviations of the mean? Round to four decimal places.

Explain why it is unlikely that X will fall outside this interval.

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

5) In an exit poll, for which the sample size is 3088, the sampling distribution of the sample proportion voting for the incumbent has mean 0.592 and standard deviation 0.009. Find an interval of values within which the sample proportion will almost certainly fall.

B) (0.583, 0.601) C) (0.592, 0.619) D) (0.565, 0.619) A) (0.574, 0.61)

5)

6) The body temperatures of adults have a mean of 98.6 ° F and a standard deviation of 0.60 ° F. If 36 adults are randomly selected, find the probability that their mean body temperature is greater than 98.4° F. A) not enough information to determine B) 0.9772 C) 0.0228 D) 0.8188 E) 0.9360

6)

7) Assume that the heights of adult Caucasian women have a mean of 63.6 inches and a standard deviation of 2.5 inches. If 75 women are randomly selected, find the probability that they have a mean height between 63 and 65 inches.

A) 0.3071 B) 0.9811 C) 0.2119 D) not enough information to determine E) 0.0188

7)

Is the observed sample proportion unusual?

8) Based on previous studies, researchers believe that 6% of children are born with a gene that is linked to a certain childhood disease. If the researchers test 950 newborns for the presence of this gene, would it be unlikely for them to find fewer than 25 children with the gene? Answer by calculating the appropriate z-score. Round to the nearest hundredth when necessary.

A) Yes, z = -6.59 B) Yes, z = -4.41 C) No, z = -0.005 D) No, z = -6.59 E) No, z = -4.41

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8)

Select the most appropriate answer.

9) A population distribution has mean 50 and standard deviation 20. For a random sample of size 100, the sampling distribution of the sample mean has A) mean and standard deviation that are unknown unless we know the exact shape of the population distribution.

B) mean 50/10 and standard deviation 20/10.

C) mean 50/100 and standard deviation 20/100.

D) mean 50 and standard deviation 2.

E) mean 50 and standard deviation 0.20.

9)

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

Provide an appropriate response.

10) If the proportion of American adults who believe that America is ready for a woman president is 0.70, what are the mean and standard deviation for the proportion of people who believe that America is ready for a woman president for a sample of size 1000?

10)

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

Is the observed sample proportion unusual?

11) Assume that 20% of students at a university wear contact lenses. We randomly pick 200 students.

Would it be unusual to obtain a sample proportion of 22%? Answer by calculating the appropriate z-score. Round to the nearest hundredth when necessary.

A) Yes, z = 0.71 B) Yes, z = 25 C) No, z = 0.71 D) No, z = 0.68 E) No, z = 25

11)

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

Provide an appropriate response.

12) If the proportion of American adults who feel that increases in gasoline prices have caused financial hardship for their family is 63%, what are the mean and standard deviation for the number of people who feel that increases in gasoline prices have caused their family financial hardship for a random sample of 100?

12)

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

13) In one region, the September energy consumption levels for single -family homes had a mean of 1050 kWh and a standard deviation of 218 kWh. If 50 different homes are randomly selected, find the probability that their mean energy consumption level for September is greater than 1075 kWh. B) 0.2910 C) 0.2090 D) 0.4562 E) 0.0438 A) 0.4180 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

14) The sampling distribution of sample means is from a highly skewed population with μ = 4.47 and σ = 1.40. For repeated random samples of size 100 from this population: a. Find the mean and standard deviation of the sampling distribution of the sample mean. b. Explain why the sampling distribution of the sample mean is bell -shaped, even though the population was highly skewed.

Copyright © 2013 Pearson Education, Inc. 100

14)

13)

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

Select the most appropriate answer.

15) The closer p is to 0 or 1, the larger n must be in order for the sampling distribution of the sample proportion to A) be approximately normal.

B) have a standard deviation equal to [p(1 - p)/n].

C) have a standard deviation equal to [n(p)(1 - p)].

D) be centered at p.

E) be approximately binomial.

Provide an appropriate response.

16) The body temperatures of adults have a mean of 98.6°F and a standard deviation of 0.60° F. Describe the center and variability of the sampling distribution of the sample mean for a random sample of 50 adults.

A) center = 98.6, variability = 0.07 B) center = 0.60, variability = 0.07 C) center = 98.6, variability = 0.14 D) center = 98.6, variability = 0.08 E) center = 98.6, variability = 0.008

15)

16)

17) The body temperatures of adults have a mean of 98.6°F and a standard deviation of 0.60° F. Describe the center and variability of the sampling distribution of the sample mean for a random sample of 75 adults.

A) center = 0.60, variability = 0.07 B) center = 98.6, variability = 0.008 C) center = 98.6, variability = 0.60 D) center = 98.6, variability = 0.14 E) center = 98.6, variability = 0.07

17)

18) Which of the following sampling distributions of x has the least amount of variability?

I) μ = 50, σ = 10, n = 100 II) μ = 5, σ = 5, n = 100 III) μ = 50, σ = 10, n = 30 A) II B) not enough information because the variability depends upon the shape of the population distribution C) III D) both I and II E) I

18)

19) In one region, the September energy consumption levels for single -family homes had a mean of 1050 kWh and a standard deviation of 218 kWh. Describe the center and variability of the sampling distribution of the sample mean for a random sample of 80 single-family homes from this region.

A) center = 1050, variability = 92.49 B) center = 1050, variability = 30.83 C) center = 1050, variability = 61.66 D) center = 1050, variability = 24.37 E) center = 1050, variability = 218

19)

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20) Which of the following is effected by a change in the sample size, n?

I) the population distribution

20)

II) the mean of the sampling distribution of x III) the standard deviation of the sampling distribution of x A) I only B) both II and III C) none of these D) III only E) II only 21) Assume that blood pressure readings have a mean of 120 and a standard deviation of 8. If 100 people are randomly selected, find the probability that their mean blood pressure will be greater than 122.

A) 0.8819 B) not enough information to determine C) 0.8615 D) 0.0062 E) 0.9938

21)

22) As the sample size increases, which of the following are true: I) the sample mean tends to fall closer to the population mean

22)

II) the sampling distribution of the sample mean x approximates the population distribution III) the standard deviation decreases A) I only B) both I and III C) III only D) all of these E) II only 23) In an exit poll, for which the sample size is 2656, the sampling distribution of the sample proportion voting for the incumbent has mean 0.493 and standard deviation 0.014. Would a

23)

^

sample proportion from the exit poll of p = 0.536 be a plausible value expected in the exit poll?

Why? A) No. It does not lie within one standard deviation of the mean sample proportion.

B) No. It does not lie within three standard deviations of the mean sample proportion.

C) Yes. It lies within two standard deviations of the mean sample proportion.

D) Yes. It lies within three standard deviations of the mean sample proportion.

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

24) A recent poll was taken to gauge the approval of adults for the European currency. Of the 1000 people sampled in a particular country in the European Union, consider the sample proportion of people who indicate approval of the euro. a. Find the mean and standard deviation of the sampling distribution for this sample proportion, if the population proportion equals 0.67. b. What shape would you expect this sampling distribution to have? Explain. Within what limits would the sample proportion almost certainly fall? Explain.

Copyright © 2013 Pearson Education, Inc. 102

24)

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

Find the mean and standard deviation of the sampling distribution of the proportion.

25) Assume that 26% of students at a university wear contact lenses. We randomly pick 300 students.

Describe the sampling distribution model of the proportion of students in this group who wear contact lenses.

A) mean = 26%; standard deviation = 1.1% B) mean = 26%; standard deviation = 2.5% C) There is not enough information to describe the distribution.

D) mean = 74%; standard deviation = 2.5% E) mean = 74%; standard deviation = 1.1%

Copyright © 2013 Pearson Education, Inc. 103

25)

Answer Key Testname: CHAPTER_7_EXAM_A

1) A 2) D 3) E 4) a. 700; b. 14.4914; c. 656.5258 to 743.4742; It is unlikely that X will fall outside this interval b/c np and n(1 - p) are both much greater than 15 which implies that X is approximately normally distributed. Therefore, the probability is very close to 1.0 that the number in this category would fall within 3 standard deviations of 700.

5) D 6) B 7) B 8) B 9) D 10) mean = 0.70, standard deviation = 0.014 11) C 12) mean = 63, standard deviation = 4.83 13) C 14) a. mean = 4.47, standard deviation = 0.14; b. The central limit theorem holds no matter what the shape of the population distribution. It states that for random samples of sufficiently large size (at least about 30), the sampling distribution of the sample means is approximately normal.

15) A 16) D 17) E 18) D 19) D 20) D 21) D 22) B 23) B 24) a. mean = 0.67, standard deviation = 0.0149; b. The sampling distribution would be approximately normal, b/c both np and n(1 - p) are much larger than 15. The sample proportion would almost certainly fall within 3(0.0149) = 0.0447 of the mean of 0.67, because the probability is very close to 1.0 that the sample proportion would fall within 3 standard deviations of the mean of 0.67 given that the sample proportions approximately follow a normal distribution.

25) B

Copyright © 2013 Pearson Education, Inc. 104

Chapter 7 Exam B Name___________________________________

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

Provide an appropriate response.

1) If the proportion of American adults who feel that increases in gasoline prices have caused financial hardship for their family is 63%, what are the mean and standard deviation for the number of people who feel that increases in gasoline prices have caused their family financial hardship for a random sample of 100?

1)

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

2) In one region, the September energy consumption levels for single -family homes had a mean of 1050 kWh and a standard deviation of 218 kWh. Describe the center and variability of the sampling distribution of the sample mean for a random sample of 80 single-family homes from this region.

A) center = 1050, variability = 30.83 B) center = 1050, variability = 24.37 C) center = 1050, variability = 218 D) center = 1050, variability = 61.66 E) center = 1050, variability = 92.49

2)

3) The body temperatures of adults have a mean of 98.6°F and a standard deviation of 0.60° F. Describe the center and variability of the sampling distribution of the sample mean for a random sample of 75 adults.

A) center = 98.6, variability = 0.07 B) center = 98.6, variability = 0.60 C) center = 0.60, variability = 0.07 D) center = 98.6, variability = 0.008 E) center = 98.6, variability = 0.14

3)

4) Which of the following is effected by a change in the sample size, n?

I) the population distribution

4)

II) the mean of the sampling distribution of x III) the standard deviation of the sampling distribution of x A) III only B) none of these C) I only D) II only E) both II and III 5) As the sample size increases, which of the following are true: I) the sample mean tends to fall closer to the population mean II) the sampling distribution of the sample mean x approximates the population distribution III) the standard deviation decreases A) III only B) all of these C) II only D) both I and III E) I only Copyright © 2013 Pearson Education, Inc. 105

5)

6) Assume that the heights of adult Caucasian women have a mean of 63.6 inches and a standard deviation of 2.5 inches. If 100 women are randomly selected, find the probability that they have a mean height greater than 63.0 inches.

A) 0.9918 B) 0.8989 C) not enough information to determine D) 0.0082 E) 0.2881

6)

7) Which of the following sampling distributions of x has the least amount of variability?

I) μ = 50, σ = 10, n = 100 II) μ = 50, σ = 5, n = 30 III) μ = 50, σ = 10, n = 30 A) II B) not enough information because the variability depends upon the shape of the population distribution C) III D) I E) not enough information because the variability depends upon the shape of the sampling distribution

7)

8) In an exit poll, for which the sample size is 3088, the sampling distribution of the sample proportion voting for the incumbent has mean 0.592 and standard deviation 0.009. Find an interval of values within which the sample proportion will almost certainly fall.

B) (0.565, 0.619) C) (0.592, 0.619) D) (0.583, 0.601) A) (0.574, 0.61)

8)

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

9) A recent poll of 1000 British adults asked, ʺIf there were a referendum on the issue, would you favor Britain becoming a republic or remaining a monarchy?ʺ Suppose that the population proportion favoring the monarchy equals 0.70. (This was, in fact, the value for the sample proportion.) For a random sample of 1000 residents, let X denote the number in this category.

9)

a. Find the mean of the probability distribution of X. b. Find the standard deviation of the probability distribution of X. Round to four decimal places. c. What range of values falls within 3 standard deviations of the mean? Round to four decimal places.

Explain why it is unlikely that X will fall outside this interval.

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

10) In one region, the September energy consumption levels for single -family homes had a mean of 1050 kWh and a standard deviation of 218 kWh. If 50 different homes are randomly selected, find the probability that their mean energy consumption level for September is greater than 1075 kWh. A) 0.0438 B) 0.2910 C) 0.2090 D) 0.4180 E) 0.4562 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

11) If the proportion of American adults who believe that America is ready for a woman president is 0.70, what are the mean and standard deviation for the proportion of people who believe that America is ready for a woman president for a sample of size 1000?

Copyright © 2013 Pearson Education, Inc. 106

11)

10)

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

12) Which of the following sampling distributions of x has the least amount of variability?

I) μ = 50, σ = 10, n = 100 II) μ = 5, σ = 5, n = 100 III) μ = 50, σ = 10, n = 30 A) not enough information because the variability depends upon the shape of the population distribution B) both I and II C) III D) II E) I

12)

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

13) The sampling distribution of sample means is from a highly skewed population with μ = 4.47 and σ = 1.40. For repeated random samples of size 100 from this population:

13)

a. Find the mean and standard deviation of the sampling distribution of the sample mean. b. Explain why the sampling distribution of the sample mean is bell -shaped, even though the population was highly skewed.

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

14) In an exit poll, for which the sample size is 2656, the sampling distribution of the sample proportion voting for the incumbent has mean 0.493 and standard deviation 0.014. Would a

14)

^

sample proportion from the exit poll of p = 0.536 be a plausible value expected in the exit poll?

Why? A) No. It does not lie within three standard deviations of the mean sample proportion.

B) No. It does not lie within one standard deviation of the mean sample proportion.

C) Yes. It lies within three standard deviations of the mean sample proportion.

D) Yes. It lies within two standard deviations of the mean sample proportion.

15) Assume that blood pressure readings have a mean of 120 and a standard deviation of 8. If 100 people are randomly selected, find the probability that their mean blood pressure will be greater than 122.

A) 0.9938 B) 0.8819 C) not enough information to determine D) 0.8615 E) 0.0062

15)

16) Assume that the heights of adult Caucasian women have a mean of 63.6 inches and a standard deviation of 2.5 inches. If 75 women are randomly selected, find the probability that they have a mean height between 63 and 65 inches.

A) 0.9811 B) not enough information to determine C) 0.3071 D) 0.0188 E) 0.2119

16)

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

17) A recent poll was taken to gauge the approval of adults for the European currency. Of the 1000 people sampled in a particular country in the European Union, consider the sample proportion of people who indicate approval of the euro.

17)

a. Find the mean and standard deviation of the sampling distribution for this sample proportion, if the population proportion equals 0.67. b. What shape would you expect this sampling distribution to have? Explain. Within what limits would the sample proportion almost certainly fall? Explain.

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

18) The body temperatures of adults have a mean of 98.6 ° F and a standard deviation of 0.60 ° F. If 36 adults are randomly selected, find the probability that their mean body temperature is greater than 98.4° F. A) 0.9772 B) not enough information to determine C) 0.9360 D) 0.8188 E) 0.0228

18)

19) The body temperatures of adults have a mean of 98.6°F and a standard deviation of 0.60° F. Describe the center and variability of the sampling distribution of the sample mean for a random sample of 50 adults.

A) center = 98.6, variability = 0.008 B) center = 98.6, variability = 0.07 C) center = 0.60, variability = 0.07 D) center = 98.6, variability = 0.14 E) center = 98.6, variability = 0.08

19)

Select the most appropriate answer.

20) The closer p is to 0 or 1, the larger n must be in order for the sampling distribution of the sample proportion to A) have a standard deviation equal to [n(p)(1 - p)].

B) be approximately normal.

C) be approximately binomial.

D) have a standard deviation equal to [p(1 - p)/n].

E) be centered at p.

21) A population distribution has mean 50 and standard deviation 20. For a random sample of size 100, the sampling distribution of the sample mean has A) mean 50 and standard deviation 0.20.

B) mean 50 and standard deviation 2.

C) mean 50/10 and standard deviation 20/10.

D) mean 50/100 and standard deviation 20/100.

E) mean and standard deviation that are unknown unless we know the exact shape of the population distribution.

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20)

21)

Is the observed sample proportion unusual?

22) Assume that 20% of students at a university wear contact lenses. We randomly pick 200 students.

Would it be unusual to obtain a sample proportion of 22%? Answer by calculating the appropriate z-score. Round to the nearest hundredth when necessary.

A) No, z = 0.71 B) Yes, z = 0.71 C) No, z = 25 D) No, z = 0.68 E) Yes, z = 25 23) Based on previous studies, researchers believe that 6% of children are born with a gene that is linked to a certain childhood disease. If the researchers test 950 newborns for the presence of this gene, would it be unlikely for them to find fewer than 25 children with the gene? Answer by calculating the appropriate z-score. Round to the nearest hundredth when necessary.

A) No, z = -4.41 B) No, z = -6.59 C) Yes, z = -4.41 D) No, z = -0.005 E) Yes, z = -6.59 Find the mean and standard deviation of the sampling distribution of the proportion.

24) Assume that 26% of students at a university wear contact lenses. We randomly pick 300 students.

Describe the sampling distribution model of the proportion of students in this group who wear contact lenses.

A) mean = 74%; standard deviation = 2.5% B) mean = 26%; standard deviation = 2.5% C) There is not enough information to describe the distribution.

D) mean = 26%; standard deviation = 1.1% E) mean = 74%; standard deviation = 1.1%

22)

23)

24)

For samples of the specified size from the population described, find the mean and standard deviation of the sampling distribution of the sample mean x.

25) The mean and the standard deviation of the sampled population are, respectively, 77.4 and 4.0. n = 225 A) mean = 77.4; standard deviation = 0.3 B) mean = 20.6; standard deviation = 0.3 C) mean =0.3; standard deviation =77.4 D) mean = 77.4; standard deviation = 0.02 E) mean = 20.6; standard deviation = 0.8

Copyright © 2013 Pearson Education, Inc. 109

25)

Answer Key Testname: CHAPTER_7_EXAM_B 1) mean = 63, standard deviation = 4.83 2) B 3) A 4) A 5) D 6) A 7) A 8) B 9) a. 700; b. 14.4914; c. 656.5258 to 743.4742; It is unlikely that X will fall outside this interval b/c np and n(1 - p) are both much greater than 15 which implies that X is approximately normally distributed. Therefore, the probability is very close to 1.0 that the number in this category would fall within 3 standard deviations of 700.

10) C 11) mean = 0.70, standard deviation = 0.014 12) B 13) a. mean = 4.47, standard deviation = 0.14; b. The central limit theorem holds no matter what the shape of the population distribution. It states that for random samples of sufficiently large size (at least about 30), the sampling distribution of the sample means is approximately normal.

14) A 15) E 16) A 17) a. mean = 0.67, standard deviation = 0.0149; b. The sampling distribution would be approximately normal, b/c both np and n(1 - p) are much larger than 15. The sample proportion would almost certainly fall within 3(0.0149) = 0.0447 of the mean of 0.67, because the probability is very close to 1.0 that the sample proportion would fall within 3 standard deviations of the mean of 0.67 given that the sample proportions approximately follow a normal distribution.

18) A 19) E 20) B 21) B 22) A 23) C 24) B 25) A

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Chapter 8 Exam A Name___________________________________

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

Find the margin of error 1) In a survey of 2300 T.V. viewers, 690 said they watch network news programs. Find the margin of error for the 95% confidence interval used to estimate the population proportion.

A) 0.0215 B) 0.0187 C) 0.0245 D) 0.0140 E) 0.0374 Select the most appropriate answer.

2) In an effort to monitor the level of lead in the air after an explosion at a battery factory, the following lead readings were taken for 6 days following the explosion (in ug/ m 3 ). What is the

1)

2)

point estimate for the population mean lead level in the air over the 6 days following the explosion?

Monday 5.40 A) 1.54

Tuesday 1.10 B) 2.91

Wednesday 0.42

Thursday 0.73

C) 0.50

Friday 0.48

Saturday 1.10

D) 0.42

E) 0.73

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

Provide an appropriate response.

3) When it is difficult to derive a standard error or confidence interval formula by using mathematical techniques, the method is used.

3)

4) A city council votes to appropriate funds for a new civic auditorium. The mayor of the city threatens to veto this decision unless it can be shown that a majority of citizens would use it at least twice a year. The council commissions a poll of city residents. For a random sample of 400 residents, 230 say they would use the facility at least twice a year. Find a 95% confidence interval for the proportion of all residents of the town who would say they would use the proposed auditorium at least twice a year. Interpret the interval and advise the mayor.

4)

5) How tall is your average English classmate? To determine this, you measure the height of a random sample of 15 of your 100 fellow students, finding a 95% confidence interval for the mean height of 67.25 to 69.75 inches.

5)

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

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion.

6) A survey of 865 voters in one state reveals that 408 favor approval of an issue before the 6) legislature. Construct a 95% confidence interval for the proportion of all voters in the state who favor approval.

A) (0.423, 0.520) B) (0.469, 0.475) C) (0.431, 0.512) D) (0.444, 0.500) E) (0.438, 0.505) Copyright © 2013 Pearson Education, Inc. 111

Select the most appropriate answer.

7) When determining the sample size for estimating a population proportion for a given level of confidence and a desired margin of error, the closer to 0.50 that p is estimated to be A) has no effect on the sample size required.

B) the smaller the sample size required.

C) the larger the sample size required.

D) has an undeterminable effect on the sample size required.

E) the farther from 0.50 that 1 - p is estimated to be.

7)

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

Provide an appropriate response.

8) Alarmed at the rising gas prices in your town, you decide to estimate the average gas price for a gallon of regular gas. From your sample of 25 gas stations, you calculate a 90% confidence interval of ($2.99, $3.11)

8)

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

9) In monitoring lead in the air after an explosion at a battery factory, it is found that the amounts of lead (in ug/m3) over a 6 day period had a standard error of 1.91. Find the margin of error that corresponds to a 95% confidence interval.

A) 1.91 B) 95 C) 3.74 D) 5.65 E) none of these Find the sample size 10) The drying times for a certain type of cement are normally distributed with a standard deviation of 73 minutes. A researcher wishes to estimate the mean drying time for this type of cement. Find the sample size needed to assure with 68% confidence that the sample mean will not differ from the population mean by more than 4 minutes.

B) 19 C) 5 D) 178 E) 3 A) 330 Select the most appropriate answer.

11) The large sample confidence interval formula for estimating p should only be used when A) n ≥ 30 ^

^

C) np ≥ 15 or n(1 - p) ≥ 15 ^

^

D) np ≥ 15 and n(1 - p) ≥ 15 ^

E) n(1 - p) ≥ 15 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

12) Thirty randomly selected students took the statistics final. If the sample mean was 82 and the standard deviation was 12.2, construct a 99% confidence interval for the mean score of all students.

13) A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 246 milligrams with s = 11.7 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.

Copyright © 2013 Pearson Education, Inc. 112

10)

11)

B) np ≥ 15 ^

9)

12)

13)

14) Which of the following statements about the t distribution is true?

14)

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

Find the margin of error 15) In a survey of 280 adults over 50, 75% said they were taking vitamin supplements. Find the margin of error for this survey if we want a 99% confidence in our estimate of the percentage of adults over 50 who take vitamin supplements.

B) 6.66% C) 5.07% D) 6.03% E) 13.3% A) 7.00%

15)

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

Provide an appropriate response.

16) A sample of 81 calculus students at a large college had a mean mathematics ACT score of 26 with a standard deviation of 6. Find a 95% confidence interval for the mean mathematics ACT score for all calculus students at this college.

16)

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

Find the margin of error 17) A recent poll of 500 residents in a large town found that only 36% were in favor of a proposed referendum to build a new high school. Find the margin of error for this poll if we want 95% confidence in our estimate of the percentage of residents in favor of this proposed referendum.

B) 5.53% C) 2.5% D) 3.52% E) 8.42% A) 4.21%

17)

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

Provide an appropriate response.

18) Physiologists often use the forced vital capacity as a way to assess a personʹs ability to move air in and out of their lungs. A researcher wishes to estimate the forced vital capacity of people suffering from asthma. A random sample of 15 asthmatics yields the following data on forced vital capacity, in liters.

18)

5.1 5.3 4.4 3.9 4.3 3.3 3.6 4.3 3.4 3.1 3.2 3.5 4.8 4.0 5.1 Use the data to obtain a point estimate of the mean forced vital capacity for all asthmatics.

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

Find the margin of error 19) A survey found that 89% of a random sample of 1024 American adults approved of cloning endangered animals. Find the margin of error for this survey if we want 90% confidence in our estimate of the percentage of American adults who approve of cloning endangered animals.

B) 4.85% C) 16.5% D) 1.92% E) 1.10% A) 1.61%

Copyright © 2013 Pearson Education, Inc. 113

19)

Provide an appropriate response.

20) In a poll of registered voters nationwide, the responses to the question ʺWho do you blame the most for the recent increase in gasoline prices: oil producing countries, oil companies, the President, Americans who drive vehicles that use a lot of gasoline, or normal supply and demand pressures?ʺ are given in the table that follows. Based on these responses, find a point estimate for the population proportion who would answer ʺthe President.ʺ

20)

Oil Companies 736 the President 342 Supply & Demand 222 Oil Producing Countries 188 American Drivers 68 Total 1556 A) 0.22 B) 311 C) 0.34 D) none of these E) 0.47 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

21) A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 95% confidence interval for the mean score of all such subjects.

21)

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

22) In practice a

is an estimated standard deviation of a sampling distribution.

22)

A) none of these B) sample standard deviation C) standard error.

D) margin of error E) population standard deviation 23) A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.3%, 5.1%). What is the point estimate of the mean percentage of reservations that are canceled on the day of the flight?

A) 3.20% B) 3.80% C) 1.90% D) 2.55% E) 5.10% Select the most appropriate answer.

24) The width of a confidence interval estimate for a proportion is A) narrower when the sample proportion is 0.10 than when the sample proportion is 0.45.

B) narrowest when the sample proportion is 0.5.

C) wider for 90% confidence than for 95% confidence.

D) narrower for a sample size of 50 than for a sample size of 100.

E) wider when the sample proportion is 0.95 than when the sample proportion is 0.55.

Copyright © 2013 Pearson Education, Inc. 114

23)

24)

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

Provide an appropriate response.

25) A poll asked whether marijuana should be legalized for medical purposes. 72% said definitely yes, 20% said probably, 2% said probably not, 5% said definitely not, and 2% had no opinion. a. Assuming that this was a random sample, construct a 95% confidence interval for the population proportion who would answer definitely yes or probably. Can you conclude that a majority of all Canadians would answer this way? Explain. b. Check that the sample size was large enough to construct the interval in (a).

Copyright © 2013 Pearson Education, Inc. 115

25)

Answer Key Testname: CHAPTER_8_EXAM_A

1) B 2) A 3) bootstrap 4) The 95% CI for p is (0.527, 0.623). None of the numbers in the confidence interval fall at or below 0.50. So we infer that more than half the population would use the new civic auditorium at least twice a year and advise the mayor not to veto the city councilʹs decision.

5) 1.25 inches 6) E 7) C 8) $0.06 9) C 10) A 11) D 12) (75.86, 88.14) 13) (238.6, 253.4) 14) It assumes the population is normally distributed.

15) B 16) (24.7, 27.3) 17) A 18) 4.09 liters 19) A 20) A 21) (67.7, 84.7) 22) C 23) A 24) A 25) a. A 95% CI for p is (0.896, 0.0944). Yes, since none of the values in the CI are at or below 0.50, one can conclude that a ^

^

majority of all Canadians would answer this way; b. Both np = 500(0.92) = 460 and n(1 - p) = 500(0.08) = 40 are at least 15, so the CI is valid.

Copyright © 2013 Pearson Education, Inc. 116

Chapter 8 Exam B Name___________________________________

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

Provide an appropriate response.

1) A poll asked whether marijuana should be legalized for medical purposes. 72% said definitely yes, 20% said probably, 2% said probably not, 5% said definitely not, and 2% had no opinion. a. Assuming that this was a random sample, construct a 95% confidence interval for the population proportion who would answer definitely yes or probably. Can you conclude that a majority of all Canadians would answer this way? Explain. b. Check that the sample size was large enough to construct the interval in (a).

1)

2) Which of the following statements about the t distribution is true?

2)

3) Physiologists often use the forced vital capacity as a way to assess a personʹs ability to move air in and out of their lungs. A researcher wishes to estimate the forced vital capacity of people suffering from asthma. A random sample of 15 asthmatics yields the following data on forced vital capacity, in liters.

3)

5.1 5.3 4.4 3.9 4.3 3.3 3.6 4.3 3.4 3.1 3.2 3.5 4.8 4.0 5.1 Use the data to obtain a point estimate of the mean forced vital capacity for all asthmatics.

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

4) In a poll of registered voters nationwide, the responses to the question ʺWho do you blame the most for the recent increase in gasoline prices: oil producing countries, oil companies, the President, Americans who drive vehicles that use a lot of gasoline, or normal supply and demand pressures?ʺ are given in the table that follows. Based on these responses, find a point estimate for the population proportion who would answer ʺthe President.ʺ Oil Companies 736 the President 342 Supply & Demand 222 Oil Producing Countries 188 American Drivers 68 Total 1556 A) none of these B) 311 C) 0.22 D) 0.47 E) 0.34

Copyright © 2013 Pearson Education, Inc. 117

4)

5) In monitoring lead in the air after an explosion at a battery factory, it is found that the amounts of lead (in ug/m3) over a 6 day period had a standard error of 1.91. Find the margin of error that corresponds to a 95% confidence interval.

A) 3.74 B) 5.65 C) 1.91 D) 95 E) none of these

5)

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

6) A sample of 81 calculus students at a large college had a mean mathematics ACT score of 26 with a standard deviation of 6. Find a 95% confidence interval for the mean mathematics ACT score for all calculus students at this college.

6)

7) A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 246 milligrams with s = 11.7 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.

7)

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

8) A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.3%, 5.1%). What is the point estimate of the mean percentage of reservations that are canceled on the day of the flight?

B) 5.10% C) 2.55% D) 3.20% E) 1.90% A) 3.80%

8)

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

9) Thirty randomly selected students took the statistics final. If the sample mean was 82 and the standard deviation was 12.2, construct a 99% confidence interval for the mean score of all students.

9)

10) Alarmed at the rising gas prices in your town, you decide to estimate the average gas price for a gallon of regular gas. From your sample of 25 gas stations, you calculate a 90% confidence interval of ($2.99, $3.11)

10)

11) A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 95% confidence interval for the mean score of all such subjects.

11)

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

12) In practice a

is an estimated standard deviation of a sampling distribution.

A) margin of error B) standard error.

C) population standard deviation D) none of these E) sample standard deviation

Copyright © 2013 Pearson Education, Inc. 118

12)

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

13) When it is difficult to derive a standard error or confidence interval formula by using method is used. mathematical techniques, the

13)

14) A city council votes to appropriate funds for a new civic auditorium. The mayor of the city threatens to veto this decision unless it can be shown that a majority of citizens would use it at least twice a year. The council commissions a poll of city residents. For a random sample of 400 residents, 230 say they would use the facility at least twice a year. Find a 95% confidence interval for the proportion of all residents of the town who would say they would use the proposed auditorium at least twice a year. Interpret the interval and advise the mayor.

14)

15) How tall is your average English classmate? To determine this, you measure the height of a random sample of 15 of your 100 fellow students, finding a 95% confidence interval for the mean height of 67.25 to 69.75 inches.

15)

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

Select the most appropriate answer.

16) The width of a confidence interval estimate for a proportion is A) narrower when the sample proportion is 0.10 than when the sample proportion is 0.45.

B) narrowest when the sample proportion is 0.5.

C) wider for 90% confidence than for 95% confidence.

D) wider when the sample proportion is 0.95 than when the sample proportion is 0.55.

E) narrower for a sample size of 50 than for a sample size of 100.

16)

17) When determining the sample size for estimating a population proportion for a given level of confidence and a desired margin of error, the closer to 0.50 that p is estimated to be A) has an undeterminable effect on the sample size required.

B) the smaller the sample size required.

C) the larger the sample size required.

D) has no effect on the sample size required.

E) the farther from 0.50 that 1 - p is estimated to be.

17)

18) The large sample confidence interval formula for estimating p should only be used when

18)

^

A) np ≥ 15 ^

B) n(1 - p) ≥ 15 ^

^

C) np ≥ 15 or n(1 - p) ≥ 15 ^

^

D) np ≥ 15 and n(1 - p) ≥ 15 E) n ≥ 30 19) In an effort to monitor the level of lead in the air after an explosion at a battery factory, the following lead readings were taken for 6 days following the explosion (in ug/ m 3 ). What is the point estimate for the population mean lead level in the air over the 6 days following the explosion?

Monday 5.40 A) 2.91

Tuesday 1.10 B) 0.50

Wednesday 0.42

Thursday 0.73

C) 0.42

Friday 0.48 D) 0.73

Copyright © 2013 Pearson Education, Inc. 119

Saturday 1.10 E) 1.54

19)

Find the margin of error 20) A recent poll of 500 residents in a large town found that only 36% were in favor of a proposed referendum to build a new high school. Find the margin of error for this poll if we want 95% confidence in our estimate of the percentage of residents in favor of this proposed referendum.

B) 2.5% C) 5.53% D) 4.21% E) 3.52% A) 8.42%

20)

21) In a survey of 280 adults over 50, 75% said they were taking vitamin supplements. Find the margin of error for this survey if we want a 99% confidence in our estimate of the percentage of adults over 50 who take vitamin supplements.

A) 5.07% B) 6.66% C) 13.3% D) 6.03% E) 7.00%

21)

22) In a survey of 2300 T.V. viewers, 690 said they watch network news programs. Find the margin of error for the 95% confidence interval used to estimate the population proportion.

A) 0.0374 B) 0.0245 C) 0.0215 D) 0.0140 E) 0.0187

22)

23) A survey found that 89% of a random sample of 1024 American adults approved of cloning endangered animals. Find the margin of error for this survey if we want 90% confidence in our estimate of the percentage of American adults who approve of cloning endangered animals.

A) 1.92% B) 16.5% C) 1.61% D) 1.10% E) 4.85%

23)

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion.

24) A survey of 865 voters in one state reveals that 408 favor approval of an issue before the 24) legislature. Construct a 95% confidence interval for the proportion of all voters in the state who favor approval.

A) (0.423, 0.520) B) (0.469, 0.475) C) (0.438, 0.505) D) (0.431, 0.512) E) (0.444, 0.500) Find the sample size 25) The drying times for a certain type of cement are normally distributed with a standard deviation of 73 minutes. A researcher wishes to estimate the mean drying time for this type of cement. Find the sample size needed to assure with 68% confidence that the sample mean will not differ from the population mean by more than 4 minutes.

B) 19 C) 178 D) 5 E) 3 A) 330

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25)

Answer Key Testname: CHAPTER_8_EXAM_B

1) a. A 95% CI for p is (0.896, 0.0944). Yes, since none of the values in the CI are at or below 0.50, one can conclude that a ^

^

majority of all Canadians would answer this way; b. Both np = 500(0.92) = 460 and n(1 - p) = 500(0.08) = 40 are at least 15, so the CI is valid.

2) It assumes the population is normally distributed.

3) 4.09 liters 4) C 5) A 6) (24.7, 27.3) 7) (238.6, 253.4) 8) D 9) (75.86, 88.14) 10) $0.06 11) (67.7, 84.7) 12) B 13) bootstrap 14) The 95% CI for p is (0.527, 0.623). None of the numbers in the confidence interval fall at or below 0.50. So we infer that more than half the population would use the new civic auditorium at least twice a year and advise the mayor not to veto the city councilʹs decision.

15) 1.25 inches 16) A 17) C 18) D 19) E 20) D 21) B 22) E 23) C 24) C 25) A

Copyright © 2013 Pearson Education, Inc. 121

Chapter 9 Exam A Name___________________________________

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

Determine the null and alternative hypotheses.

1) In the past, the mean running time for a certain type of radio battery has been 9.6 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has changed as a result.

A) H0 : μ ≠ 9.6 hours

1)

Ha : μ = 9.6 hours B) H0 : μ = 9.6hours Ha : μ > 9.6 hours C) H0 : μ = 9.6 hours Ha : μ ≠ 9.6 hours D) H0 : μ ≥ 9.6 hours Ha : μ = 9.6 hours E) H0 : μ > 9.6hours Ha : μ > 9.6 hours Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic t.

2) Test the claim that the mean lifetime of a particular car engine is greater than 220,000 miles.

2) Sample data are summarized as n = 23, x = 226,450 miles, and s = 11,500 miles. Use a significance level of α = 0.01. Find the test statistic t.

A) -2.69 B) 2.24 C) -2.24 D) 12.9 E) 2.69 Find the P-value for the indicated hypothesis test.

3) A manufacturer claims that fewer than 6% of its fax machines are defective. In a random sample of 100 such fax machines, 5% are defective. Find the P -value for testing the manufacturerʹs claim.

A) 0.17 B) 0.16 C) 0.34 D) 0.06 E) 0.33 Provide an appropriate response.

4) Suppose 1000 tests are run to test a null hypothesis using α = 0.05. If the null hypothesis is true, about how many of these tests would you expect to show statistically significant results?

A) 50 B) 1000 C) 0 D) cannot be determined from the information given E) 5 For the given significance test, determine the probability of a Type II error or the power, as specified.

5) Suppose we wish to test H0 : p = 0.25 against H1 : p > 0.25 using α = 0.05. If p is actually equal to 0.4, what is the power of the test assuming n = 55?

B) 0.27 C) 0.73 A) 0.93

D) 0.79

B) 0.90

C) 0.10

D) 0.05

Copyright © 2013 Pearson Education, Inc. 122

4)

5)

E) 0.21

Select the most appropriate answer.

6) Given Ha ≠ p0 . What is the P-value if the test statistics is calculated to be z = -0.12?

A) 0.95

3)

6) E) 0.12

7) A small P-value indicates which of the following?

I) the parameter value indicated by the null hypothesis is not plausible II) the null hypothesis should be rejected in favor of the alternative hypothesis III) the difference between the parameter value and the value specified in the null hypothesis is practically significant A) I, II, and III B) both I and II C) II only D) III only E) I only Provide an appropriate response.

8) A study uses a random sample of size 9. The test statistic for testing H0 : μ = 12 versus Ha : μ > 12

7)

8)

is t = 1.8. Find the approximate P-value.

A) 0.05 B) 0.95 C) Cannot be determined without the sample standard deviation.

D) 0.025 E) 0.10 For the given sample data and null hypothesis, compute the value of the test statistic, z 9) 410 people were asked if they were satisfied with their jobs. 37% of the responses were affirmative.

H0 : p = 0.30 A) 2.61

B) 0.04

C) 0.15

D) 4.12

9)

E) 3.09

For the given significance test, explain the meaning of a Type I error, a Type II error, or a correct decision as specified.

10) 10) A health insurer has determined that the ʺreasonable and customaryʺ fee for a certain medical procedure is $1200. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200. The insurer performs a significance test to determine whether their suspicion is correct using α = 0.05. The hypotheses are: H0 : μ = $1200 Ha : μ > $1200 If the P-value is 0.09 and a decision error is made, what type of error is it? Explain.

A) Type II error. We conclude that the average fee charged for the procedure is higher than $1200 when it actually is not higher.

B) Type I error. We conclude that the average fee charged for the procedure is not higher than $1200 when it actually is higher.

C) Type II error. We conclude that the average fee charged for the procedure is not higher than $1200 when it actually is higher.

D) Type I error. We conclude that the average fee charged for the procedure is higher than $1200 when it actually is not higher.

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

Provide an appropriate response.

11) A sample was used to obtain a 95% confidence interval for the population mean age of graduate students at a large university. The 95% confidence interval for μ was (23, 27). If the same sample had been used to test the null hypothesis that the population mean age is equal to 28 versus the alternative hypothesis that the population mean age differs from 28, would the null hypothesis be rejected at α = 0.05? Explain.

Copyright © 2013 Pearson Education, Inc. 123

11)

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

For the given significance test, determine the probability of a Type II error or the power, as specified.

12) Suppose we wish to test H0 : p = 0.5 against H1 : p < 40 using α = 0.05. If p is actually equal to 0.4, what is the probability of a type II error assuming n = 150?

B) 0.21 C) 0.69 A) 0.31

D) 0.79

12)

E) 0.05

For the given significance test, explain the meaning of a Type I error, a Type II error, or a correct decision as specified.

13) At one school, the average amount of time tenth-graders spend watching television each week is 13) 21.6 hours. The principal introduces a campaign to encourage the students to watch less television.

One year later, the principal performs a significance test using α = 0.05 to determine whether the average amount of time spent watching television per week has decreased. The hypotheses are: H0 : μ = 21.6 hours Ha : μ < 21.6 hours If the P-value = 0.04 and a decision error is made, what type of error is it? Explain.

A) Type I error. We conclude that the average amount of time spent watching television each week is less than 21.6 hours when it in fact is not.

B) Type II error. We conclude that the average amount of time spent watching television each week is less than 21.6 hours when it in fact is not.

C) Type II error. We conclude that the average amount of time spent watching television each week is 21.6 hours when it is in fact less.

D) Type I error. We conclude that the average amount of time spent watching television each week is 21.6 hours when it is in fact less.

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

Provide an appropriate response.

14) About 4% of Americans are vegetarians. For a random sample of 400 students at University X, suppose that none are vegetarians.

14)

a. Set up null and alternative hypotheses for testing whether the proportion of vegetarians is the same or different at that university than nationwide. Check that the sample size is large enough for the test. b. Find the sample proportion, standard error, and test statistic. c. Find the P-value. Is there strong evidence that the proportion of vegetarians at the university differs from 0.04?

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

Select the most appropriate answer.

15) The test statistic for testing H0 : μ = 100 against Ha : μ ≠ 100 was t = 3.3, with P-value 0.001. Which of the following is the appropriate conclusion?

A) In order to interpret the results, we must first know the sample size.

B) Since the P-value is very small, we are unable to conclude that μ ≠ 100.

C) Since the P-value is very small, we conclude that μ = 100.

D) Since the P-value is very small, we are unable to conclude that μ = 100.

E) Since the P-value is very small, we conclude that μ ≠ 100.

Copyright © 2013 Pearson Education, Inc. 124

15)

16) Which of the following would be an appropriate null hypothesis?

A) The sample mean is equal to 3.4.

B) The population mean is greater than 3.4.

C) The sample mean is greater than 3.4.

D) The population mean is not equal to 3.4.

E) The population mean is equal to 3.4.

16)

17) A researcher claims that less than 20% of American adults are allergic to pollen. In a random sample of 100 adults, 15% indicate that they have such an allergy. Calculate the test statistic z for the population proportion.

A) -1.25 B) none of these C) 1.645 D) 1.25 E) 1.96

17)

Find the P-value for the indicated hypothesis test.

18) A medical school claims that more than 28% of its students plan to go into general practice. It is found that among a random sample of 130 of the schoolʹs students, 39% of them plan to go into general practice. Find the P-Value for testing the schoolʹs claim.

B) 0.3078 C) 0.0026 D) 0.3461 E) 0.0280 A) 0.1635 Classify the conclusion of the significance test as a Type I error, a Type II error, or No error.

19) A health insurer has determined that the ʺreasonable and customaryʺ fee for a certain medical procedure is $1200. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200. The insurer wants to perform a significance test to determine whether their suspicion is correct. The hypotheses are: H0 : μ = $1200

18)

19)

Ha : μ > $1200 Suppose that the results of the sample lead to rejection of the null hypothesis. Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the average fee charged by the clinic is $1200 .

B) No error C) Type I error A) Type II error State hypotheses for the significance test.

20) Last year, the results of a survey at one college suggested that 28% of students smoked regularly.

This year, after an intensive college-wide anti-smoking campaign, a researcher wishes to investigate whether the proportion of smokers has changed. Let p represent the proportion of students who smoke regularly today. State hypotheses for a significance test, letting the alternative hypothesis reflect the possibility that the proportion of students who smoke today is different from the proportion last year.

B) H0 : p = 28% C) H0 : p ≠ 28% D) H0 : p = 28% A) H0 : p > 28% Ha : p < 28%

Ha : p ≥ 28%

Ha : p = 28%

Select the most appropriate answer.

21) Which of the following would be an appropriate alternative hypothesis?

A) The sample proportion is not equal to 0.41.

B) The population proportion is equal to 0.41.

C) The sample proportion is less than 0.41.

D) The population proportion is less than 0.41.

E) The sample proportion is equal to 0.41.

Copyright © 2013 Pearson Education, Inc. 125

20)

Ha : p ≠ 28%

21)

Determine the null and alternative hypotheses.

22) A health insurer has determined that the ʺreasonable and customaryʺ fee for a certain medical procedure is $1200. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200. The insurer wants to perform a hypothesis test to determine whether their suspicion is correct.

A) H0 : μ = $1200

22)

Ha : μ < $1200 B) H0 : μ > $1200 Ha : μ < $1200 C) H0 : μ = $1200 Ha : μ ≥ $1200 D) H0 : μ = $1200 Ha : μ > $1200 E) H0 : μ > $1200 Ha : μ = $1200 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

23) The mean score for all U.S. high school seniors taking the SAT college entrance exam equals 500. A study is conducted to see whether a different mean applies to Canadian seniors. For a random sample of 100 Canadian seniors, suppose the mean and standard deviation on this exam equal 508 and 100. a. b.

23)

Set up hypotheses for a significance test, and compute the test statistic.

The P-value is 0.43. Interpret it, and make a decision about H0 , using a significance

level of 0.05. c. If the decision in (b) was in error, what type of error is it? d. A 95% confidence interval for μ is (488.2, 527.8). Show the correspondence between the decision in the test and whether 500 falls in this confidence interval.

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

Assume that a simple random sample has been selected from a normally distributed population. State the final conclusion.

24) Test the claim that for the population of female college students at a particular university, the 24) mean weight is given by μ = 132 lb. Sample data are summarized as n = 20, x = 137 lb, and s = 14.2 lb. Use a significance level of α = 0.1.

H0 : μ = 132 Ha : μ ≠ 132 State your conclusion about H0 .

A) t = 7.04, reject H0 B) t = 1.57, do not reject H0 C) z = 1.57, do not reject H0 D) t = 1.57, reject H0 E) t = -1.57, do not reject H0

Copyright © 2013 Pearson Education, Inc. 126

Select the most appropriate answer.

25) A research company claims that more than 55% of Americans regularly watch public access television. You decide to test this claim and ask a random sample of 425 Americans if they watch these programs regularly. Of the 425, 255 respond yes. Calculate the test statistic z for the population proportion.

A) none of these B) -2.07 C) 2.07 D) 1.645 E) -1.96

Copyright © 2013 Pearson Education, Inc. 127

25)

Answer Key Testname: CHAPTER_9_EXAM_A

1) C 2) E 3) C 4) A 5) D 6) B 7) E 8) A 9) E 10) C 11) Yes, because all of the values in the confidence interval differ from 28.

12) B 13) A ^

^

14) a. H0 : p = 0.04, Ha : p ≠ 0.04, both np0 and n(1-p0 ) are at least 15; b. p = 0, SE(p) = 0.0098, z = -4.08; c.

P-value < 0.0001, There is sufficient evidence at α = 0.05 that the proportion of vegetarians at the university differs from 0.04. Note: Because the P-value is so small, the result is statistically significant at α = 0.01 as well.

15) E 16) E 17) A 18) C 19) C 20) D 21) D 22) D 23) a. H0 : μ = 500, Ha : μ ≠ 500, t = 0.8; b. the approximate probability that x takes a value of greater than or equal to 508 or less than or equal to 492 if H0 is true is 0.43, at α = 0.05, P-value > α, fail to reject H0 , there is not sufficient evidence that a different mean applies to Canadian seniors; c. Type II error; d. The 95% CI does contain the H0 value. This indicates (as the two-sided test at a 0.05 significance level indicated) that there is not sufficient evidence that a different mean applies to Canadian seniors.

24) B 25) C

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Chapter 9 Exam B Name___________________________________

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

Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic t.

1) Test the claim that the mean lifetime of a particular car engine is greater than 220,000 miles.

1) Sample data are summarized as n = 23, x = 226,450 miles, and s = 11,500 miles. Use a significance level of α = 0.01. Find the test statistic t.

A) 12.9 B) -2.24 C) 2.69 D) -2.69 E) 2.24 For the given significance test, determine the probability of a Type II error or the power, as specified.

2) Suppose we wish to test H0 : p = 0.5 against H1 : p < 40 using α = 0.05. If p is actually equal to 0.4, what is the probability of a type II error assuming n = 150?

A) 0.79 B) 0.31 C) 0.21

D) 0.69

E) 0.05

3) Suppose we wish to test H0 : p = 0.25 against H1 : p > 0.25 using α = 0.05. If p is actually equal to 0.4, what is the power of the test assuming n = 55?

A) 0.21 B) 0.27 C) 0.79

D) 0.73

2)

3)

E) 0.93

Select the most appropriate answer.

4) A small P-value indicates which of the following?

I) the parameter value indicated by the null hypothesis is not plausible II) the null hypothesis should be rejected in favor of the alternative hypothesis III) the difference between the parameter value and the value specified in the null hypothesis is practically significant A) III only B) I, II, and III C) II only D) I only E) both I and II

4)

5) Which of the following would be an appropriate null hypothesis?

A) The population mean is greater than 3.4.

B) The population mean is not equal to 3.4.

C) The population mean is equal to 3.4.

D) The sample mean is equal to 3.4.

E) The sample mean is greater than 3.4.

5)

6) A research company claims that more than 55% of Americans regularly watch public access television. You decide to test this claim and ask a random sample of 425 Americans if they watch these programs regularly. Of the 425, 255 respond yes. Calculate the test statistic z for the population proportion.

A) 1.645 B) -2.07 C) 2.07 D) none of these E) -1.96

6)

Copyright © 2013 Pearson Education, Inc. 129

7) Given Ha ≠ p0 . What is the P-value if the test statistics is calculated to be z = -0.12?

A) 0.95

B) 0.10

C) 0.05

D) 0.90

7) E) 0.12

8) The test statistic for testing H0 : μ = 100 against Ha : μ ≠ 100 was t = 3.3, with P-value 0.001. Which

8)

of the following is the appropriate conclusion?

A) Since the P-value is very small, we conclude that μ = 100.

B) Since the P-value is very small, we are unable to conclude that μ = 100.

C) Since the P-value is very small, we conclude that μ ≠ 100.

D) Since the P-value is very small, we are unable to conclude that μ ≠ 100.

E) In order to interpret the results, we must first know the sample size.

9) Which of the following would be an appropriate alternative hypothesis?

A) The population proportion is less than 0.41.

B) The sample proportion is equal to 0.41.

C) The sample proportion is less than 0.41.

D) The sample proportion is not equal to 0.41.

E) The population proportion is equal to 0.41.

9)

10) A researcher claims that less than 20% of American adults are allergic to pollen. In a random sample of 100 adults, 15% indicate that they have such an allergy. Calculate the test statistic z for the population proportion.

A) 1.645 B) none of these C) 1.96 D) 1.25 E) -1.25

10)

Assume that a simple random sample has been selected from a normally distributed population. State the final conclusion.

11) Test the claim that for the population of female college students at a particular university, the 11) mean weight is given by μ = 132 lb. Sample data are summarized as n = 20, x = 137 lb, and s = 14.2 lb. Use a significance level of α = 0.1.

H0 : μ = 132 Ha : μ ≠ 132 State your conclusion about H0 .

A) z = 1.57, do not reject H0 B) t = -1.57, do not reject H0 C) t = 1.57, reject H0 D) t = 1.57, do not reject H0 E) t = 7.04, reject H0 Find the P-value for the indicated hypothesis test.

12) A medical school claims that more than 28% of its students plan to go into general practice. It is found that among a random sample of 130 of the schoolʹs students, 39% of them plan to go into general practice. Find the P-Value for testing the schoolʹs claim.

A) 0.3078 B) 0.0026 C) 0.1635 D) 0.0280 E) 0.3461 13) A manufacturer claims that fewer than 6% of its fax machines are defective. In a random sample of 100 such fax machines, 5% are defective. Find the P -value for testing the manufacturerʹs claim.

A) 0.33 B) 0.16 C) 0.34 D) 0.06 E) 0.17 Copyright © 2013 Pearson Education, Inc. 130

12)

13)

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

Provide an appropriate response.

14) The mean score for all U.S. high school seniors taking the SAT college entrance exam equals 500. A study is conducted to see whether a different mean applies to Canadian seniors. For a random sample of 100 Canadian seniors, suppose the mean and standard deviation on this exam equal 508 and 100. a. b.

14)

Set up hypotheses for a significance test, and compute the test statistic.

The P-value is 0.43. Interpret it, and make a decision about H0 , using a significance

level of 0.05. c. If the decision in (b) was in error, what type of error is it? d. A 95% confidence interval for μ is (488.2, 527.8). Show the correspondence between the decision in the test and whether 500 falls in this confidence interval.

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

15) Suppose 1000 tests are run to test a null hypothesis using α = 0.05. If the null hypothesis is true, about how many of these tests would you expect to show statistically significant results?

A) 50 B) 5 C) cannot be determined from the information given D) 0 E) 1000

15)

16) A study uses a random sample of size 9. The test statistic for testing H0 : μ = 12 versus Ha : μ > 12

16)

is t = 1.8. Find the approximate P-value.

A) 0.05 B) 0.025 C) Cannot be determined without the sample standard deviation.

D) 0.95 E) 0.10 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

17) A sample was used to obtain a 95% confidence interval for the population mean age of graduate students at a large university. The 95% confidence interval for μ was (23, 27). If the same sample had been used to test the null hypothesis that the population mean age is equal to 28 versus the alternative hypothesis that the population mean age differs from 28, would the null hypothesis be rejected at α = 0.05? Explain.

17)

18) About 4% of Americans are vegetarians. For a random sample of 400 students at University X, suppose that none are vegetarians.

18)

a. Set up null and alternative hypotheses for testing whether the proportion of vegetarians is the same or different at that university than nationwide. Check that the sample size is large enough for the test. b. Find the sample proportion, standard error, and test statistic. c. Find the P-value. Is there strong evidence that the proportion of vegetarians at the university differs from 0.04?

Copyright © 2013 Pearson Education, Inc. 131

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

Classify the conclusion of the significance test as a Type I error, a Type II error, or No error.

19) A health insurer has determined that the ʺreasonable and customaryʺ fee for a certain medical procedure is $1200. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200. The insurer wants to perform a significance test to determine whether their suspicion is correct. The hypotheses are: H0 : μ = $1200

19)

Ha : μ > $1200 Suppose that the results of the sample lead to rejection of the null hypothesis. Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the average fee charged by the clinic is $1200 .

B) Type I error C) No error A) Type II error For the given significance test, explain the meaning of a Type I error, a Type II error, or a correct decision as specified.

20) At one school, the average amount of time tenth-graders spend watching television each week is 20) 21.6 hours. The principal introduces a campaign to encourage the students to watch less television.

One year later, the principal performs a significance test using α = 0.05 to determine whether the average amount of time spent watching television per week has decreased. The hypotheses are: H0 : μ = 21.6 hours Ha : μ < 21.6 hours If the P-value = 0.04 and a decision error is made, what type of error is it? Explain.

A) Type I error. We conclude that the average amount of time spent watching television each week is 21.6 hours when it is in fact less.

B) Type II error. We conclude that the average amount of time spent watching television each week is less than 21.6 hours when it in fact is not.

C) Type II error. We conclude that the average amount of time spent watching television each week is 21.6 hours when it is in fact less.

D) Type I error. We conclude that the average amount of time spent watching television each week is less than 21.6 hours when it in fact is not.

21) A health insurer has determined that the ʺreasonable and customaryʺ fee for a certain medical procedure is $1200. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200. The insurer performs a significance test to determine whether their suspicion is correct using α = 0.05. The hypotheses are: H0 : μ = $1200 Ha : μ > $1200 If the P-value is 0.09 and a decision error is made, what type of error is it? Explain.

A) Type II error. We conclude that the average fee charged for the procedure is not higher than $1200 when it actually is higher.

B) Type I error. We conclude that the average fee charged for the procedure is not higher than $1200 when it actually is higher.

C) Type II error. We conclude that the average fee charged for the procedure is higher than $1200 when it actually is not higher.

D) Type I error. We conclude that the average fee charged for the procedure is higher than $1200 when it actually is not higher.

Copyright © 2013 Pearson Education, Inc. 132

21)

Determine the null and alternative hypotheses.

22) In the past, the mean running time for a certain type of radio battery has been 9.6 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has changed as a result.

A) H0 : μ ≠ 9.6 hours

22)

Ha : μ = 9.6 hours B) H0 : μ = 9.6hours Ha : μ > 9.6 hours C) H0 : μ > 9.6hours Ha : μ > 9.6 hours D) H0 : μ ≥ 9.6 hours Ha : μ = 9.6 hours E) H0 : μ = 9.6 hours Ha : μ ≠ 9.6 hours 23) A health insurer has determined that the ʺreasonable and customaryʺ fee for a certain medical procedure is $1200. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200. The insurer wants to perform a hypothesis test to determine whether their suspicion is correct.

A) H0 : μ = $1200

23)

Ha : μ < $1200 B) H0 : μ > $1200 Ha : μ < $1200 C) H0 : μ > $1200 Ha : μ = $1200 D) H0 : μ = $1200 Ha : μ > $1200 E) H0 : μ = $1200 Ha : μ ≥ $1200 For the given sample data and null hypothesis, compute the value of the test statistic, z 24) 410 people were asked if they were satisfied with their jobs. 37% of the responses were affirmative.

H0 : p = 0.30 A) 2.61

B) 4.12

C) 0.15

D) 0.04

E) 3.09

State hypotheses for the significance test.

25) Last year, the results of a survey at one college suggested that 28% of students smoked regularly.

This year, after an intensive college-wide anti-smoking campaign, a researcher wishes to investigate whether the proportion of smokers has changed. Let p represent the proportion of students who smoke regularly today. State hypotheses for a significance test, letting the alternative hypothesis reflect the possibility that the proportion of students who smoke today is different from the proportion last year.

B) H0 : p = 28% C) H0 : p > 28% D) H0 : p ≠ 28% A) H0 : p = 28% Ha : p ≥ 28%

Ha : p ≠ 28%

Ha : p < 28%

Copyright © 2013 Pearson Education, Inc. 133

24)

Ha : p = 28%

25)

Answer Key Testname: CHAPTER_9_EXAM_B

1) C 2) C 3) C 4) D 5) C 6) C 7) D 8) C 9) A 10) E 11) D 12) B 13) C 14) a. H0 : μ = 500, Ha : μ ≠ 500, t = 0.8; b. the approximate probability that x takes a value of greater than or equal to 508 or less than or equal to 492 if H0 is true is 0.43, at α = 0.05, P-value > α, fail to reject H0 , there is not sufficient evidence that a different mean applies to Canadian seniors; c. Type II error; d. The 95% CI does contain the H0 value. This indicates (as the two-sided test at a 0.05 significance level indicated) that there is not sufficient evidence that a different mean applies to Canadian seniors.

15) A 16) A 17) Yes, because all of the values in the confidence interval differ from 28. ^

^

18) a. H0 : p = 0.04, Ha : p ≠ 0.04, both np0 and n(1-p0 ) are at least 15; b. p = 0, SE(p) = 0.0098, z = -4.08; c.

P-value < 0.0001, There is sufficient evidence at α = 0.05 that the proportion of vegetarians at the university differs from 0.04. Note: Because the P-value is so small, the result is statistically significant at α = 0.01 as well.

19) B 20) D 21) A 22) E 23) D 24) E 25) B

Copyright © 2013 Pearson Education, Inc. 134

Chapter 10 Exam A Name___________________________________

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

Use the paired t-interval procedure to obtain the required confidence interval for the mean difference. Assume that the conditions and assumptions for inference are satisfied.

1) 1) Ten families are randomly selected and their daily water usage (in gallons) before and after viewing a conservation video. Construct a 90% confidence interval for the mean of the difference of the ʺbeforeʺ minus the ʺafterʺ times if d(after-before) = -4.8 and sd = 5.2451 Before 33 33 38 33 35 35 40 40 40 31 After 34 28 25 28 35 33 31 28 35 33 A) (2.1,7.5) B) (1.5,8.1) C) (2.5,7.1)

D) (3.8,5.8)

E) (1.8,7.8)

Find the appropriate test statistic/p-value.

2) Do motivation levels between mid-level and upper-level managers differ? A randomly selected group of each were administered a survey, which measures motivation for upward mobility. The scores are summarized below:

Sample Size Mean Score Standard Deviation

upper-level 173 77.4 11.06

2)

mid-level 109 79.71 6.43

Given that the P-value is 0.03, which of the following is the appropriate conclusion?

A) At α = .025, reject H0 .

B) At α = .025, fail to reject H0 .

C) At α = .02, accept H0 .

D) At α = .01, reject H0 .

E) At α = .02, reject H0 .

Provide an appropriate response.

3) An agricultural company would like to predict cotton yield per acre in a certain area using rainfall (in inches). Identify the response variable.

A) rainfall in inches B) farm size C) variety of cotton grown D) yield per acre E) the agricultural company

Copyright © 2013 Pearson Education, Inc. 135

3)

Interpret the given confidence interval.

4) A survey was conducted to determine the difference in gasoline mileage for two truck models. A random sample was taken for each model of truck, and the mean gasoline mileage, in miles per gallon, was calculated. A 98% confidence interval for the difference in the mean mileage for model A trucks minus the mean mileage for model B trucks, μA - μB, was determined to be (2.5, 4.7).

4)

A) The probability that a randomly selected Model A truck will have a gas mileage that is lower than a randomly selected model B truck is 0.98.

B) 98% of model A trucks have a gas mileage that is between 2.5 and 4.7 miles per gallon higher than model B trucks.

C) The probability that a randomly selected Model A truck will have a gas mileage that is higher than a randomly selected model B truck is 0.98.

D) Based on this sample, we are 98% confident that the average mileage for model B trucks is between 2.5 and 4.7 miles per gallon higher than the average mileage for model A trucks.

E) Based on this sample, we are 98% confident that the average mileage for model A trucks is between 2.5 and 4.7 miles per gallon higher than the average mileage for model B trucks. ^

^

From the sample statistics, find the value of p1 - p2 , the point estimate of the difference of proportions. Unless otherwise indicated, round to the nearest thousandth when necessary.

5) n 1 = 1927 n 2 = 541

5)

x1 = 689

x2 = 160 A) none of these B) 0.062 C) 0.214 D) 0.382 E) -0.62

Provide an appropriate response.

6) Do motivation levels between mid-level and upper-level managers differ? A randomly selected group of each were administered a survey, which measures motivation for upward mobility. The scores are summarized below:

Sample Size Mean Score Standard Deviation

upper-level 73 77.4 10.06

mid-level 109 79.71 6.43

Assuming equal population standard deviations, calculate the test statistic for determining whether the mean scores differ for upper-level and mid-level managers.

A) none of these B) -0.29 C) -63.69 D) -1.89 E) -1.74

Copyright © 2013 Pearson Education, Inc. 136

6)

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

7) When testing for a difference between the means of a treatment group and a placebo group, the computer display below is obtained.

Variable: TREATMENT N Mean Std Dev

Std Error

treatment 50 placebo 50

0.403 0.453

65.107 66.183

2.847 3.205

7)

Use technology to find a 95% confidence interval for the difference of the mean of the treatment and the mean of the placebo group.

8) Using the formula se =

s1 2 s2 2 , show that the standard error of (x1 - x2 ) is greater + n1 n2

8)

than both se(x1 ) and se(x2 ).

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

Answer true or false.

9) The F test for comparing standard deviations is robust.

A) True B) False Provide an appropriate response.

10) The recent admissions for the humanities and sciences at a certain college are given in the table below. What percentage of men who applied within the two areas was accepted? What percentage of women who applied within the two areas was accepted?

Humanities Accepted Rejected Sciences Accepted Rejected Total

Men

Women

190 140

503 422

160 210 700

27 48 1000

9)

10)

A) 50% of men and 53% of women who applied within the two areas were accepted.

B) 21% of men and 31% of women who applied within the two areas were accepted.

C) 23% of men and 2.7% of women who applied within the two areas were accepted.

D) 51% of men and 45% of women who applied within the two areas were accepted.

E) 27% of men and 50% of women who applied within the two areas were accepted.

11) A researcher is interested in the academic performance differences between individuals using an optimistic versus a pessimistic approach to their studies. If the researcher fails to find a significant difference, when in fact one exists in the population: A) the null hypothesis was correctly rejected.

B) the research hypothesis was correctly accepted.

C) a Type II error has been made.

D) the null hypothesis was correctly accepted.

E) a Type I error has been made.

Copyright © 2013 Pearson Education, Inc. 137

11)

^

^

From the sample statistics, find the value of p1 - p2 , the point estimate of the difference of proportions. Unless otherwise indicated, round to the nearest thousandth when necessary.

12) A survey asked respondents whether marijuana should be made legal. A 95% confidence interval for PA - PB is given by (0.08, 0.14) where PA is the proportion of respondents who answered

12)

ʺlegalʺ in state A and PB is the proportion of respondents who responded ʺlegalʺ in state B. Based on the 95% confidence interval, what can we conclude about the percentage of respondents who favor legalization in state B versus state A? A) Since all of the values in the confidence interval are less than 1, we are unable to conclude that there is a significant difference between the percentage in favor of legalization in state B and the percentage in favor of legalization in state A. B) Since all of the values in the confidence interval are greater than 0, we can conclude that the percentage in favor of legalization was greater in state A than it was in state B. C) Since all of the values in the confidence interval are greater than 0, we can conclude that the percentage in favor of legalization was greater in state B than it was in state A. D) Since all of the values in the confidence interval are less than 1, we can conclude that there is a significant difference between the percentage in favor of legalization in state B and the percentage in favor of legalization in state A. 13) n 1 = 100

n 2 = 100

x1 = 34

x2 = 30

13)

A) none of these B) 0.02 C) -0.04 D) 0.04 E) -0.02 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

14) Three editors of large-city newspapers are selected at random and asked to rate on a score of 0 to 100 the fairness of the news media in political reporting (0 corresponds to very unfair). The same question is posed to three editors of small -town papers. The large-city editors gave scores of 55, 90, and 95; while, the small-town editors gave scores of 40, 60, and 80. The table shows a computer printout for results of a two -sample comparison of means.

Variable: FAIRNESS PAPER N Mean

Std Dev

Std Error

large small

21.794 20.000

12.583 11.547

3 3

80.00 60.00

14)

Use technology to find a 95% confidence interval for the difference of the means.

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

Answer true or false.

15) The width of the confidence interval for (μ1 - μ2 ) increases as s1 and s2 increase.

A) True

B) False

Copyright © 2013 Pearson Education, Inc. 138

15)

Select the most appropriate answer.

16) For 12 pairs of females, the reported means are 24.8 on the well-being measure for the children of alcoholics and 29.0 for the control group. A t test statistic of 2.67 for the test comparing the means was obtained. Assuming that this is the result of a dependent-samples analysis testing for a difference between the group means, report the P-value.

A) 0.02 < P-value < 0.05 B) 0.005 < P-value < 0.01 C) 0.0076 D) 0.01 < P-value < 0.02 E) 0.0152 Provide an appropriate response.

17) The data given were collected to determine whether the life span of randomly selected mammals, in years, can be predicted from their corresponding gestation periods.

Gestation 8 2.1 1.3 1 11.5 5.3 3.8 24.3 Life span 30 13 8 4 28 11 12 42 Identify the explanatory variable A) mammal breed B) gestation C) months D) life span E) climate 18) Do motivation levels between mid-level and upper-level managers differ? A randomly selected group of each were administered a survey, which measures motivation for upward mobility. The scores are summarized below:

Sample Size Mean Score Standard Deviation

upper-level 73 77.4 10.06

mid-level 109 79.71 6.43

Assuming equal population standard deviations, find the P-value for testing that the mean scores differ for upper-level and mid-level managers. Interpret using a 5% significance level.

A) P-value = 0.08; since the P-value > 0.05, we fail to reject the null hypothesis.

B) P-value = 0.03; since the P-value < 0.05, we reject the null hypothesis.

C) P-value = 0.04; since the P-value < 0.05, we reject the null hypothesis.

D) P-value = 0.06; since the P-value > 0.05, we fail to reject the null hypothesis.

Copyright © 2013 Pearson Education, Inc. 139

16)

17)

18)

^

^

From the sample statistics, find the value of p1 - p2 , the point estimate of the difference of proportions. Unless otherwise indicated, round to the nearest thousandth when necessary.

19) A study was conducted to compare the effectiveness of two weight loss strategies for obese participants. The proportion of obese clients who lost at least 10% of their body weight was compared for the two strategies. The resulting 98% confidence interval for p1 - p2 is (-0.13, 0.09).

19)

Give an interpretation of this confidence interval.

A) If samples were repeatedly drawn from the same populations under the same circumstances, the true population difference (p1 - p2 ) would be between -0.13 and 0.09 98% of the time.

B) We are 98% confident that the proportion of obese clients losing weight under strategy 2 is between 13% less and 9% more than the proportion of obese clients losing weight under strategy 1.

C) We are 98% confident that the proportion of obese clients losing weight under strategy 1 is between 13% less and 9% more than the proportion of obese clients losing weight under strategy 2.

D) There is a 98% probability that the proportion of obese clients losing weight under strategy 2 is between 13% less and 9% more than the proportion of obese clients losing weight under strategy 1.

E) There is a 98% probability that the proportion of obese clients losing weight under strategy 1 is between 13% less and 9% more than the proportion of obese clients losing weight under strategy 2. ^

From the sample statistics, find the value of the pooled estimate p used.

20) n 1 = 100 n 2 = 100 ^

p1 = 0.1

20)

^

p2 = 0.12

A) 0.22 B) none of these C) 0.0022 D) 0.11 E) 0.33 Provide an appropriate response.

21) The recent admissions for the humanities and sciences at a certain college are given in the table below. What percentage of men applying to the humanities was accepted? What percentage of women applying to the humanities was accepted?

Humanities Accepted Rejected Sciences Accepted Rejected Total

Men

Women

190 140

503 422

160 210 700

27 48 1000

A) In the humanities, 27% of males were accepted whereas 50% of females were accepted.

B) In the humanities, 50% of males were accepted and 53% of females were accepted.

C) In the humanities, 58% of males were accepted whereas only 54% of females were accepted.

D) In the humanities, 27% of males were accepted whereas 73% of females were accepted.

E) In the humanities, 11% of males were accepted whereas 30% of females were accepted.

Copyright © 2013 Pearson Education, Inc. 140

21)

22) A 95% confidence interval for the difference in means for a collection of paired sample data is (0, 3.4). Based on the same sample, a traditional significance test fails to support the claim of μd >

22)

0. What can you conclude about the significance level α (α = 1 - .95) of the hypothesis test?

A) α > 0.05 B) α < 0.05 C) α = 0.95 D) α = 0.05 E) α = 0.01 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

23) Denote the observation for subject i by xi at time 1 and by yi at time 2. Let di = yi - xi.

23)

Letting x, y, and xd denote the means, show that xd = y - x.

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

24) At the end of a highschool football season two teams are compared to determine which team had a higher percentage of successful scoring attempts after a touchdown. The data is summarized in the following table: Type of Attempt Field Goal 2-Point Conversion Overall

Team A 89% (25/29) 40% (2/5) 79% (27/34)

24)

Team B 86% (31/36) 0% (0/2) 82% (31/38)

Identify the control variable.

A) Team A B) Field Goal C) Team B D) 2-Point conversion E) Type of attempt 25) At the end of a highschool football season two teams are compared to determine which team had a higher percentage of successful scoring attempts after a touchdown. The data is summarized in the following table: Type of Attempt Field Goal 2-Point Conversion Overall

Team A 89% (25/29) 40% (2/5) 79% (27/34)

Team B 86% (31/36) 0% (0/2) 82% (31/38)

Identify the explanatory variable.

A) Number of attempts B) Type of attempt C) Which Team D) None of these E) Whether or not the team scored

Copyright © 2013 Pearson Education, Inc. 141

25)

Answer Key Testname: CHAPTER_10_EXAM_A

1) E 2) B 3) D 4) E 5) B 6) D 7) (-2.279, 0.1273) 8) Since se(x1 - x2 ) =

[se(x1 )]2 + [se(x2 )]2 , se(x1 - x2 ) > se(x1 ). To see this, square each side of the inequality

[se(x1 )]2 + [se(x2 )]2 > se(x1 ) to get [se(x1 )]2 + [se(x2 )]2 > [se(x1 )]2 . Subtract [se(x1 )]2 from each side of the inequality [se(x1 )]2 + [se(x2 )]2 > [se(x1 )]2 to get [se(x2 )]2 > 0. Take the square root of each side of the inequality [se(x2 )]2 > 0 to get se(x2 ) > 0. Since x2 is a random variable which varies from sample to sample or since x2 is not a constant, se(x2 ) must be greater than 0. Therefore, se(x1 - x2 ) > se(x1 ). Likewise, it can be shown that se(x1 - x2 ) > se(x2 ). se(x2 ) < se(x1 - x2 ).

9) B 10) A 11) E 12) B 13) D 14) (-27.55, 67.55) 15) A 16) A 17) B 18) D 19) C 20) D 21) C 22) B

23) xd = ( ∑di )/n = [ ∑(yi - xi) ]/n = ( ∑yi - ∑xi )/n = ( ∑yi )/n - ( ∑xi )/n = y - x.

24) E 25) C

Copyright © 2013 Pearson Education, Inc. 142

Chapter 10 Exam B Name___________________________________

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

Provide an appropriate response.

1) Using the formula se =

s1 2 s2 2 , show that the standard error of (x1 - x2 ) is greater + n2 n1

1)

than both se(x1 ) and se(x2 ).

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

2) A researcher is interested in the academic performance differences between individuals using an optimistic versus a pessimistic approach to their studies. If the researcher fails to find a significant difference, when in fact one exists in the population: A) the null hypothesis was correctly accepted.

B) a Type I error has been made.

C) a Type II error has been made.

D) the null hypothesis was correctly rejected.

E) the research hypothesis was correctly accepted.

2)

3) A 95% confidence interval for the difference in means for a collection of paired sample data is (0, 3.4). Based on the same sample, a traditional significance test fails to support the claim of μd >

3)

0. What can you conclude about the significance level α (α = 1 - .95) of the hypothesis test?

A) α = 0.05 B) α = 0.95 C) α > 0.05 D) α = 0.01 E) α < 0.05 4) The recent admissions for the humanities and sciences at a certain college are given in the table below. What percentage of men who applied within the two areas was accepted? What percentage of women who applied within the two areas was accepted?

Humanities Accepted Rejected Sciences Accepted Rejected Total

Men

Women

190 140

503 422

160 210 700

27 48 1000

A) 27% of men and 50% of women who applied within the two areas were accepted.

B) 51% of men and 45% of women who applied within the two areas were accepted.

C) 21% of men and 31% of women who applied within the two areas were accepted.

D) 23% of men and 2.7% of women who applied within the two areas were accepted.

E) 50% of men and 53% of women who applied within the two areas were accepted.

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

5) Denote the observation for subject i by xi at time 1 and by yi at time 2. Let di = yi - xi.

Letting x, y, and xd denote the means, show that xd = y - x.

Copyright © 2013 Pearson Education, Inc. 143

5)

4)

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

6) At the end of a highschool football season two teams are compared to determine which team had a higher percentage of successful scoring attempts after a touchdown. The data is summarized in the following table: Type of Attempt Field Goal 2-Point Conversion Overall

Team A 89% (25/29) 40% (2/5) 79% (27/34)

Team B 86% (31/36) 0% (0/2) 82% (31/38)

Identify the control variable.

A) Team A B) Field Goal C) 2-Point conversion D) Type of attempt E) Team B SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

7) Three editors of large-city newspapers are selected at random and asked to rate on a score of 0 to 100 the fairness of the news media in political reporting (0 corresponds to very unfair). The same question is posed to three editors of small -town papers. The large-city editors gave scores of 55, 90, and 95; while, the small-town editors gave scores of 40, 60, and 80. The table shows a computer printout for results of a two -sample comparison of means.

Variable: FAIRNESS PAPER N Mean

Std Dev

Std Error

large small

21.794 20.000

12.583 11.547

3 3

80.00 60.00

Use technology to find a 95% confidence interval for the difference of the means.

Copyright © 2013 Pearson Education, Inc. 144

7)

6)

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

8) The recent admissions for the humanities and sciences at a certain college are given in the table below. What percentage of men applying to the humanities was accepted? What percentage of women applying to the humanities was accepted?

Humanities Accepted Rejected Sciences Accepted Rejected Total

Men

Women

190 140

503 422

160 210 700

27 48 1000

8)

A) In the humanities, 27% of males were accepted whereas 73% of females were accepted.

B) In the humanities, 50% of males were accepted and 53% of females were accepted.

C) In the humanities, 58% of males were accepted whereas only 54% of females were accepted.

D) In the humanities, 11% of males were accepted whereas 30% of females were accepted.

E) In the humanities, 27% of males were accepted whereas 50% of females were accepted.

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

9) When testing for a difference between the means of a treatment group and a placebo group, the computer display below is obtained.

Variable: TREATMENT N Mean Std Dev

Std Error

treatment 50 placebo 50

0.403 0.453

65.107 66.183

2.847 3.205

9)

Use technology to find a 95% confidence interval for the difference of the mean of the treatment and the mean of the placebo group.

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

10) Do motivation levels between mid-level and upper-level managers differ? A randomly selected group of each were administered a survey, which measures motivation for upward mobility. The scores are summarized below:

Sample Size Mean Score Standard Deviation

upper-level 73 77.4 10.06

mid-level 109 79.71 6.43

Assuming equal population standard deviations, calculate the test statistic for determining whether the mean scores differ for upper-level and mid-level managers.

A) -63.69 B) none of these C) -1.89 D) -1.74 E) -0.29 Copyright © 2013 Pearson Education, Inc. 145

10)

11) An agricultural company would like to predict cotton yield per acre in a certain area using rainfall (in inches). Identify the response variable.

A) variety of cotton grown B) the agricultural company C) farm size D) rainfall in inches E) yield per acre

11)

12) The data given were collected to determine whether the life span of randomly selected mammals, in years, can be predicted from their corresponding gestation periods.

Gestation 8 2.1 1.3 1 11.5 5.3 3.8 24.3 Life span 30 13 8 4 28 11 12 42 Identify the explanatory variable A) months B) gestation C) life span D) climate E) mammal breed

12)

13) Do motivation levels between mid-level and upper-level managers differ? A randomly selected group of each were administered a survey, which measures motivation for upward mobility. The scores are summarized below:

13)

Sample Size Mean Score Standard Deviation

upper-level 73 77.4 10.06

mid-level 109 79.71 6.43

Assuming equal population standard deviations, find the P-value for testing that the mean scores differ for upper-level and mid-level managers. Interpret using a 5% significance level.

A) P-value = 0.08; since the P-value > 0.05, we fail to reject the null hypothesis.

B) P-value = 0.06; since the P-value > 0.05, we fail to reject the null hypothesis.

C) P-value = 0.03; since the P-value < 0.05, we reject the null hypothesis.

D) P-value = 0.04; since the P-value < 0.05, we reject the null hypothesis.

14) At the end of a highschool football season two teams are compared to determine which team had a higher percentage of successful scoring attempts after a touchdown. The data is summarized in the following table: Type of Attempt Field Goal 2-Point Conversion Overall

Team A 89% (25/29) 40% (2/5) 79% (27/34)

Team B 86% (31/36) 0% (0/2) 82% (31/38)

Identify the explanatory variable.

A) Which Team B) Type of attempt C) Number of attempts D) None of these E) Whether or not the team scored

Copyright © 2013 Pearson Education, Inc. 146

14)

Find the appropriate test statistic/p-value.

15) Do motivation levels between mid-level and upper-level managers differ? A randomly selected group of each were administered a survey, which measures motivation for upward mobility. The scores are summarized below:

Sample Size Mean Score Standard Deviation

upper-level 173 77.4 11.06

15)

mid-level 109 79.71 6.43

Given that the P-value is 0.03, which of the following is the appropriate conclusion?

A) At α = .025, fail to reject H0 .

B) At α = .02, accept H0 .

C) At α = .02, reject H0 .

D) At α = .025, reject H0 .

E) At α = .01, reject H0 . ^

^

From the sample statistics, find the value of p1 - p2 , the point estimate of the difference of proportions. Unless otherwise indicated, round to the nearest thousandth when necessary.

16) n 1 = 100 n 2 = 100 x1 = 34

16)

x2 = 30

A) -0.04 B) none of these C) 0.02 D) 0.04 E) -0.02 17) n 1 = 1927 x1 = 689

n 2 = 541 x2 = 160

17)

A) 0.062 B) 0.382 C) none of these D) -0.62 E) 0.214

Copyright © 2013 Pearson Education, Inc. 147

18) A study was conducted to compare the effectiveness of two weight loss strategies for obese participants. The proportion of obese clients who lost at least 10% of their body weight was compared for the two strategies. The resulting 98% confidence interval for p1 - p2 is (-0.13, 0.09).

18)

Give an interpretation of this confidence interval.

A) We are 98% confident that the proportion of obese clients losing weight under strategy 2 is between 13% less and 9% more than the proportion of obese clients losing weight under strategy 1.

B) We are 98% confident that the proportion of obese clients losing weight under strategy 1 is between 13% less and 9% more than the proportion of obese clients losing weight under strategy 2.

C) There is a 98% probability that the proportion of obese clients losing weight under strategy 1 is between 13% less and 9% more than the proportion of obese clients losing weight under strategy 2.

D) If samples were repeatedly drawn from the same populations under the same circumstances, the true population difference (p1 - p2 ) would be between -0.13 and 0.09 98% of the time.

E) There is a 98% probability that the proportion of obese clients losing weight under strategy 2 is between 13% less and 9% more than the proportion of obese clients losing weight under strategy 1.

19) A survey asked respondents whether marijuana should be made legal. A 95% confidence interval for PA - PB is given by (0.08, 0.14) where PA is the proportion of respondents who answered

19)

ʺlegalʺ in state A and PB is the proportion of respondents who responded ʺlegalʺ in state B. Based on the 95% confidence interval, what can we conclude about the percentage of respondents who favor legalization in state B versus state A? A) Since all of the values in the confidence interval are less than 1, we can conclude that there is a significant difference between the percentage in favor of legalization in state B and the percentage in favor of legalization in state A. B) Since all of the values in the confidence interval are less than 1, we are unable to conclude that there is a significant difference between the percentage in favor of legalization in state B and the percentage in favor of legalization in state A. C) Since all of the values in the confidence interval are greater than 0, we can conclude that the percentage in favor of legalization was greater in state B than it was in state A. D) Since all of the values in the confidence interval are greater than 0, we can conclude that the percentage in favor of legalization was greater in state A than it was in state B. Interpret the given confidence interval.

20) A survey was conducted to determine the difference in gasoline mileage for two truck models. A random sample was taken for each model of truck, and the mean gasoline mileage, in miles per gallon, was calculated. A 98% confidence interval for the difference in the mean mileage for model A trucks minus the mean mileage for model B trucks, μA - μB, was determined to be (2.5, 4.7).

A) The probability that a randomly selected Model A truck will have a gas mileage that is higher than a randomly selected model B truck is 0.98.

B) Based on this sample, we are 98% confident that the average mileage for model B trucks is between 2.5 and 4.7 miles per gallon higher than the average mileage for model A trucks.

C) 98% of model A trucks have a gas mileage that is between 2.5 and 4.7 miles per gallon higher than model B trucks.

D) Based on this sample, we are 98% confident that the average mileage for model A trucks is between 2.5 and 4.7 miles per gallon higher than the average mileage for model B trucks.

E) The probability that a randomly selected Model A truck will have a gas mileage that is lower than a randomly selected model B truck is 0.98.

Copyright © 2013 Pearson Education, Inc. 148

20)

Answer true or false.

21) The F test for comparing standard deviations is robust.

A) True B) False

21)

22) The width of the confidence interval for (μ1 - μ2 ) increases as s1 and s2 increase.

A) False

22)

B) True

Use the paired t-interval procedure to obtain the required confidence interval for the mean difference. Assume that the conditions and assumptions for inference are satisfied.

23) 23) Ten families are randomly selected and their daily water usage (in gallons) before and after viewing a conservation video. Construct a 90% confidence interval for the mean of the difference of the ʺbeforeʺ minus the ʺafterʺ times if d(after-before) = -4.8 and sd = 5.2451 Before 33 33 38 33 35 35 40 40 40 31 After 34 28 25 28 35 33 31 28 35 33 A) (2.1,7.5) B) (2.5,7.1) C) (1.8,7.8)

D) (3.8,5.8)

E) (1.5,8.1)

^

From the sample statistics, find the value of the pooled estimate p used.

24) n 1 = 100 n 2 = 100 ^

p1 = 0.1

24)

^

p2 = 0.12 A) 0.22 B) 0.11 C) none of these D) 0.0022 E) 0.33

Select the most appropriate answer.

25) For 12 pairs of females, the reported means are 24.8 on the well-being measure for the children of alcoholics and 29.0 for the control group. A t test statistic of 2.67 for the test comparing the means was obtained. Assuming that this is the result of a dependent-samples analysis testing for a difference between the group means, report the P-value.

A) 0.005 < P-value < 0.01 B) 0.0152 C) 0.01 < P-value < 0.02 D) 0.02 < P-value < 0.05 E) 0.0076

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25)

Answer Key Testname: CHAPTER_10_EXAM_B

1) Since se(x1 - x2 ) =

[se(x1 )]2 + [se(x2 )]2 , se(x1 - x2 ) > se(x1 ). To see this, square each side of the inequality

[se(x1 )]2 + [se(x2 )]2 > se(x1 ) to get [se(x1 )]2 + [se(x2 )]2 > [se(x1 )]2 . Subtract [se(x1 )]2 from each side of the inequality [se(x1 )]2 + [se(x2 )]2 > [se(x1 )]2 to get [se(x2 )]2 > 0. Take the square root of each side of the inequality [se(x2 )]2 > 0 to get se(x2 ) > 0. Since x2 is a random variable which varies from sample to sample or since x2 is not a constant, se(x2 ) must be greater than 0. Therefore, se(x1 - x2 ) > se(x1 ). Likewise, it can be shown that se(x1 - x2 ) > se(x2 ). se(x2 ) < se(x1 - x2 ).

2) B 3) E 4) E

5) xd = ( ∑di )/n = [ ∑(yi - xi) ]/n = ( ∑yi - ∑xi )/n = ( ∑yi )/n - ( ∑xi )/n = y - x.

6) D 7) (-27.55, 67.55) 8) C 9) (-2.279, 0.1273) 10) C 11) E 12) B 13) B 14) A 15) A 16) D 17) A 18) B 19) D 20) D 21) B 22) B 23) C 24) B 25) D

Copyright © 2013 Pearson Education, Inc. 150

Chapter 11 Exam A Name___________________________________

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

State the null and alternative hypothesis.

1) A sample survey obtains information on characteristics of book readers. A book reader is defined to be anyone who has read one or more books in the six months prior to the survey; a non-book reader is defined to be anyone who read newspapers or magazines but no books in the six months prior to the survey; a nonreader is defined to be anyone 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 1429 persons 16 years old and over in an effort to determine whether or not the proportions of book readers, non-book readers, and non-readers are the same for each income bracket. State the hypotheses for a chi-squared test of independence between the two variables, classification and household income.

A) H0 : The classifications have the same distribution for each household income bracket.

Ha : The classifications do not have the same distribution for each household income bracket.

B) H0 : There is a relationship between household income and book readership.

Ha : Household income and book readership are not related.

C) H0 : There is no relationship between household income and book readership.

Ha : Household income and book readership are not related.

D) H0 : Household income and book readership are independent.

Ha : Household income and book readership are not dependent.

Copyright © 2013 Pearson Education, Inc. 151

1)

Provide an appropriate response.

2)

2)

The contingency table above shows the blood types of a sample of patients cross classified by sex.

How many people in the sample have blood type B? A) 29 B) 13 C) 58 D) 16 E) 112 3) At a high school debate tournament, half of the teams were asked to wear suits and ties and the rest were asked to wear jeans and t-shirts. The wins and losses according to attire are given in the table below. Using α = 0.05, test the hypothesis that the proportion of wins is the same for teams wearing suits as for teams wearing jeans.

Suit T-shirt

Win Loss 22 28 28 22

H0 : The proportion of wins is the same for teams wearing suits as for teams wearing jeans.

Ha : The proportions are different.

Test statistic: χ 2 = 1.440. Critical value: χ 2 = 3.841.

A) Since the critical value > 1, we reject H0 and conclude that the proportion of wins differs for the teams wearing suits and those wearing jeans.

B) Since the test statistic is less than the critical value, we accept H0 and conclude that the proportion of wins is the same for the teams wearing suits and for those wearing jeans.

C) Since the test statistic is less than the critical value, we fail to reject H0 . There is not enough evidence to conclude that the proportion of wins differs for the teams wearing suits versus those wearing jeans.

D) Since the test statistic > 1, we reject H0 and conclude that the proportion of wins differs for the teams wearing suits and those wearing jeans.

E) Since the test statistic is less than the critical value, we reject H0 and conclude that the proportion of wins differs for the teams wearing suits and those wearing jeans.

Copyright © 2013 Pearson Education, Inc. 152

3)

State the null and alternative hypothesis.

4) A researcher performed a study to determine whether an association exists between sex and blood type. He obtained the following sample data. State the hypotheses for a chi -squared test of independence between the two variables.

4)

A) H0 : Gender and blood type are independent.

Ha : Gender and blood type are not independent.

B) H0 : Gender and blood type are dependent.

Ha : Gender and blood type are independent.

C) H0 : Gender and blood type are dependent.

Ha : Gender and blood type are not dependent.

D) H0 : There is a relationship between gender and blood type.

Ha : There is no relationship between gender and blood type.

Use the contingency table to estimate expected cell count.

5) The contingency table below shows the results of a random sample of 300 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliation.

Assuming the row and column classification are independent, find an estimate for the expected cell count of row 2, column 2. Round your answer to tenths.

Opinion Party Approve Disapprove No Opinion 30 21 Republican 63 75 36 27 Democrat 15 24 9 Independent A) 33.3 B) 70.4 C) 36

D) 41.4

E) 34.2

Select the most appropriate answer.

6) As the degrees of freedom increase, the mean and standard deviation of the chi -squared distribution A) decrease and increase, respectively.

B) Increase and decrease, respectively.

C) increase and increase, respectively.

D) are both unaffected.

E) decrease and decrease, respectively.

Copyright © 2013 Pearson Education, Inc. 153

5)

6)

Provide an appropriate response.

7) The two-way table below summarizes data from a survey at a small liberal arts college:

7)

New Hires Tenure Adjunct Total Men 20 24 44 Women 23 18 41 Total 43 42 85 What is the probability (rounded to two decimal places) that a tenure -track new hire is female?

A) 0.53 B) 0.27 C) 0.43 D) 0.56 E) 0.51 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

8)

8) A survey of senior high school students in Dayton, Ohio produced the following contingency table relating the studentsʹ alcohol use and marijuana use.

ALCOHOL USE

Yes No

MARIJUANA USE Yes No 955 994 5 322

Treating marijuana use as the response variable, find and interpret the relative risk.

9) The side effect of flu syndrome was reported by 8 people taking Botox and 2 people taking a placebo. For comparing these, software reports the following results:

9)

Rows: Treatment Columns: Flu

Botox Placebo

No 397 130

Yes 8 2

Fisherʹs exact test: P-Value = 1 a. b. c.

Specify the parameters that are in the null hypothesis for this test.

Conduct the test.

Why was Fisherʹs exact test used instead of the chi-squared test?

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

Use the chi-squared table.

10) Use the appropriate table to find P(χ 2 ≥ 7.38) assuming df = 2.

A) 0.950 B) 0.975 C) 0.025

10) D) 0.050

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E) 0.500

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

A chi-square test has been performed on the given data, with the results shown. Use a statistical package to calculate the standardized residuals for the data and comment on your findings.

11) 11) A researcher wishes to test whether the proportion of college students who smoke is the same in four different colleges. She randomly selects 100 students from each college and records the number that smoke. The results are shown below.

Smoke Donʹt smoke

College A College B College C College D 17 26 11 34 83 74 89 66

Test statistic: χ 2 = 17.832 P-value = 0.0004763 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

12) Which of the following is NOT a property of the relative risk?

A) The relative risk is a number between 0 and 1.

B) Values farther from 1.0 represent stronger associations.

C) The relative risk can equal any nonnegative number.

D) When p1 = p2 , the variables are independent and the relative risk = 1.0.

12)

E) Two values for the relative risk represent the same strength of association, but in opposite directions, when one value is the reciprocal of the other.

Calculate χ2 from contingency table.

13) Responses to a survey question are broken down according to gender and the sample results are given below. Using a significance level of 0.05, calculate the chi-squared test statistic for testing the claim that response and gender are independent.

Male Female

Yes No Undecided 25 50 15 20 30 10

A) 0.579

B) 2.706

C) 3.841

D) 5.991

Copyright © 2013 Pearson Education, Inc. 155

E) 6.502

13)

Provide an appropriate response.

14) At a high school debate tournament, half of the teams were asked to wear suits and ties and the rest were asked to wear jeans and t-shirts. The wins and losses according to attire are given in the table below.

Suit T-shirt

Win Loss 22 28 28 22

Estimate the difference in the proportion of wins for those wearing suits versus those wearing t-shirts. Interpret.

A) -0.12; for the sample, the number of wins was higher for those wearing suits than for those wearing t-shirts.

B) -0.12; for the sample, the number of wins was higher for those wearing t -shirts than for those wearing suits.

C) 0.79; for the sample, those wearing suits were less likely to win.

D) 0.50; for the sample, it is equally likely that those wearing t -shirts or those wearing suits will win.

E) 0.79; for the sample, those wearing t-shirts were less likely to win.

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14)

15) O Female 42 Sex Male Total 95

Blood Type A B AB Total 55 5 117 48 15 5 121 30 10

15)

The contingency table above shows the blood types of a sample of patients cross classified by sex.

Fill in the missing entries.

A) Blood Type O A B AB Total 55 45 5 117 Sex Female 42 Male 137 48 15 5 121 Total 95 103 30 10 238 B)

Blood Type O A B AB Total Female 42 55 15 5 117 Sex Male 53 48 15 5 121 Total 95 103 30 10 238

C)

Blood Type O A B AB Total Female 42 55 15 5 117 Sex Male 53 48 15 5 121 Total 95 103 30 10 476

D)

Blood Type A B AB Total 55 45 5 117 48 15 5 121 103 30 10 476 E) Blood Type O A B AB Total Female 42 55 64 5 117 Sex Male 79 48 15 5 121 Total 95 103 30 10 238 O Female 42 Sex Male 137 Total 95

Use the contingency table to estimate expected cell count.

16) A sports researcher is interested in determining if there is a relationship between the number of home team and visiting team wins and different sports. A random sample of 526 games is selected and the results are given below. Assuming the row and column classification are independent, find an estimate for the expected cell count of row 2, column 2. Round your answer to tenths.

Home team wins Visiting team wins A) 20.3

Football Basketball Soccer Baseball 38 157 26 82 29 97 22 75 B) 97 C) 146.3

D) 65.75

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E) 107.7

16)

State the null hypothesis to test for independence.

17) Tests for adverse reactions to a new drug yielded the results given in the table below. At the 0.05 significance level, state the null hypothesis for testing the claim that the treatment (drug or placebo) is independent of the reaction (whether or not headaches were experienced).

Headaches No headaches

17)

Drug Placebo 11 7 73 91

A) H0 : Treatment and reaction are independent.

B) Ha : Treatment and reaction are dependent.

C) Ha : Treatment and reaction are independent.

D) H0 : Treatment and reaction are dependent.

Provide an appropriate response.

18) The contingency table below shows the income level for a random sample of adults cross classified by sex.

18)

Find the conditional distribution of the variable ʺincome bracketʺ for men.

A) Male: 52.6%; Female: 47.4% B) Male: 59.2%; Female: 40.8% C) Low: 28%; Middle: 36.6%; High: 35.4% D) Low: 46.9%; Middle: 51.7%; High: 59.2% E) Low: 14.7%; Middle: 19.2%; High: 18.6% Use the contingency table.

19) A sports researcher is interested in determining if there is a relationship between the number of home team and visiting team wins among different sports. A random sample of 526 games is selected and the number of wins of each type by sport are listed below.

Home team wins Visiting team wins

Football Basketball Soccer Baseball 39 156 25 83 31 98 19 75

Calculate the chi-square test statistic χ 2 to test the claim that the number of home team and visiting team wins is independent of the sport.

A) 4.192 B) 3.290 C) 1.226 D) 2.919 E) 5.391

Copyright © 2013 Pearson Education, Inc. 158

19)

Provide an appropriate response.

20) A researcher wishes to test the effectiveness of a flu vaccination. 150 people are vaccinated, 180 people are vaccinated with a placebo, and 100 people are not vaccinated. The number in each group who later caught the flu was recorded. The results are shown below.

Caught the flu Did not catch the flu

20)

Vaccinated Placebo Control 8 19 21 142 161 79

Find and interpret the relative risk of catching the flu, comparing those who were vaccinated to those in the control group.

A) 0.25; those who were vaccinated were 0.25 times as likely to contract the flu as those in the control group B) 0.16; those who were vaccinated were 0.16 times as likely to contract the flu as those in the control group C) 0.25; those who were in the control group were 0.25 times as likely to contract the flu as those who were vaccinated D) 0.21; those who were vaccinated were 0.21 times as likely to contract the flu as those in the control group E) 0.38; those who were vaccinated were 0.38 times as likely to contract the flu as those in the control group Group the bivariate data into a contingency table.

21) The table below provides data on sex, political party affiliation, and income bracket for a sample of people questioned during a poll. Group the bivariate data for the two variables ʺsexʺ and ʺincome bracketʺ into a contingency table.

Sex M F F M F M F M M F M F F M M F M F M F M M F

Political Party Income Bracket Rep Dem Dem Dem Other Rep Rep Rep Dem Rep Dem Rep Dem Dem Rep Dem Rep Other Other Dem Dem Rep Dem

High Middle Middle Low Middle Low High High High Low High Middle Middle Middle Low High Low High Middle Low Middle Low Middle

Copyright © 2013 Pearson Education, Inc. 159

21)

A)

B)

C)

D)

E) None of these Provide an appropriate response.

22) The two-way table below summarizes data from a survey at a small liberal arts college:

22)

New Hires Tenure Adjunct Total Men 19 25 44 Women 25 17 42 Total 44 42 86 What is the probability (rounded to two decimal places) that a randomly selected new hire is a tenure-track woman?

A) 0.60 B) 0.29 C) 0.20 D) 0.25 E) 0.49 Select the most appropriate answer.

23) When the null hypothesis in the chi-squared test of independence of two categorical variables is true, the standardized residuals have approximately a A) binomial distribution.

B) standard normal distribution.

C) Studentʹs t distribution.

D) chi-squared distribution.

E) conditional distribution.

Copyright © 2013 Pearson Education, Inc. 160

23)

Calculate χ2 from contingency table.

24) Use the sample data below to calculate the chi-squared test statistic for testing whether car color affects the likelihood of being in an accident. Use a significance level of 0.01.

Red Blue White Car has been in accident 28 33 36 Car has not been in accident 23 22 30 A) 9.210

B) 0.050

C) 0.579

D) 0.4287

E) 6.635

Group the bivariate data into a contingency table.

25) The table below provides data on sex, political party affiliation, and income bracket for a sample of people questioned during a poll. Group the bivariate data for the two variables ʺpolitical partyʺ and ʺincome bracketʺ into a contingency table.

Sex M F F M F M F M M F M F F M M F M F M F M M F

Political Party Income Bracket Rep Dem Dem Dem Other Rep Rep Rep Dem Rep Dem Rep Dem Dem Rep Dem Rep Other Other Dem Dem Rep Dem

High Middle Middle Low Middle Low High High High Low High Middle Middle Middle Low High Low High Middle Low Middle Low Middle

A)

Copyright © 2013 Pearson Education, Inc. 161

24)

25)

B)

C)

D)

E) None of these

Copyright © 2013 Pearson Education, Inc. 162

Answer Key Testname: CHAPTER_11_EXAM_A

1) A 2) A 3) C 4) A 5) D 6) C 7) A 8) Treating marijuana use as the response variable and the adverse outcome as yes, the relative risk is 32.0. Therefore, the proportion of students using alcohol who also used marijuana was 32 times the proportion of students not using alcohol who used marijuana. A relative risk of 32 represents a strong association.

9) a. H0 : p1 = p2 , where p1 = proportion of people taking Botox who experienced the side effect of flu syndrome and p2 = proportion of people taking the placebo who experienced the side effect of flu syndrome; b. (1) Assumptions: two binary categorical variables, randomization; (2) H0 : p1 = p2 , Ha : p1 ≠ p2 ; (4) P-value = 1; (5) Since the P-value is above 0.05, we can not reject H0 . We cannot conclude that an association exists between taking Botox and experiencing the side effect of flu syndrome at α = 0.05; c. Fisherʹs exact test was used instead of the chi-squared test, because not all of the expected cell counts were at least 5.

10) C 11) We reject the null hypothesis that the proportion of smokers is the same at all four colleges. The standardized residuals are given by -1.394 1.115 -3.066 3.345 .

1.394 -1.115 3.066 -3.345 The residuals for smokers at college D and non-smokers at college C are both greater than 3 and larger than expected under the null hypothesis of independence. The residuals for smokers at college C and non -smokers at college D are both less than -3 and smaller than expected under the null hypothesis of independence.

12) A 13) A 14) B 15) B 16) E 17) A 18) C 19) B 20) A 21) B 22) B 23) B 24) D 25) C

Copyright © 2013 Pearson Education, Inc. 163

Chapter 11 Exam B Name___________________________________

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

State the null and alternative hypothesis.

1) A sample survey obtains information on characteristics of book readers. A book reader is defined to be anyone who has read one or more books in the six months prior to the survey; a non-book reader is defined to be anyone who read newspapers or magazines but no books in the six months prior to the survey; a nonreader is defined to be anyone 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 1429 persons 16 years old and over in an effort to determine whether or not the proportions of book readers, non-book readers, and non-readers are the same for each income bracket. State the hypotheses for a chi-squared test of independence between the two variables, classification and household income.

A) H0 : The classifications have the same distribution for each household income bracket.

Ha : The classifications do not have the same distribution for each household income bracket.

B) H0 : There is a relationship between household income and book readership.

Ha : Household income and book readership are not related.

C) H0 : There is no relationship between household income and book readership.

Ha : Household income and book readership are not related.

D) H0 : Household income and book readership are independent.

Ha : Household income and book readership are not dependent.

Copyright © 2013 Pearson Education, Inc. 164

1)

Provide an appropriate response.

2)

2)

The contingency table above shows the blood types of a sample of patients cross classified by sex.

How many people in the sample have blood type B? A) 29 B) 13 C) 58 D) 16 E) 112 3) At a high school debate tournament, half of the teams were asked to wear suits and ties and the rest were asked to wear jeans and t-shirts. The wins and losses according to attire are given in the table below. Using α = 0.05, test the hypothesis that the proportion of wins is the same for teams wearing suits as for teams wearing jeans.

Suit T-shirt

Win Loss 22 28 28 22

H0 : The proportion of wins is the same for teams wearing suits as for teams wearing jeans.

Ha : The proportions are different.

Test statistic: χ 2 = 1.440. Critical value: χ 2 = 3.841.

A) Since the critical value > 1, we reject H0 and conclude that the proportion of wins differs for the teams wearing suits and those wearing jeans.

B) Since the test statistic is less than the critical value, we accept H0 and conclude that the proportion of wins is the same for the teams wearing suits and for those wearing jeans.

C) Since the test statistic is less than the critical value, we fail to reject H0 . There is not enough evidence to conclude that the proportion of wins differs for the teams wearing suits versus those wearing jeans.

D) Since the test statistic > 1, we reject H0 and conclude that the proportion of wins differs for the teams wearing suits and those wearing jeans.

E) Since the test statistic is less than the critical value, we reject H0 and conclude that the proportion of wins differs for the teams wearing suits and those wearing jeans.

Copyright © 2013 Pearson Education, Inc. 165

3)

State the null and alternative hypothesis.

4) A researcher performed a study to determine whether an association exists between sex and blood type. He obtained the following sample data. State the hypotheses for a chi -squared test of independence between the two variables.

4)

A) H0 : Gender and blood type are independent.

Ha : Gender and blood type are not independent.

B) H0 : Gender and blood type are dependent.

Ha : Gender and blood type are independent.

C) H0 : Gender and blood type are dependent.

Ha : Gender and blood type are not dependent.

D) H0 : There is a relationship between gender and blood type.

Ha : There is no relationship between gender and blood type.

Use the contingency table to estimate expected cell count.

5) The contingency table below shows the results of a random sample of 300 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliation.

Assuming the row and column classification are independent, find an estimate for the expected cell count of row 2, column 2. Round your answer to tenths.

Opinion Party Approve Disapprove No Opinion 30 21 Republican 63 75 36 27 Democrat 15 24 9 Independent A) 33.3 B) 70.4 C) 36

D) 41.4

E) 34.2

Select the most appropriate answer.

6) As the degrees of freedom increase, the mean and standard deviation of the chi -squared distribution A) decrease and increase, respectively.

B) Increase and decrease, respectively.

C) increase and increase, respectively.

D) are both unaffected.

E) decrease and decrease, respectively.

Copyright © 2013 Pearson Education, Inc. 166

5)

6)

Provide an appropriate response.

7) The two-way table below summarizes data from a survey at a small liberal arts college:

7)

New Hires Tenure Adjunct Total Men 20 24 44 Women 23 18 41 Total 43 42 85 What is the probability (rounded to two decimal places) that a tenure -track new hire is female?

A) 0.53 B) 0.27 C) 0.43 D) 0.56 E) 0.51 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

8)

8) A survey of senior high school students in Dayton, Ohio produced the following contingency table relating the studentsʹ alcohol use and marijuana use.

ALCOHOL USE

Yes No

MARIJUANA USE Yes No 955 994 5 322

Treating marijuana use as the response variable, find and interpret the relative risk.

9) The side effect of flu syndrome was reported by 8 people taking Botox and 2 people taking a placebo. For comparing these, software reports the following results:

9)

Rows: Treatment Columns: Flu

Botox Placebo

No 397 130

Yes 8 2

Fisherʹs exact test: P-Value = 1 a. b. c.

Specify the parameters that are in the null hypothesis for this test.

Conduct the test.

Why was Fisherʹs exact test used instead of the chi-squared test?

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

Use the chi-squared table.

10) Use the appropriate table to find P(χ 2 ≥ 7.38) assuming df = 2.

A) 0.950 B) 0.975 C) 0.025

10) D) 0.050

Copyright © 2013 Pearson Education, Inc. 167

E) 0.500

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

A chi-square test has been performed on the given data, with the results shown. Use a statistical package to calculate the standardized residuals for the data and comment on your findings.

11) 11) A researcher wishes to test whether the proportion of college students who smoke is the same in four different colleges. She randomly selects 100 students from each college and records the number that smoke. The results are shown below.

Smoke Donʹt smoke

College A College B College C College D 17 26 11 34 83 74 89 66

Test statistic: χ 2 = 17.832 P-value = 0.0004763 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Provide an appropriate response.

12) Which of the following is NOT a property of the relative risk?

A) The relative risk is a number between 0 and 1.

B) Values farther from 1.0 represent stronger associations.

C) The relative risk can equal any nonnegative number.

D) When p1 = p2 , the variables are independent and the relative risk = 1.0.

12)

E) Two values for the relative risk represent the same strength of association, but in opposite directions, when one value is the reciprocal of the other.

Calculate χ2 from contingency table.

13) Responses to a survey question are broken down according to gender and the sample results are given below. Using a significance level of 0.05, calculate the chi-squared test statistic for testing the claim that response and gender are independent.

Male Female

Yes No Undecided 25 50 15 20 30 10

A) 0.579

B) 2.706

C) 3.841

D) 5.991

Copyright © 2013 Pearson Education, Inc. 168

E) 6.502

13)

Provide an appropriate response.

14) At a high school debate tournament, half of the teams were asked to wear suits and ties and the rest were asked to wear jeans and t-shirts. The wins and losses according to attire are given in the table below.

Suit T-shirt

Win Loss 22 28 28 22

Estimate the difference in the proportion of wins for those wearing suits versus those wearing t-shirts. Interpret.

A) -0.12; for the sample, the number of wins was higher for those wearing suits than for those wearing t-shirts.

B) -0.12; for the sample, the number of wins was higher for those wearing t -shirts than for those wearing suits.

C) 0.79; for the sample, those wearing suits were less likely to win.

D) 0.50; for the sample, it is equally likely that those wearing t -shirts or those wearing suits will win.

E) 0.79; for the sample, those wearing t-shirts were less likely to win.

Copyright © 2013 Pearson Education, Inc. 169

14)

15) O Female 42 Sex Male Total 95

Blood Type A B AB Total 55 5 117 48 15 5 121 30 10

15)

The contingency table above shows the blood types of a sample of patients cross classified by sex.

Fill in the missing entries.

A) Blood Type O A B AB Total 55 45 5 117 Sex Female 42 Male 137 48 15 5 121 Total 95 103 30 10 238 B)

Blood Type O A B AB Total Female 42 55 15 5 117 Sex Male 53 48 15 5 121 Total 95 103 30 10 238

C)

Blood Type O A B AB Total Female 42 55 15 5 117 Sex Male 53 48 15 5 121 Total 95 103 30 10 476

D)

Blood Type A B AB Total 55 45 5 117 48 15 5 121 103 30 10 476 E) Blood Type O A B AB Total Female 42 55 64 5 117 Sex Male 79 48 15 5 121 Total 95 103 30 10 238 O Female 42 Sex Male 137 Total 95

Use the contingency table to estimate expected cell count.

16) A sports researcher is interested in determining if there is a relationship between the number of home team and visiting team wins and different sports. A random sample of 526 games is selected and the results are given below. Assuming the row and column classification are independent, find an estimate for the expected cell count of row 2, column 2. Round your answer to tenths.

Home team wins Visiting team wins A) 20.3

Football Basketball Soccer Baseball 38 157 26 82 29 97 22 75 B) 97 C) 146.3

D) 65.75

Copyright © 2013 Pearson Education, Inc. 170

E) 107.7

16)

State the null hypothesis to test for independence.

17) Tests for adverse reactions to a new drug yielded the results given in the table below. At the 0.05 significance level, state the null hypothesis for testing the claim that the treatment (drug or placebo) is independent of the reaction (whether or not headaches were experienced).

Headaches No headaches

17)

Drug Placebo 11 7 73 91

A) H0 : Treatment and reaction are independent.

B) Ha : Treatment and reaction are dependent.

C) Ha : Treatment and reaction are independent.

D) H0 : Treatment and reaction are dependent.

Provide an appropriate response.

18) The contingency table below shows the income level for a random sample of adults cross classified by sex.

18)

Find the conditional distribution of the variable ʺincome bracketʺ for men.

A) Male: 52.6%; Female: 47.4% B) Male: 59.2%; Female: 40.8% C) Low: 28%; Middle: 36.6%; High: 35.4% D) Low: 46.9%; Middle: 51.7%; High: 59.2% E) Low: 14.7%; Middle: 19.2%; High: 18.6% Use the contingency table.

19) A sports researcher is interested in determining if there is a relationship between the number of home team and visiting team wins among different sports. A random sample of 526 games is selected and the number of wins of each type by sport are listed below.

Home team wins Visiting team wins

Football Basketball Soccer Baseball 39 156 25 83 31 98 19 75

Calculate the chi-square test statistic χ 2 to test the claim that the number of home team and visiting team wins is independent of the sport.

A) 4.192 B) 3.290 C) 1.226 D) 2.919 E) 5.391

Copyright © 2013 Pearson Education, Inc. 171

19)

Provide an appropriate response.

20) A researcher wishes to test the effectiveness of a flu vaccination. 150 people are vaccinated, 180 people are vaccinated with a placebo, and 100 people are not vaccinated. The number in each group who later caught the flu was recorded. The results are shown below.

Caught the flu Did not catch the flu

20)

Vaccinated Placebo Control 8 19 21 142 161 79

Find and interpret the relative risk of catching the flu, comparing those who were vaccinated to those in the control group.

A) 0.25; those who were vaccinated were 0.25 times as likely to contract the flu as those in the control group B) 0.16; those who were vaccinated were 0.16 times as likely to contract the flu as those in the control group C) 0.25; those who were in the control group were 0.25 times as likely to contract the flu as those who were vaccinated D) 0.21; those who were vaccinated were 0.21 times as likely to contract the flu as those in the control group E) 0.38; those who were vaccinated were 0.38 times as likely to contract the flu as those in the control group Group the bivariate data into a contingency table.

21) The table below provides data on sex, political party affiliation, and income bracket for a sample of people questioned during a poll. Group the bivariate data for the two variables ʺsexʺ and ʺincome bracketʺ into a contingency table.

Sex M F F M F M F M M F M F F M M F M F M F M M F

Political Party Income Bracket Rep Dem Dem Dem Other Rep Rep Rep Dem Rep Dem Rep Dem Dem Rep Dem Rep Other Other Dem Dem Rep Dem

High Middle Middle Low Middle Low High High High Low High Middle Middle Middle Low High Low High Middle Low Middle Low Middle

Copyright © 2013 Pearson Education, Inc. 172

21)

A)

B)

C)

D)

E) None of these Provide an appropriate response.

22) The two-way table below summarizes data from a survey at a small liberal arts college:

22)

New Hires Tenure Adjunct Total Men 19 25 44 Women 25 17 42 Total 44 42 86 What is the probability (rounded to two decimal places) that a randomly selected new hire is a tenure-track woman?

A) 0.60 B) 0.29 C) 0.20 D) 0.25 E) 0.49 Select the most appropriate answer.

23) When the null hypothesis in the chi-squared test of independence of two categorical variables is true, the standardized residuals have approximately a A) binomial distribution.

B) standard normal distribution.

C) Studentʹs t distribution.

D) chi-squared distribution.

E) conditional distribution.

Copyright © 2013 Pearson Education, Inc. 173

23)

Calculate χ2 from contingency table.

24) Use the sample data below to calculate the chi-squared test statistic for testing whether car color affects the likelihood of being in an accident. Use a significance level of 0.01.

Red Blue White Car has been in accident 28 33 36 Car has not been in accident 23 22 30 A) 9.210

B) 0.050

C) 0.579

D) 0.4287

E) 6.635

Group the bivariate data into a contingency table.

25) The table below provides data on sex, political party affiliation, and income bracket for a sample of people questioned during a poll. Group the bivariate data for the two variables ʺpolitical partyʺ and ʺincome bracketʺ into a contingency table.

Sex M F F M F M F M M F M F F M M F M F M F M M F

Political Party Income Bracket Rep Dem Dem Dem Other Rep Rep Rep Dem Rep Dem Rep Dem Dem Rep Dem Rep Other Other Dem Dem Rep Dem

High Middle Middle Low Middle Low High High High Low High Middle Middle Middle Low High Low High Middle Low Middle Low Middle

A)

Copyright © 2013 Pearson Education, Inc. 174

24)

25)

B)

C)

D)

E) None of these

Copyright © 2013 Pearson Education, Inc. 175

Answer Key Testname: CHAPTER_11_EXAM_B

1) A 2) A 3) C 4) A 5) D 6) C 7) A 8) Treating marijuana use as the response variable and the adverse outcome as yes, the relative risk is 32.0. Therefore, the proportion of students using alcohol who also used marijuana was 32 times the proportion of students not using alcohol who used marijuana. A relative risk of 32 represents a strong association.

9) a. H0 : p1 = p2 , where p1 = proportion of people taking Botox who experienced the side effect of flu syndrome and p2 = proportion of people taking the placebo who experienced the side effect of flu syndrome; b. (1) Assumptions: two binary categorical variables, randomization; (2) H0 : p1 = p2 , Ha : p1 ≠ p2 ; (4) P-value = 1; (5) Since the P-value is above 0.05, we can not reject H0 . We cannot conclude that an association exists between taking Botox and experiencing the side effect of flu syndrome at α = 0.05; c. Fisherʹs exact test was used instead of the chi-squared test, because not all of the expected cell counts were at least 5.

10) C 11) We reject the null hypothesis that the proportion of smokers is the same at all four colleges. The standardized residuals are given by -1.394 1.115 -3.066 3.345 .

1.394 -1.115 3.066 -3.345 The residuals for smokers at college D and non-smokers at college C are both greater than 3 and larger than expected under the null hypothesis of independence. The residuals for smokers at college C and non -smokers at college D are both less than -3 and smaller than expected under the null hypothesis of independence.

12) A 13) A 14) B 15) B 16) E 17) A 18) C 19) B 20) A 21) B 22) B 23) B 24) D 25) C

Copyright © 2013 Pearson Education, Inc. 176

Chapter 12 Exam A Name___________________________________

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

Provide an appropriate response.

1) The index (x) of exposure to radioactive waste and the cancer mortality rates (y)(deaths per 100,000) were recorded for nine different Texas counties. The regression analysis is given below.

Use the analysis to find the slope of the regression line.

Coef SE(Coef) Predictor Constant 114.7156 8.045663 Index of Exp 9.231456 1.418787 A) 8.045663 B) 114.7156

T P 14.25807 0.00000198 6.506584 0.000332 C) 1.418787

D) 9.231456

E) 14.25807

Answer true or false.

2) The parameter β in the straight-line model μy = α + βx represents a multiplicative effect on the mean of y for a one-unit increase in x.

A) True

2)

B) False

Select the most appropriate answer.

3) The error involved in estimating the population mean of y at a particular value of x is ____________________ the error involved in predicting an individual value of y at that same particular value of x.

A) greater than B) less than or equal to C) greater than or equal to D) equal to E) less than Provide an appropriate response.

4) The typing speeds (x) (in words per minute) and reading speeds (y)(in words per minute) of nine randomly selected secretaries were recorded. Use the regression analysis provided below to predict the reading speed for a typing speed of 10 words per minute. Round your answer to the nearest word. ^

The regression equation is y = 290.2093 + 3.502052x R-sq = 12.385% 9 - 2 = 7 degrees of freedom Predictor Coef SE(Coef) Constant 290.2093 215.4116 Typing speed 3.502052 3.520579 A) 352 words per minute B) 322 words per minute C) 330 words per minute D) 250 words per minute E) 290 words per minute

1)

T 1.347231 0.994737

P 0.219884 0.352998

Copyright © 2013 Pearson Education, Inc. 177

3)

4)

5) A tennis ball is dropped from 15 different heights, x, (in inches) and the height of the bounce, y, is

5)

^

recorded (in inches). A regression analysis gives the the model y = -0.4 + 0.70x. A tennis ball dropped 71 inches bounced 53.3 inches. What is the residual for this bounce height?

A) -4 inches B) 4 inches C) 5 inches D) 2.8 inches E) 49.3 inches Select the most appropriate answer.

6) To use regression in an inferential manner, which of the following assumptions is/are necessary?

A) All of these.

B) The population values of y at each value of x follow a normal distribution.

C) The population means of y at different values of x have a straight -line relationship with x.

D) The population values of y at each value of x have the same standard deviation.

E) The data were gathered using randomization, such as random sampling or a randomized experiment.

6)

Answer true or false.

7) The predictor x is relatively closer to its mean than the predicted y is to its mean.

A) True B) False

7)

Provide an appropriate response.

8) Records were kept on the relationship between the rainfall (in inches) and the yield of cotton (bushels per acre). The equation of the least squares regression line is found to be

8)

^

y = 4.267 + 4.379x. Use the regression line to predict the yield of cotton for an area with a rainfall of 10 inches.

10.5 8.8 13.4 12.5 18.8 10.3 7.0 15.6 16.0 Rain fall (in inches), x Yield (bushels per acre), y 50.5 46.2 58.8 59.0 82.4 49.2 31.9 76.0 78.8 A) 45 bushels per acre B) 50 bushels per acre C) 48 bushels per acre D) 47 bushels per acre E) 31 bushels per acre 9) Suppose that for a certain country, the population size can be predicted by the exponential ^ regression model y = 2.21 × 1.08x where y is the population size (in millions) and x is the number of decades since 2000. What is the predicted population size for 2030? Round to two decimal places.

A) 2.78 million B) 7.16 million C) 22.24 million D) 71.60 million E) 2.58 million

Copyright © 2013 Pearson Education, Inc. 178

9)

10) Ten college students were randomly selected. Their grade point averages (GPAs) when they entered the program were between 3.5 and 4.0. The studentsʹ GPAs on entering the program (x) and their current GPAs (y) were recorded. The regression analysis is given below. Use the analysis to find the equation of the regression line.

Predictor

Coef

SE(Coef)

Constant Entering GPA

3.584756 0.090953

0.078183 0.022162

T

10)

P

45.85075 5.66 × 10-11 4.103932 0.003419

^

A) y = 3.584756 - 0.022162x ^

B) y = 3.584756x + 0.090953 ^

C) y = 3.584756 + 0.090953x ^

D) y = 3.584756 + 0.022162x ^

E) y = 45.85075 + 0.090953x Select the most appropriate answer.

11) For exponential regression, a plot of

versus the x-values is approximately linear.

A) the exponential of the y-values C) the residuals

Solve the problem.

12) Fell running, a popular sport in England, involves running long distances over mountainous terrain. The times for 28 female runners to complete a particular 10 -mile course are recorded along with the amount of time each runner had spent training for the race in the month prior to the event. The regression of time to complete the race (in minutes) on training time (in hours) has the following regression output: Predictor Constant Training time

Coef SE Coef 129.701 7.414 0.01690 -0.1492

11)

B) the logarithm of the y-values D) the y-values

T 17.49 -8.83

12)

P 0.000 0.000

Interpret the y-intercept of the prediction equation.

A) A runner who has trained for one hour, is predicted to complete the race in 129.5518 minutes.

B) For each additional hour of training time, the predicted time to complete the race will decrease by 0.1492 minutes.

C) A runner who has not trained at all for the race is predicted to complete the race in 129.701 minutes.

D) A runner who has not trained at all for the race is predicted to complete the race in 129.5518 minutes.

Provide an appropriate response.

13) In order for a prediction interval for y or a confidence interval for μ to be valid, which of the following must hold?

I. The true relationship between x and y must be close to linear.

II. The variability of the y-values must be about the same at each fixed x value.

III. The variability of the x-values must be about the same at each fixed y value.

A) III only B) II only C) I only D) I, II, and III E) both I and II Copyright © 2013 Pearson Education, Inc. 179

13)

Fill in the blank. ^ 2 14) The sum ∑(y-y) is called the sum of squared ___________.

A) regression B) errors C) residuals

14) D) mean

^

E) total ^

15) The difference y - y between an observed outcome y and its predicted value y is called a/an ______________.

A) slope B) equation C) mean D) constant E) residual Provide an appropriate response.

16) Fast food is often considered unhealthy because much fast food is high in both fat and sodium.

Using the table below find the correlation between fat and sodium. Round your answer to three decimals places.

Fat in grams (x) 19 31 34 35 39 39 43 Sodium in milligrams (y) 920 1500 1310 860 1180 940 1260 A) 0.199 B) 0.040 C) 0.210 D) -0.199 E) 0.335 17) The typing speeds (x) (in words per minute) and reading speeds (y)(in words per minute) of nine randomly selected secretaries were recorded. Use the regression analysis provided below to calculate the residual for a typist with a typing speed of 50 words per minute and a reading speed of 480 words per minute.

15)

16)

17)

^

The regression equation is y = 290.2093 + 3.502052x R-sq = 12.385% 9 - 2 = 7 degrees of freedom Predictor Constant Typing speed A) -14.69

Coef SE(Coef) 290.2093 215.4116 3.502052 3.520579 B) -304.9

T P 1.347231 0.219884 0.994737 0.352998 C) 14.69

D) 465.31

E) 304.9

Use technology to provide an appropriate response.

18) Managers rate employees according to job performance (x) and attitude (y). The results for several randomly selected employees are given below. Determine the regression line for this data. Round to the values to two decimal places. x 59 63 65 69 77 76 69 70 64 58 y 72 67 78 82 87 92 83 87 78 75

18)

^

A) y = 11.7 + 1.02x ^

B) y = 2.81 + 1.35x ^

C) y = 92.3 - 0.669x ^

D) y = 11.7x + 1.02 ^

E) y = -47.3 + 2.02x Provide an appropriate response.

19) The data given below are the gestation periods, in months, of randomly selected mammals and their corresponding life span, in years.

Gestation 8 2.1 1.3 1 11.5 5.3 3.8 24.3 Life span 30 13 8 4 28 11 12 42 Identify the explanatory variable A) gestation B) life span C) mammals D) months E) climate

Copyright © 2013 Pearson Education, Inc. 180

19)

Answer true or false.

20) The slope describes the strength of linear association.

A) True B) False

20)

Provide an appropriate response.

21) The data given are the gestation periods, in months, of randomly selected mammals and their corresponding life span, in years. Calculate the correlation coefficient r. Round your answer to three decimal places.

Gestation (x) 8 2.1 1.3 1 11.5 5.3 3.8 24.3 Life span (y) 30 12 6 3 25 12 10 40 A) -0.916 B) 0.839 C) 1 D) -0.839 E) 0.916 Select the most appropriate answer.

22) A table that reports the sums of squares used in regression analysis is called a(n) ____________________ table.

A) sums of squares B) residual C) analysis of variance D) contingency E) regression

21)

22)

Provide an appropriate response.

23) The data below are the ages and systolic blood pressures (measured in millimeters of mercury) of 9 randomly selected adults. The equation of the least squares regression line is found to be

23)

^

y = 60.46 + 1.488x. Use the regression line to predict the systolic blood pressure of a person who is 52 years old. Round to the nearest millimeter.

38 41 45 48 51 53 57 61 65 Age, x Pressure, y 116 120 123 131 142 145 148 150 152 A) 80 mmHg B) 150 mmHg C) 138 mmHg D) 141 mmHg E) 130 mmHg 24) The regression equation relating dexterity scores (x) and productivity scores (y) for the randomly ^

selected employees of a company is y = 5.50 + 1.91x. Find the estimated mean of the productivity scores for all those who had dexterity scores of x = 37. Round to the nearest tenth.

A) 70.7 B) 56.3 C) 58.2 D) 76.2 E) 205.4 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

25) An observation in regression analysis is influential when what two things happen?

Copyright © 2013 Pearson Education, Inc. 181

25)

24)

Answer Key Testname: CHAPTER_12_EXAM_A

1) D 2) B 3) E 4) A 5) B 6) A 7) B 8) C 9) A 10) C 11) B 12) C 13) E 14) C 15) E 16) A 17) C 18) A 19) A 20) B 21) E 22) C 23) C 24) D 25) (1) Its x value is low or high compared to the rest of the data and (2) It does not fall in the straight -line pattern that the rest of the data have.

Copyright © 2013 Pearson Education, Inc. 182

Chapter 12 Exam B Name___________________________________

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

Provide an appropriate response.

1) The typing speeds (x) (in words per minute) and reading speeds (y)(in words per minute) of nine randomly selected secretaries were recorded. Use the regression analysis provided below to predict the reading speed for a typing speed of 10 words per minute. Round your answer to the nearest word.

1)

^

The regression equation is y = 290.2093 + 3.502052x R-sq = 12.385% 9 - 2 = 7 degrees of freedom Predictor Coef SE(Coef) Constant 290.2093 215.4116 Typing speed 3.502052 3.520579 A) 330 words per minute B) 352 words per minute C) 322 words per minute D) 290 words per minute E) 250 words per minute

T 1.347231 0.994737

P 0.219884 0.352998

2) The index (x) of exposure to radioactive waste and the cancer mortality rates (y)(deaths per 100,000) were recorded for nine different Texas counties. The regression analysis is given below.

Use the analysis to find the slope of the regression line.

Predictor Coef SE(Coef) Constant 114.7156 8.045663 Index of Exp 9.231456 1.418787 A) 14.25807 B) 1.418787

T P 14.25807 0.00000198 6.506584 0.000332 C) 9.231456

D) 8.045663

E) 114.7156

3) Suppose that for a certain country, the population size can be predicted by the exponential ^ regression model y = 2.21 × 1.08x where y is the population size (in millions) and x is the number of decades since 2000. What is the predicted population size for 2030? Round to two decimal places.

A) 2.78 million B) 71.60 million C) 7.16 million D) 22.24 million E) 2.58 million

Copyright © 2013 Pearson Education, Inc. 183

2)

3)

4) In order for a prediction interval for y or a confidence interval for μ to be valid, which of the following must hold?

I. The true relationship between x and y must be close to linear.

II. The variability of the y-values must be about the same at each fixed x value.

III. The variability of the x-values must be about the same at each fixed y value.

A) II only B) III only C) both I and II D) I only E) I, II, and III

4)

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

5) An observation in regression analysis is influential when what two things happen?

5)

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

6) A tennis ball is dropped from 15 different heights, x, (in inches) and the height of the bounce, y, is

6)

^

recorded (in inches). A regression analysis gives the the model y = -0.4 + 0.70x. A tennis ball dropped 71 inches bounced 53.3 inches. What is the residual for this bounce height?

A) 5 inches B) -4 inches C) 4 inches D) 2.8 inches E) 49.3 inches 7) The regression equation relating dexterity scores (x) and productivity scores (y) for the randomly

7)

^

selected employees of a company is y = 5.50 + 1.91x. Find the estimated mean of the productivity scores for all those who had dexterity scores of x = 37. Round to the nearest tenth.

A) 205.4 B) 58.2 C) 56.3 D) 76.2 E) 70.7 8) Fast food is often considered unhealthy because much fast food is high in both fat and sodium.

Using the table below find the correlation between fat and sodium. Round your answer to three decimals places.

Fat in grams (x) 19 31 34 35 39 39 43 Sodium in milligrams (y) 920 1500 1310 860 1180 940 1260 A) 0.040 B) 0.335 C) -0.199 D) 0.199 E) 0.210

8)

9) The data given are the gestation periods, in months, of randomly selected mammals and their corresponding life span, in years. Calculate the correlation coefficient r. Round your answer to three decimal places.

Gestation (x) 8 2.1 1.3 1 11.5 5.3 3.8 24.3 Life span (y) 30 12 6 3 25 12 10 40 A) -0.916 B) 0.916 C) 0.839 D) -0.839 E) 1

9)

Copyright © 2013 Pearson Education, Inc. 184

10) Ten college students were randomly selected. Their grade point averages (GPAs) when they entered the program were between 3.5 and 4.0. The studentsʹ GPAs on entering the program (x) and their current GPAs (y) were recorded. The regression analysis is given below. Use the analysis to find the equation of the regression line.

Predictor

Coef

SE(Coef)

Constant Entering GPA

3.584756 0.090953

0.078183 0.022162

T

10)

P

45.85075 5.66 × 10-11 4.103932 0.003419

^

A) y = 3.584756x + 0.090953 ^

B) y = 45.85075 + 0.090953x ^

C) y = 3.584756 + 0.090953x ^

D) y = 3.584756 - 0.022162x ^

E) y = 3.584756 + 0.022162x 11) The data below are the ages and systolic blood pressures (measured in millimeters of mercury) of 9 randomly selected adults. The equation of the least squares regression line is found to be

11)

^

y = 60.46 + 1.488x. Use the regression line to predict the systolic blood pressure of a person who is 52 years old. Round to the nearest millimeter.

38 41 45 48 51 53 57 61 65 Age, x Pressure, y 116 120 123 131 142 145 148 150 152 A) 150 mmHg B) 141 mmHg C) 138 mmHg D) 130 mmHg E) 80 mmHg 12) Records were kept on the relationship between the rainfall (in inches) and the yield of cotton (bushels per acre). The equation of the least squares regression line is found to be

12)

^

y = 4.267 + 4.379x. Use the regression line to predict the yield of cotton for an area with a rainfall of 10 inches.

10.5 8.8 13.4 12.5 18.8 10.3 7.0 15.6 16.0 Rain fall (in inches), x Yield (bushels per acre), y 50.5 46.2 58.8 59.0 82.4 49.2 31.9 76.0 78.8 A) 31 bushels per acre B) 47 bushels per acre C) 48 bushels per acre D) 45 bushels per acre E) 50 bushels per acre 13) The data given below are the gestation periods, in months, of randomly selected mammals and their corresponding life span, in years.

Gestation 8 2.1 1.3 1 11.5 5.3 3.8 24.3 Life span 30 13 8 4 28 11 12 42 Identify the explanatory variable A) climate B) gestation C) mammals D) months E) life span

Copyright © 2013 Pearson Education, Inc. 185

13)

14) The typing speeds (x) (in words per minute) and reading speeds (y)(in words per minute) of nine randomly selected secretaries were recorded. Use the regression analysis provided below to calculate the residual for a typist with a typing speed of 50 words per minute and a reading speed of 480 words per minute.

14)

^

The regression equation is y = 290.2093 + 3.502052x R-sq = 12.385% 9 - 2 = 7 degrees of freedom Predictor Constant Typing speed A) -304.9

Coef SE(Coef) 290.2093 215.4116 3.502052 3.520579 B) 14.69

T P 1.347231 0.219884 0.994737 0.352998 C) -14.69

D) 465.31

E) 304.9

Select the most appropriate answer.

15) A table that reports the sums of squares used in regression analysis is called a(n) ____________________ table.

A) sums of squares B) regression C) analysis of variance D) residual E) contingency

15)

16) To use regression in an inferential manner, which of the following assumptions is/are necessary?

A) The population values of y at each value of x follow a normal distribution.

B) The data were gathered using randomization, such as random sampling or a randomized experiment.

C) The population values of y at each value of x have the same standard deviation.

D) The population means of y at different values of x have a straight -line relationship with x.

E) All of these.

16)

17) The error involved in estimating the population mean of y at a particular value of x is ____________________ the error involved in predicting an individual value of y at that same particular value of x.

A) equal to B) greater than or equal to C) less than or equal to D) greater than E) less than

17)

18) For exponential regression, a plot of

18)

versus the x-values is approximately linear.

A) the exponential of the y-values C) the residuals

B) the y-values D) the logarithm of the y-values

Fill in the blank. ^ 2 19) The sum ∑(y-y) is called the sum of squared ___________.

A) errors B) mean C) residuals

19) D) total

^

E) regression ^

20) The difference y - y between an observed outcome y and its predicted value y is called a/an ______________.

A) mean B) constant C) equation D) slope E) residual Copyright © 2013 Pearson Education, Inc. 186

20)

Answer true or false.

21) The predictor x is relatively closer to its mean than the predicted y is to its mean.

A) True B) False 22) The parameter β in the straight-line model μy = α + βx represents a multiplicative effect on the mean of y for a one-unit increase in x.

A) True

Solve the problem.

24) Fell running, a popular sport in England, involves running long distances over mountainous terrain. The times for 28 female runners to complete a particular 10 -mile course are recorded along with the amount of time each runner had spent training for the race in the month prior to the event. The regression of time to complete the race (in minutes) on training time (in hours) has the following regression output: Coef SE Coef 129.701 7.414 0.01690 -0.1492

22)

B) False

23) The slope describes the strength of linear association.

A) True B) False

Predictor Constant Training time

21)

T 17.49 -8.83

23)

24)

P 0.000 0.000

Interpret the y-intercept of the prediction equation.

A) A runner who has not trained at all for the race is predicted to complete the race in 129.5518 minutes.

B) For each additional hour of training time, the predicted time to complete the race will decrease by 0.1492 minutes.

C) A runner who has not trained at all for the race is predicted to complete the race in 129.701 minutes.

D) A runner who has trained for one hour, is predicted to complete the race in 129.5518 minutes.

Use technology to provide an appropriate response.

25) Managers rate employees according to job performance (x) and attitude (y). The results for several randomly selected employees are given below. Determine the regression line for this data. Round to the values to two decimal places. x 59 63 65 69 77 76 69 70 64 58 y 72 67 78 82 87 92 83 87 78 75 ^

A) y = -47.3 + 2.02x ^

B) y = 2.81 + 1.35x ^

C) y = 92.3 - 0.669x ^

D) y = 11.7 + 1.02x ^

E) y = 11.7x + 1.02

Copyright © 2013 Pearson Education, Inc. 187

25)

Answer Key Testname: CHAPTER_12_EXAM_B

1) B 2) C 3) A 4) C 5) (1) Its x value is low or high compared to the rest of the data and (2) It does not fall in the straight -line pattern that the rest of the data have.

6) C 7) D 8) D 9) B 10) C 11) C 12) C 13) B 14) B 15) C 16) E 17) E 18) D 19) C 20) E 21) B 22) B 23) B 24) C 25) D

Copyright © 2013 Pearson Education, Inc. 188

Chapter 13 Exam A Name___________________________________

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

Provide an appropriate response.

1) A researcher found a significant relationship between a personʹs age, x1 , the number of hours a

1)

person works per week, x2 , and the number of accidents, y, the person has per year. The ^

relationship can be represented by the multiple regression equation y = -3.2 + 0.012x1 + 0.23x2 .

Predict the number of accidents per year (to the nearest whole number) for a person aged 41 who works 31 hours per week.

A) 3 B) 7 C) 4 D) 5 E) 6 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

2) Suppose that the prediction equation relating number of years of education to gender

2)

^

(x1 = 1 for males, x1 = 0 for females) is y = 13.0 + 1.0 x1 . a. Find the estimated mean education for (i) females, (ii) males. b. Explain how to interpret the coefficient of the indicator variable.

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

3) What factors affect the sale price of oceanside condominium units? To answer this question, the following data were recorded for each of the n = 105 units sold at auction: y = sale price (in thousands of dollars) x1 = floor height (1, 2, 3, . . ., 8) x2 = 1 if ocean view, 0 is bay view ^

The least squares prediction equation is y = 17.770 - 0.073 x1 + 3.137 x2 . Interpret the estimated effect of floor height.

A) The correlation between selling price and floor height is -0.073.

B) Expected sale price increases by $0.73 for each one floor increase in floor height for the same view type.

C) Expected sale price decreases by $0.73 for each one floor increase in floor height for the same view type.

D) Expected sale price decreases by $73 for each one floor increase in floor height for the same view type.

E) Expected sale price increases by $73 for each one floor increase in floor height for the same view type.

Copyright © 2013 Pearson Education, Inc. 189

3)

4) A family doctor wants to examine the variables that affect his female patientsʹ total cholesterol. He randomly selects 14 of his female patients and asks them to determine their average daily consumption of saturated fat. The output from MINITAB gives the following regression analysis: Predictor Coef Constant 90.84 AGE 1.0142 FAT 3.2443 R-Sq = 84.7%

SE Coef 15.99 0.2427 0.6632

T 5.68 4.18 4.89

4)

P 0.000 0.002 0.000

Interpret the coefficient for age.

A) For every 1 year increase in age, total cholesterol is expected to increase by 90.84, holding average daily consumption of saturated fat constant.

B) For every 1 year increase in age, total cholesterol is expected to increase by 1.0142, holding average daily consumption of saturated fat constant.

C) For every 1 unit increase in total cholesterol, age is expected to be 1.0142 years greater, holding average daily consumption of saturated fat constant.

D) For every 1 year increase in age, total cholesterol is expected to increase by 91.8542, holding average daily consumption of saturated fat constant.

E) For every 1 year increase in age, total cholesterol is expected to increase by 0.2427, holding average daily consumption of saturated fat constant.

Determine whether the scatter plot shows little or no association, a negative association, a linear association, a moderately strong association, or a very strong association (multiple associations are possible).

5) 5)

A) Positive association, linear association, moderately strong association B) Little or no association C) Linear association, moderately strong association D) Moderately strong association E) Positive association

Copyright © 2013 Pearson Education, Inc. 190

Provide an appropriate response.

6) A logistic regression model was fit to a random sample of Americans of voting age to describe the relationship between the probability of voting in the 2004 presidential election, p, and a personʹs age, x. Part of the logistic regression analysis from Minitab follows.

6)

Predictor Coef SE Coef Z P Constant -0.811552 0.200876 -4.04 0.000 Age 0.0251255 0.0047960 5.24 0.000 At what age does the estimated probability of voting in the 2004 presidential election equal 0.50?

Round your answer to the nearest year.

A) 33 B) 32 C) 42 D) None of these E) 31 7) Use the following computer data, which refers to bear measurements, to answer the question.

7)

Dependent variable is Weight R-Sq = 96.9% Predictor Coef Constant -285.21 Age -1.3838 Head Width -11.24 Neck 28.594

SE Coef T 78.45 -3.64 0.9022 -1.53 20.88 -0.54 5.870 4.87

P 0.022 0.200 0.619 0.007

Write the equation of the regression model.

A) Weight = -285.21 + 78.45 Age - 3.64 Head Width + 0.022 Neck B) Weight = -285.21 + 1.3838 Age + 11.24 Head Width + 28.594 Neck C) Weight = 78.45 + 0.9022 Age + 20.88 Head Width + 5.870 Neck D) Weight = -285.21 - 1.3838 Age - 11.24 Head Width + 28.594 Neck E) Weight = 78.45 - 0.9022 Age - 20.88 Head Width + 5.870 Neck 8) Suppose you fit the multiple regression model μy = α + β 1 x1 + β 2 x2 to n = 28 data values and

8)

^

obtain the prediction equation y = 4 + 1.57 x1 + 1.15 x2 . The estimates of the standard deviations ^

^

of the sampling distributions of β 1 and β 2 are 1.96 and 0.63, respectively. Calculate the test statistic and P-value for testing H0 : β 2 = 0 against Ha : β 2 ≠ 0.

A) t = 1.83; 0.05 < P-value < 0.10 B) t = 9.66; P-value< 0.002 C) t = 0.80; P-value > 0.20 D) t = 1.83; 0.025 < P-value < 0.05 E) t = 0.80; P-value > 0.10 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

9) Explain why the overall F test is done before the individual t tests in a multiple regression analysis.

Copyright © 2013 Pearson Education, Inc. 191

9)

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

Select the most appropriate answer.

10) In order to predict the length of time a house will remain on the market until it is sold in a particular county, the selling price (x1 ), square footage (x2 ) and whether or not the house is in the

10)

city (x3 = 1 for city and 0 otherwise) were recorded for a random sample of 250 homes. What is the regression model for a house that is located in the city?

A) μ = α + β 3 x3 B) μ = α + β 1 x1 + β 2 x2 C) μ = α + β 1 x1 + β 2 x2 + β 3 x3 ^

D) y = α + β 1 x1 + β 2 x2 + β 3 E) μ = α + β 1 x1 + β 2 x2 + β 3 Provide an appropriate response.

11) Use the multiple regression equation given below to predict the y-value for the given values of the

11)

^

independent variables. The regression line is y = 6101 + 31.8 x1 - 0.589 x2 . Estimate y for x1 = 1517 and x2 = 1558. Round to the nearest thousandth.

A) 55259.262

B) 53,423.938

C) 49158.262

D) 47322.938

E) 53455.738

12) Use the following computer data, which refers to bear measurements, to answer the question.

12)

Dependent variable is Weight R-Sq = 96.9% Predictor Coef Constant -285.21 Age -1.3838 Head Width -11.24 Neck 28.594

SE Coef T 78.45 -3.64 0.9022 -1.53 20.88 -0.54 5.870 4.87

P 0.022 0.200 0.619 0.007

Which measurement is the best predictor of weight, after allowing for the linear effects of the other variables in the model?

A) Sex B) Constant C) Neck D) Age E) Head Width 13) A regression equation was fit relating a studentʹs weight to the number of hours they spent on the computer, x1 , the number of hours they spent watching television, x2 , and the number of hours ^

they spent on the telephone, x3 . The fitted equation is y = 125.5 + 3.26 x1 +4.27 x2 + 1.75 x3 . What is a studentʹs predicted weight if the student spends 4 hours on the computer, 2 hours viewing television, and 3 hours on the telephone?

A) 155.86 B) 154.35 C) 153.22 D) 152.33 E) 151.83

Copyright © 2013 Pearson Education, Inc. 192

13)

14) What factors affect the sale price of oceanside condominium units? To answer this question, the following data were recorded for each of the n = 105 units sold at auction: y = sale price (in thousands of dollars) x1 = floor height (1, 2, 3, . . ., 8)

14)

x2 = 1 if ocean view, 0 is bay view prob>F Source DF SS MS F Constant 2 19.08 8.04 4.14 0.025 Error 102 197.96 1.94 Total 104 217.04 R-sq = 88.0% Assume you are testing the null hypothesis H0 : β 1 = β 2 = 0 at α = 0.05.

State your conclusion for H0 .

A) Since R2 is large, reject H0 and conclude that at least one of the predictors has an effect on sale price.

B) Since the P-value is less than 0.05, reject H0 and conclude that all of the predictors have an effect on sale price.

C) Since the F-value is greater than 0.05, do not reject H0 . There is not enough evidence to conclude that any of the predictors have an effect on sale price.

D) Since the P-value is less than 0.05, reject H0 and conclude that at least one of the predictors has an effect on sale price.

E) Since the P-value is less than 0.05, reject H0 and conclude that both of the predictors are highly correlated to sale price.

Select the most appropriate answer.

15) Average resting heart rate for adults between the ages of 18 and 65 is to be estimated based on the personʹs gender (x1 = 0 for female, 1 for male), the personʹs age (x2 ) and their weight (x3 ). What is the regression model for an adult male weighing 185 pounds?

A) μ = α + β 1 x1 + β 2 x2 + β 3 x3 ^

B) y = α + β 1 + β 2 x2 + 185β 3 C) μ = α + β 1 + β 2 x2 + 185β 3 D) μ = α + β 1 + 185β 3 E) μ = α + β 2 x2 + 185β 3

Copyright © 2013 Pearson Education, Inc. 193

15)

Determine whether the scatter plot shows little or no association, a negative association, a linear association, a moderately strong association, or a very strong association (multiple associations are possible).

16) 16)

A) Positive association, linear association, very strong association B) Linear association, very strong association C) Positive association, linear association D) Positive association, moderately strong association E) Linear association, moderately strong association Provide an appropriate response.

17) A computer utility was applied to data collected in a study of generalized health index as a function of weight/height ratio, cholesterol, and hours of sleep. A partial output is shown below Predictor Constant Weight/Height (lb/in x1 )

Coef 65 2.4

SE Coef 6.431 1.495

T 7.32 0.12

P 0.000 0.765

Cholesterol x2

0.06

0.235

0.21

0.549

Hours sleep x3

1.4

0.199

8.27

0.000

R-sq = 93.1% Regression

F = 221.12

p = 0.000

Determine the proper conclusion about the use of the multiple regression equation.

A) It is useful because of the high R2 value and low P-value.

B) It is useful because of the low R2 value and high P-value.

C) It is useful because of the low R2 value and low P-value.

D) It is not useful because of the high R2 value and low P-value.

E) It is not useful because of the low R2 value and high P-value.

Copyright © 2013 Pearson Education, Inc. 194

17)

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

18) For theʺhouse selling pricesʺ data file, the table shows Minitab output for a regression model with y = selling price of home, x1 = size of home, x2 = number of bedrooms, and x3 = region

18)

(1 = NW, 0 = other).

Regression of selling price on size of home, bedrooms, and region Predictor Constant size Bedrooms region

Coef -1522 82.466 -6651 29651

SE Coef 17848 7.573 6439 7996

T -0.09 10.89 -1.03 3.71

P 0.932 0.000 0.304 0.000

a. Report the prediction equation. By setting x3 = 1 and then 0, construct the two separate equations for homes in the NW and for homes not in the NW. b. Explain how to interpret the coefficient of x3 in the prediction equation.

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

19) For a sample of 20 cars of a certain model, a car dealer records selling price, age of car, and mileage at time of sale. He performs initially a simple regression of selling price (y) on age of car (x) and obtains R2 = 0.78. He then performs a second regression in which he includes mileage as a second

19)

predictor and finds that R2 increases by only a little to 0.82. What can we reasonably conclude?

I. Mileage is highly positively correlated with age. If age is already included as a predictor, including mileage doesnʹt add much new power for predicting selling price.

II. Mileage is not strongly correlated with selling price.

III. A regression of selling price on mileage alone would have a very small R2 .

A) II and III

B) I and II

C) I only

D) I, II, and III

20) Which of the following graphs shows interaction between x1 and x2 in their effects on y? a)

b)

A) b B) cannot be determined from the information given C) neither a nor b D) a E) a and b

Copyright © 2013 Pearson Education, Inc. 195

20)

21) Which of the following graphs shows interaction between x1 and x2 in their effects on y? a)

21)

b)

A) a and b B) neither a nor b C) cannot be determined from the information given D) b E) a Select the most appropriate answer.

22) Which of the following is not true regarding R2 ?

22)

A) Adding correlated variables to the model will not increase R2 .

B) R2 is independent of the units of measurement.

C) If R2 = 0 then each predicted y value is equal to the mean of the y values.

D) If R2 = 1 then each predicted y value is equal to the corresponding observed y value.

E) The closer R2 is to 1, the better the explanatory variables collectively predict y.

Provide an appropriate response.

23) Use the multiple regression equation given below to predict the y-value for the given values of the

23)

^

independent variables. The regression line is y = 9.876 + 0.173 x1 + 0.051 x2 . Estimate y for x1 = 48 and x2 = 16. Round to the nearest thousandth.

A) 19.000

B) 17.364

C) 19.001

D) 9.120

E) 18.996

24) A computer utility gives the following results of a multiple regression analysis. Find the regression equation.

Predictor Constant x1

Coef SE Coef 8.882 0.299 0.201 0.022

T 18.667 5.228

x2

0.049

1.771

S = 0.437

R-sq = 88.1%

0.041

^

A) y = 18.667+ 5.228 x1 + 1.771 x2 ^

B) y = 8.882 + 0.201 x1 ^

C) y = 8.882 + 0.201 x1 + 0.049 x2 ^

D) y = 0.201 x1 + 0.049 x2 ^

E) y = 0.299 + 0.022 x1 + 0.041 x2 Copyright © 2013 Pearson Education, Inc. 196

24)

25) What factors affect the sale price of oceanside condominium units? To answer this question, the following data were recorded for each of the n = 105 units sold at auction: y = sale price (in thousands of dollars) x1 = floor height (1, 2, 3, . . ., 8) x2 = 1 if ocean view, 0 is bay view ^

The least squares prediction equation is y = 17.770 - 0.073 x1 + 3.137 x2 . Interpret the estimated effect of an ocean view.

A) The expected sale price increases by $20,907 for units with an ocean view, holding floor height constant.

B) The expected sale price increases by $3.14 for units with an ocean view, holding floor height constant.

C) The expected sale price increases by $3137 for units with an ocean view, holding floor height constant.

D) The average sale price for units with an ocean view is $20,907, holding floor height constant.

E) The correlation between sale price and view is 3.137.

Copyright © 2013 Pearson Education, Inc. 197

25)

Answer Key Testname: CHAPTER_13_EXAM_A

1) C 2) a. (i) 13.0 (ii) 14.0; b. The predicted number of years of education is 1 year more for males than for females.

3) D 4) B 5) A 6) B 7) D 8) A 9) The F test result tells us whether there is sufficient evidence to make it worthwhile to consider the individual effects.

When there are many explanatory variables, doing the F test first provides protection from doing lots of t tests and having one of them be significant merely by random variation when, in fact, there truly are no effects in the population.

10) E 11) B 12) C 13) D 14) D 15) C 16) A 17) A ^

^

^

18) a. y = -1522 + 82.466x1 - 6651x2 + 29651x3 ; NW: y = 28129 + 82.466x1 - 6651x2 ; other: y = -1522 + 82.466x1 - 6651x2 ; b. The predicted selling price of a home in the NW is $29,651 more than the predicted selling price of a home in other areas.

19) C 20) E 21) B 22) A 23) E 24) C 25) C

Copyright © 2013 Pearson Education, Inc. 198

Chapter 13 Exam B Name___________________________________

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

Provide an appropriate response.

1) What factors affect the sale price of oceanside condominium units? To answer this question, the following data were recorded for each of the n = 105 units sold at auction: y = sale price (in thousands of dollars) x1 = floor height (1, 2, 3, . . ., 8)

1)

x2 = 1 if ocean view, 0 is bay view ^

The least squares prediction equation is y = 17.770 - 0.073 x1 + 3.137 x2 . Interpret the estimated effect of floor height.

A) Expected sale price increases by $0.73 for each one floor increase in floor height for the same view type.

B) Expected sale price increases by $73 for each one floor increase in floor height for the same view type.

C) The correlation between selling price and floor height is -0.073.

D) Expected sale price decreases by $73 for each one floor increase in floor height for the same view type.

E) Expected sale price decreases by $0.73 for each one floor increase in floor height for the same view type.

2) A computer utility was applied to data collected in a study of generalized health index as a function of weight/height ratio, cholesterol, and hours of sleep. A partial output is shown below Predictor Constant Weight/Height (lb/in x1 )

Coef 65 2.4

SE Coef 6.431 1.495

T 7.32 0.12

P 0.000 0.765

Cholesterol x2

0.06

0.235

0.21

0.549

Hours sleep x3

1.4

0.199

8.27

0.000

R-sq = 93.1% Regression

F = 221.12

p = 0.000

Determine the proper conclusion about the use of the multiple regression equation.

A) It is useful because of the low R2 value and low P-value.

B) It is useful because of the low R2 value and high P-value.

C) It is not useful because of the high R2 value and low P-value.

D) It is useful because of the high R2 value and low P-value.

E) It is not useful because of the low R2 value and high P-value.

Copyright © 2013 Pearson Education, Inc. 199

2)

3) A computer utility gives the following results of a multiple regression analysis. Find the regression equation.

Predictor Constant x1

Coef SE Coef 8.882 0.299 0.201 0.022

T 18.667 5.228

x2

0.049

1.771

S = 0.437

R-sq = 88.1%

0.041

3)

^

A) y = 18.667+ 5.228 x1 + 1.771 x2 ^

B) y = 8.882 + 0.201 x1 + 0.049 x2 ^

C) y = 8.882 + 0.201 x1 ^

D) y = 0.201 x1 + 0.049 x2 ^

E) y = 0.299 + 0.022 x1 + 0.041 x2 4) Use the multiple regression equation given below to predict the y-value for the given values of the

4)

^

independent variables. The regression line is y = 6101 + 31.8 x1 - 0.589 x2 . Estimate y for x1 = 1517 and x2 = 1558. Round to the nearest thousandth.

A) 53,423.938

B) 49158.262

C) 55259.262

D) 53455.738

E) 47322.938

5) Use the following computer data, which refers to bear measurements, to answer the question.

Dependent variable is Weight R-Sq = 96.9% Predictor Coef Constant -285.21 Age -1.3838 Head Width -11.24 Neck 28.594

SE Coef T 78.45 -3.64 0.9022 -1.53 20.88 -0.54 5.870 4.87

P 0.022 0.200 0.619 0.007

Which measurement is the best predictor of weight, after allowing for the linear effects of the other variables in the model?

A) Neck B) Head Width C) Age D) Sex E) Constant

Copyright © 2013 Pearson Education, Inc. 200

5)

6) What factors affect the sale price of oceanside condominium units? To answer this question, the following data were recorded for each of the n = 105 units sold at auction: y = sale price (in thousands of dollars) x1 = floor height (1, 2, 3, . . ., 8)

6)

x2 = 1 if ocean view, 0 is bay view prob>F Source DF SS MS F Constant 2 19.08 8.04 4.14 0.025 Error 102 197.96 1.94 Total 104 217.04 R-sq = 88.0% Assume you are testing the null hypothesis H0 : β 1 = β 2 = 0 at α = 0.05.

State your conclusion for H0 .

A) Since R2 is large, reject H0 and conclude that at least one of the predictors has an effect on sale price.

B) Since the P-value is less than 0.05, reject H0 and conclude that both of the predictors are highly correlated to sale price.

C) Since the P-value is less than 0.05, reject H0 and conclude that all of the predictors have an effect on sale price.

D) Since the P-value is less than 0.05, reject H0 and conclude that at least one of the predictors has an effect on sale price.

E) Since the F-value is greater than 0.05, do not reject H0 . There is not enough evidence to conclude that any of the predictors have an effect on sale price.

7) A researcher found a significant relationship between a personʹs age, x1 , the number of hours a

7)

person works per week, x2 , and the number of accidents, y, the person has per year. The ^

relationship can be represented by the multiple regression equation y = -3.2 + 0.012x1 + 0.23x2 .

Predict the number of accidents per year (to the nearest whole number) for a person aged 41 who works 31 hours per week.

A) 6 B) 4 C) 3 D) 5 E) 7 8) For a sample of 20 cars of a certain model, a car dealer records selling price, age of car, and mileage at time of sale. He performs initially a simple regression of selling price (y) on age of car (x) and obtains R2 = 0.78. He then performs a second regression in which he includes mileage as a second predictor and finds that R2 increases by only a little to 0.82. What can we reasonably conclude?

I. Mileage is highly positively correlated with age. If age is already included as a predictor, including mileage doesnʹt add much new power for predicting selling price.

II. Mileage is not strongly correlated with selling price.

III. A regression of selling price on mileage alone would have a very small R2 .

A) I only

B) I and II

C) II and III

D) I, II, and III

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

9) Suppose that the prediction equation relating number of years of education to gender ^

(x1 = 1 for males, x1 = 0 for females) is y = 13.0 + 1.0 x1 . a. Find the estimated mean education for (i) females, (ii) males. b. Explain how to interpret the coefficient of the indicator variable.

Copyright © 2013 Pearson Education, Inc. 201

9)

8)

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

10) A family doctor wants to examine the variables that affect his female patientsʹ total cholesterol. He randomly selects 14 of his female patients and asks them to determine their average daily consumption of saturated fat. The output from MINITAB gives the following regression analysis: Predictor Coef Constant 90.84 AGE 1.0142 FAT 3.2443 R-Sq = 84.7%

SE Coef 15.99 0.2427 0.6632

T 5.68 4.18 4.89

10)

P 0.000 0.002 0.000

Interpret the coefficient for age.

A) For every 1 year increase in age, total cholesterol is expected to increase by 0.2427, holding average daily consumption of saturated fat constant.

B) For every 1 year increase in age, total cholesterol is expected to increase by 91.8542, holding average daily consumption of saturated fat constant.

C) For every 1 year increase in age, total cholesterol is expected to increase by 90.84, holding average daily consumption of saturated fat constant.

D) For every 1 year increase in age, total cholesterol is expected to increase by 1.0142, holding average daily consumption of saturated fat constant.

E) For every 1 unit increase in total cholesterol, age is expected to be 1.0142 years greater, holding average daily consumption of saturated fat constant.

11) A logistic regression model was fit to a random sample of Americans of voting age to describe the relationship between the probability of voting in the 2004 presidential election, p, and a personʹs age, x. Part of the logistic regression analysis from Minitab follows.

11)

Predictor Coef SE Coef Z P Constant -0.811552 0.200876 -4.04 0.000 Age 0.0251255 0.0047960 5.24 0.000 At what age does the estimated probability of voting in the 2004 presidential election equal 0.50?

Round your answer to the nearest year.

A) 32 B) 33 C) 42 D) None of these E) 31 12) Use the multiple regression equation given below to predict the y-value for the given values of the ^

independent variables. The regression line is y = 9.876 + 0.173 x1 + 0.051 x2 . Estimate y for x1 = 48 and x2 = 16. Round to the nearest thousandth.

A) 17.364

B) 18.996

C) 9.120

D) 19.000

Copyright © 2013 Pearson Education, Inc. 202

E) 19.001

12)

13) Suppose you fit the multiple regression model μy = α + β 1 x1 + β 2 x2 to n = 28 data values and

13)

^

obtain the prediction equation y = 4 + 1.57 x1 + 1.15 x2 . The estimates of the standard deviations ^

^

of the sampling distributions of β 1 and β 2 are 1.96 and 0.63, respectively. Calculate the test statistic and P-value for testing H0 : β 2 = 0 against Ha : β 2 ≠ 0.

A) t = 0.80; P-value > 0.10 B) t = 0.80; P-value > 0.20 C) t = 1.83; 0.05 < P-value < 0.10 D) t = 9.66; P-value< 0.002 E) t = 1.83; 0.025 < P-value < 0.05 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

14) Explain why the overall F test is done before the individual t tests in a multiple regression analysis.

14)

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

15) What factors affect the sale price of oceanside condominium units? To answer this question, the following data were recorded for each of the n = 105 units sold at auction: y = sale price (in thousands of dollars) x1 = floor height (1, 2, 3, . . ., 8)

15)

x2 = 1 if ocean view, 0 is bay view ^

The least squares prediction equation is y = 17.770 - 0.073 x1 + 3.137 x2 . Interpret the estimated effect of an ocean view.

A) The expected sale price increases by $20,907 for units with an ocean view, holding floor height constant.

B) The average sale price for units with an ocean view is $20,907, holding floor height constant.

C) The expected sale price increases by $3.14 for units with an ocean view, holding floor height constant.

D) The correlation between sale price and view is 3.137.

E) The expected sale price increases by $3137 for units with an ocean view, holding floor height constant.

16) Use the following computer data, which refers to bear measurements, to answer the question.

Dependent variable is Weight R-Sq = 96.9% Predictor Coef Constant -285.21 Age -1.3838 Head Width -11.24 Neck 28.594

SE Coef T 78.45 -3.64 0.9022 -1.53 20.88 -0.54 5.870 4.87

P 0.022 0.200 0.619 0.007

Write the equation of the regression model.

A) Weight = -285.21 + 78.45 Age - 3.64 Head Width + 0.022 Neck B) Weight = 78.45 + 0.9022 Age + 20.88 Head Width + 5.870 Neck C) Weight = 78.45 - 0.9022 Age - 20.88 Head Width + 5.870 Neck D) Weight = -285.21 - 1.3838 Age - 11.24 Head Width + 28.594 Neck E) Weight = -285.21 + 1.3838 Age + 11.24 Head Width + 28.594 Neck Copyright © 2013 Pearson Education, Inc. 203

16)

17) Which of the following graphs shows interaction between x1 and x2 in their effects on y? a)

17)

b)

A) neither a nor b B) b C) a and b D) cannot be determined from the information given E) a 18) Which of the following graphs shows interaction between x1 and x2 in their effects on y? a)

b)

A) b B) neither a nor b C) a D) cannot be determined from the information given E) a and b

Copyright © 2013 Pearson Education, Inc. 204

18)

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

19) For theʺhouse selling pricesʺ data file, the table shows Minitab output for a regression model with y = selling price of home, x1 = size of home, x2 = number of bedrooms, and x3 = region

19)

(1 = NW, 0 = other).

Regression of selling price on size of home, bedrooms, and region Predictor Constant size Bedrooms region

Coef -1522 82.466 -6651 29651

SE Coef 17848 7.573 6439 7996

T -0.09 10.89 -1.03 3.71

P 0.932 0.000 0.304 0.000

a. Report the prediction equation. By setting x3 = 1 and then 0, construct the two separate equations for homes in the NW and for homes not in the NW. b. Explain how to interpret the coefficient of x3 in the prediction equation.

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

20) A regression equation was fit relating a studentʹs weight to the number of hours they spent on the computer, x1 , the number of hours they spent watching television, x2 , and the number of hours

20)

^

they spent on the telephone, x3 . The fitted equation is y = 125.5 + 3.26 x1 +4.27 x2 + 1.75 x3 . What is a studentʹs predicted weight if the student spends 4 hours on the computer, 2 hours viewing television, and 3 hours on the telephone?

A) 153.22 B) 155.86 C) 152.33 D) 151.83 E) 154.35 Determine whether the scatter plot shows little or no association, a negative association, a linear association, a moderately strong association, or a very strong association (multiple associations are possible).

21) 21)

A) Linear association, very strong association B) Positive association, moderately strong association C) Positive association, linear association D) Positive association, linear association, very strong association E) Linear association, moderately strong association

Copyright © 2013 Pearson Education, Inc. 205

22)

22)

A) Linear association, moderately strong association B) Moderately strong association C) Little or no association D) Positive association E) Positive association, linear association, moderately strong association Select the most appropriate answer.

23) Average resting heart rate for adults between the ages of 18 and 65 is to be estimated based on the personʹs gender (x1 = 0 for female, 1 for male), the personʹs age (x2 ) and their weight (x3 ). What is

23)

the regression model for an adult male weighing 185 pounds?

A) μ = α + β 1 + β 2 x2 + 185β 3 ^

B) y = α + β 1 + β 2 x2 + 185β 3 C) μ = α + β 1 + 185β 3 D) μ = α + β 1 x1 + β 2 x2 + β 3 x3 E) μ = α + β 2 x2 + 185β 3 24) Which of the following is not true regarding R2 ?

A) The closer R2 is to 1, the better the explanatory variables collectively predict y.

24)

B) If R2 = 1 then each predicted y value is equal to the corresponding observed y value.

C) R2 is independent of the units of measurement.

D) Adding correlated variables to the model will not increase R2 .

E) If R2 = 0 then each predicted y value is equal to the mean of the y values.

25) In order to predict the length of time a house will remain on the market until it is sold in a particular county, the selling price (x1 ), square footage (x2 ) and whether or not the house is in the city (x3 = 1 for city and 0 otherwise) were recorded for a random sample of 250 homes. What is the regression model for a house that is located in the city?

A) μ = α + β 1 x1 + β 2 x2 + β 3 x3 B) μ = α + β 1 x1 + β 2 x2 C) μ = α + β 1 x1 + β 2 x2 + β 3 ^

D) y = α + β 1 x1 + β 2 x2 + β 3 E) μ = α + β 3 x3

Copyright © 2013 Pearson Education, Inc. 206

25)

Answer Key Testname: CHAPTER_13_EXAM_B

1) D 2) D 3) B 4) A 5) A 6) D 7) B 8) A 9) a. (i) 13.0 (ii) 14.0; b. The predicted number of years of education is 1 year more for males than for females.

10) D 11) A 12) B 13) C 14) The F test result tells us whether there is sufficient evidence to make it worthwhile to consider the individual effects.

When there are many explanatory variables, doing the F test first provides protection from doing lots of t tests and having one of them be significant merely by random variation when, in fact, there truly are no effects in the population.

15) E 16) D 17) A 18) E ^

^

^

19) a. y = -1522 + 82.466x1 - 6651x2 + 29651x3 ; NW: y = 28129 + 82.466x1 - 6651x2 ; other: y = -1522 + 82.466x1 - 6651x2 ; b. The predicted selling price of a home in the NW is $29,651 more than the predicted selling price of a home in other areas.

20) C 21) D 22) E 23) A 24) D 25) C

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Chapter 14 Exam A Name___________________________________

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

Provide an appropriate response.

1) Show how to construct a multiple regression model for the analysis of mean income over a three-way classification of gender (male, female), race (white, black), and type of job (blue-collar, white-collar, service). Interpret the parameters in the model. Assume that there is no interaction.

1)

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

State the null hypothesis to test for independence.

2) A golf organization wants to know which brand of golf ball goes the farthest when hit by a driver.

Three brands of golf balls are compared by using a well-known golf instructor to randomly hit each brand of ball five times. The total distance in yards is measured after each ball comes to rest.

A) H0 : μ1 ≠ μ2 ≠ μ3 vs. the alternative that all brand means are equal

2)

B) H0 : μ1 = μ2 = μ3 = μ4 = μ5 vs. the alternative that not all hit means are equal C) H0 : μ1 ≠ μ2 ≠ μ3 ≠ μ4 ≠ μ5 vs. the alternative that all hit means are equal D) H0 : μ1 = μ2 = μ3 vs. the alternative that not all hit means are equal E) H0 : μ1 = μ2 = μ3 vs. the alternative that not all brand means are equal Using the table, find the F-value for the numerator and denominator degrees of freedom. Use α = 0.05.

3) Using the table, find F-value for df1 = 3 and df2 = 12 for α = 0.05.

3)

A) 3.49 B) 8.74 C) none of these D) 3.59 E) 3.29 Determine the degrees of freedom.

4) An independent research firm conducts a study to compare the taste of four new sports drinks.

Five people are randomly assigned to each of the four drinks. Each person tastes the drink and judges it on a scale from one to five. How many degrees of freedom (df1 ) does the group sum of

4)

squares have? How many degrees of freedom ( df2 ) for the error sum of squares?

A) df1 = 4; df2 = 17 B) df1 = 4; df2 = 16 C) df1 = 3; df2 = 16 D) df1 = 16; df2 = 3 E) df1 = 3; df2 = 17 Using the table, find the F-value for the numerator and denominator degrees of freedom. Use α = 0.05.

5) Using the table, find F-value for df1 = 12 and df2 = 15 for α = 0.05.

A) none of these B) 2.48 C) 2.53 D) 2.69 E) 2.13 Copyright © 2013 Pearson Education, Inc. 208

5)

6) Using the table, find F-value for df1 = 6 and df2 = 20 for α = 0.05.

A) 2.74

B) 2.47

C) 2.85

D) 2.63

6) E) 2.60

Select the most appropriate answer.

7) Which of the following are assumptions of the analysis of variance F test for comparing population means of several groups?

A) Each group has the same standard deviation.

B) All of these.

C) The random samples drawn from each group are independent.

D) None of these.

E) Each group has a normal population distribution.

Use the MiniTab display.

8) A manager records the production output of three employees who each work on three different machines for three different days. The sample results are given below and the Minitab results follow.

Machine

I II III

A 23, 27, 29 25, 26, 24 28, 25, 26

Employee B 30, 27, 25 24, 29, 26 25, 27, 23

7)

8)

C 18, 20, 22 19, 16, 14 15, 11, 17

ANALYSIS OF VARIANCE ITEMS SOURCE DF 2 MACHINE EMPLOYEE 2 INTERACTION 4 ERROR 18 TOTAL 26

SS 34.67 504.67 26.67 98.00 664.00

MS 17.33 252.33 6.67 5.44

Using a 0.05 significance level, test the claim that the interaction between employee and machine has no effect on the number of items produced. State the null hypothesis.

A) None of these.

B) H0 : There is an interaction effect.

C) Ha : There is an interaction effect.

D) Ha : There is no interaction effect.

E) H0 : There is no interaction effect.

Select the most appropriate answer.

9) If the average crop yields are to be compared among 4 different varieties of seeds and 2 different irrigation techniques, which of the following methods of analysis seems most appropriate?

A) a factorial ANOVA B) a linear regression analysis C) a logistic regression analysis D) a two-way ANOVA E) a one-way ANOVA

Copyright © 2013 Pearson Education, Inc. 209

9)

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

Provide an appropriate response.

10) The null hypothesis of equality of means for a factor is rejected in a two-way ANOVA. Does this imply that the hypothesis will be rejected in a one-way ANOVA F test, if the data are collapsed over the levels of the second variable? Explain.

10)

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

11) A golf organization wants to know which brand of golf ball goes the farthest when hit by a driver.

Three brands of golf balls are compared by using a well-known golf instructor to randomly hit each brand of ball five times. The total distance in yards is measured after each ball comes to rest.

Calculate the F-ratio. Can you reject H0 using α = 0.05? The ANOVA table is listed below.

11)

Analysis of Variance Source SS df MS F -ratio Brand 1405.375 2 702.688 Error 1467.556 12 122.296 Total 2872.931 A) F-Ratio = 0.174; Do not reject H0 B) F-Ratio = 0.174; Reject H0 C) F-Ratio = 5.746; Reject H0 D) F-Ratio = 5.746; Do not reject H0 E) F-Ratio = 0.958; Do not reject H0 State the null hypothesis to test for independence.

12) An industrial psychologist is investigating the effects of work environment on employee attitudes.

A group of 20 recently hired sales trainees were randomly assigned to one of four different ʺhome roomsʺ - five trainees per room. Each room is identical except for wall color. The four colors used were light green, light blue, gray and red. The psychologist wants to know whether room color has an effect on attitude, and, if so, wants to compare the mean attitudes of the trainees assigned to the four room colors. At the end of the training program, the attitude of each trainee was measured on a 60-pt. scale (the lower the score, the poorer the attitude). The data was subjected to a one -way analysis of variance.

ONE-WAY ANOVA FOR ATTITUDE BY COLOR SS MS F P SOURCE DF GROUP 3 1678.15 559.3833 59.03782 0.0000 ERROR 16 151.6 9.475 TOTAL 19 1829.75 Give the null hypothesis A) H0 : μ1 = μ2 = μ3 = μ4 = μ5 , where the μi represent attitude means for the ith person in each room B) H0 : μgreen = μblue = μgray = μred, where the μʹs represent mean attitudes for the four rooms C) H0 : x1 = x2 = x3 = x4 , where the xʹs represent the room colors D) H0 : pgreen = pblue = pgray = pred, where the pʹs represent the proportion with the corresponding attitude E) none of these

Copyright © 2013 Pearson Education, Inc. 210

12)

Provide an appropriate response.

13) A birdhunterʹs society is interested in knowing whether three different brands of turkey calls are equally effective in attracting gobblers. Each turkey call is randomly assigned to five hunters, and the order of each experiment is also randomized. An experiment consists of a hunter using one brand three times and waiting fifteen minutes. The number of gobblers attracted by the calls is counted. An ANOVA F-test rejected the hypothesis of equal means. Each pair of means were then compared, and the 95% confidence intervals are shown below:

13)

A) 1 vs. 2 (-2.620, -0.180) B) 1 vs. 3 (-0.661, 1.461) C) 2 vs. 3 (0.739, 2.861) Which tests show a significant difference between the means?

B) C C) A A) A,C

D) B

E) none

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

14) Discuss the robustness of the ANOVA F test.

14)

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

State the null hypothesis to test for independence.

15) A chemist is interested in comparing four different catalysts by measuring reaction times. Each catalyst is tested five times, with each experiment randomly assigned one of the four catalysts.

A) H0 : μ1 ≠ μ2 ≠ μ3 ≠ μ4 ≠ μ5 vs. the alternative that all the test means are equal

15)

B) H0 : μ1 = μ2 = μ3 = μ4 = μ5 vs. the alternative that not all the test means are equal C) H0 : μ1 = μ2 = μ3 = μ4 vs. the alternative that not all the catalyst means are equal D) H0 : μ1 = μ2 = μ3 = μ4 vs. the alternative that not all the test means are equal E) H0 : μ1 ≠ μ2 ≠ μ3 ≠ μ4 vs. the alternative that all the catalyst means are equal 16) A telemarketing company wants to compare the effectiveness of five of its employees by looking at the percentage of survey questions completed. Data from four past surveys are randomly chosen for each of the employees, and the percentage of completed questions is calculated.

A) H0 : μ1 = μ2 = μ3 = μ4 vs. the alternative that not all employee means are equal B) H0 : μ1 = μ2 = μ3 = μ4 = μ5 vs. the alternative that not all employee means are equal C) H0 : μ1 ≠ μ2 ≠ μ3 ≠ μ4 vs. the alternative that all survey means are equal D) H0 : μ1 = μ2 = μ3 = μ4 vs. the alternative that not all survey means are equal E) H0 : μ1 ≠ μ2 ≠ μ3 ≠ μ4 ≠ μ5 vs. the alternative that all employee means are equal

Copyright © 2013 Pearson Education, Inc. 211

16)

Provide an appropriate response.

17) An industrial engineer wants to test the effect of three different ways of assembling a part on the total assembly time. Five people are randomly assigned to each of the three assembly methods, and the total assembly time (in seconds) is recorded. Calculate the F-ratio. Can you reject H0

17)

using α = 0.05? The ANOVA table is listed below.

Analysis of Variance Source SS df Method 985535.907 2 Error 276844.275 12 Total 1262380.182 A) F-Ratio = 3.560; Reject H0

MS 492767.954 23070.356

F -ratio

B) F-Ratio = 21.359; Do not reject H0 C) F-Ratio = 21.359; Reject H0 D) F-Ratio = 0.047; Reject H0 E) F-Ratio = 0.047; Don not reject H0 Select the most appropriate answer.

18) If the average weight losses are to be compared among 3 different diets, which of the following methods of analysis seems most appropriate?

A) a one-way ANOVA B) a two-way ANOVA C) a logistic regression analysis D) a linear regression analysis E) a three-way ANOVA Provide an appropriate response.

19) In a one-factor ANOVA having three group levels with five observations in each group, the between group degrees of freedom is equal to A) 10 B) 4 C) 2 D) 12 E) 15 20) A printing company is interested in comparing the speed of four different desktop printers; four different documents are used for the experiment. Each test consists of randomly assigning one printer to one of the documents. The document is printed and the time to print in seconds is recorded. Each printer/document combination is tested. The F-value from an ANOVA is 6.173.

What is the F value having a P-value of 0.05?

B) 6.39 C) 3.59 D) 3.49 E) 3.24 A) 3.01

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18)

19)

20)

Use the MiniTab display.

21) A manager records the production output of three employees who each work on three different machines for three different days. The sample results are given below and the Minitab results follow.

Machine

I II III

A 31, 34, 32 19, 26, 22 21, 18, 26

Employee B 29, 23, 22 35, 33, 30 20, 23, 24

21)

C 21, 20, 24 25, 19, 23 36, 37, 31

ANALYSIS OF VARIANCE ITEMS SOURCE MACHINE EMPLOYEE INTERACTION ERROR TOTAL

DF 2 2 4 18 26

SS 1.19 5.85 710.81 160.00 877.85

MS .59 2.93 177.70 8.89

Using a 0.05 significance level, test the claim that the interaction between employee and machine has no effect on the number of items produced. Calculate the F-statistic for this test. Round your answer to four decimal places.

B) 2.9300 C) 19.9888 D) 0.2014 E) 0.0198 A) 4.4426 Provide an appropriate response.

22) A chemist is interested in comparing four different catalysts by measuring reaction times. Each catalyst is tested five times, with each experiment randomly assigned one of the four catalysts.

Calculate the F-ratio. Can you reject H0 using α = 0.05? The ANOVA table is listed below.

Analysis of Variance Source SS df MS F -ratio Catalyst 9.310 3 3.103 Error 79.320 16 4.958 Total 88.630 A) F-Ratio = 0.626; Do not reject H0 B) F-Ratio = 0.117; Do not reject H0 C) F-Ratio = 0.626; Reject H0 D) F-Ratio = 1.598; Do not reject H0 E) F-Ratio = 1.598; Reject H0

Copyright © 2013 Pearson Education, Inc. 213

22)

Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean.

23) 23) Source DF SS MS F p Factor 3 30 10.00 1.6 0.264 Error 8 50 6.25 Total 11 80 What can you conclude about the equality of the population means?

A) Reject the null hypothesis since the p-value is greater than the significance level. We conclude that at least two of the factor means differ.

B) Do not reject the null hypothesis since the p-value is greater than the significance level.

There is not enough evidence to show that the factor means are unequal.

C) No conclusion can be made.

D) Do not reject the null hypothesis since the p-value is greater than the significance level. We conclude that the factor means are equal.

E) Reject the null hypothesis since the p-value is greater than the significance level. We conclude that all of the factor means differ.

Use the MiniTab display.

24) A manager records the production output of three employees who each work on three different machines for three different days. The sample results are given below and the Minitab results follow.

I Machine II III

A 23, 27, 29 25, 26, 24 28, 25, 26

Employee B 30, 27, 25 24, 29, 26 25, 27, 23

C 18, 20, 22 19, 16, 14 15, 11, 17

ANALYSIS OF VARIANCE ITEMS SOURCE MACHINE EMPLOYEE INTERACTION ERROR TOTAL

DF 2 2 4 18 26

SS 34.67 504.67 26.67 98.00 664.00

MS 17.33 252.33 6.67 5.44

Assume that the number of items produced is not affected by an interaction between employee and machine. Using a 0.05 significance level, test the claim that the choice of employee has no effect on the number of items produced. Calculate the F -statistic for this test. Round your answer to four decimal places.

B) 1.2261 C) 3.1857 D) 3.5500 E) 46.3842 A) 0.3538

Copyright © 2013 Pearson Education, Inc. 214

24)

25) A manager records the production output of three employees who each work on three different machines for three different days. The sample results are given below and the Minitab results follow.

Machine

I II III

Employee A B 23, 27, 29 30, 27, 25 25, 26, 24 24, 29, 26 28, 25, 26 25, 27, 23

C 18, 20, 22 19, 16, 14 15, 11, 17

ANALYSIS OF VARIANCE ITEMS SOURCE MACHINE EMPLOYEE INTERACTION ERROR TOTAL

DF 2 2 4 18 26

SS 34.67 504.67 26.67 98.00 664.00

MS 17.33 252.33 6.67 5.44

Assume that the number of items produced is not affected by an interaction between employee and machine. Using a 0.05 significance level, test the claim that the machine has no effect on the number of items produced. Calculate the F-statistic for this test. Round your answer to four decimal places.

E) 2.5982 B) 3.5500 C) 3.1857 D) 0.3538 A) 46.3842

Copyright © 2013 Pearson Education, Inc. 215

25)

Answer Key Testname: CHAPTER_14_EXAM_A

1) a. We need 4 indicator variables to indicate the two genders, the two races, and the three types of jobs. The first indicator variable is x1 = 1 for female = 0 otherwise.

The second indicator variable is x2 = 1 for black = 0 otherwise.

The third indicator variable is x3 = 1 for white-collar = 0 otherwise.

The fourth indicator variable is x4 = 1 for service = 0 otherwise.

With these indicator variables, the multiple regression equation for the mean income is μy = α + β 1 x1 + β 2 x2 + β 3 x3 + β 4 x4 . α is the mean for male, white, blue collar workers; β 1 is added to the mean if the worker is female; β 2 is added to the mean if the worker is black; β 3 is added to the mean if the worker is white-collar and β 4 is added to the mean if the worker is a service worker.

2) E 3) A 4) C 5) B 6) E 7) B 8) E 9) D 10) No. Once the second factor is no longer controlled, the effect of the first factor on the response variable could change because the residual variation could change.

11) C 12) B 13) A 14) Since the ANOVA F test is robust to moderate breakdowns in the population normality and equal standard deviation assumptions, in practice it is used unless (i) graphical methods show extreme skew for the response variable or (ii) the largest group standard deviation is more than about double the smallest group standard deviation and the sample sizes are unequal.

15) C 16) B 17) C 18) A 19) C 20) D 21) C 22) A 23) B 24) E 25) C

Copyright © 2013 Pearson Education, Inc. 216

Chapter 14 Exam B Name___________________________________

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

State the null hypothesis to test for independence.

1) An industrial psychologist is investigating the effects of work environment on employee attitudes.

A group of 20 recently hired sales trainees were randomly assigned to one of four different ʺhome roomsʺ - five trainees per room. Each room is identical except for wall color. The four colors used were light green, light blue, gray and red. The psychologist wants to know whether room color has an effect on attitude, and, if so, wants to compare the mean attitudes of the trainees assigned to the four room colors. At the end of the training program, the attitude of each trainee was measured on a 60-pt. scale (the lower the score, the poorer the attitude). The data was subjected to a one -way analysis of variance.

1)

ONE-WAY ANOVA FOR ATTITUDE BY COLOR SS MS F P SOURCE DF 3 1678.15 559.3833 59.03782 0.0000 GROUP ERROR 16 151.6 9.475 TOTAL 19 1829.75 Give the null hypothesis A) H0 : μgreen = μblue = μgray = μred, where the μʹs represent mean attitudes for the four rooms B) H0 : pgreen = pblue = pgray = pred, where the pʹs represent the proportion with the corresponding attitude C) none of these D) H0 : x1 = x2 = x3 = x4 , where the xʹs represent the room colors E) H0 : μ1 = μ2 = μ3 = μ4 = μ5 , where the μi represent attitude means for the ith person in each room 2) A golf organization wants to know which brand of golf ball goes the farthest when hit by a driver.

Three brands of golf balls are compared by using a well-known golf instructor to randomly hit each brand of ball five times. The total distance in yards is measured after each ball comes to rest.

A) H0 : μ1 = μ2 = μ3 vs. the alternative that not all brand means are equal

2)

B) H0 : μ1 = μ2 = μ3 = μ4 = μ5 vs. the alternative that not all hit means are equal C) H0 : μ1 = μ2 = μ3 vs. the alternative that not all hit means are equal D) H0 : μ1 ≠ μ2 ≠ μ3 ≠ μ4 ≠ μ5 vs. the alternative that all hit means are equal E) H0 : μ1 ≠ μ2 ≠ μ3 vs. the alternative that all brand means are equal 3) A chemist is interested in comparing four different catalysts by measuring reaction times. Each catalyst is tested five times, with each experiment randomly assigned one of the four catalysts.

A) H0 : μ1 = μ2 = μ3 = μ4 = μ5 vs. the alternative that not all the test means are equal B) H0 : μ1 ≠ μ2 ≠ μ3 ≠ μ4 vs. the alternative that all the catalyst means are equal C) H0 : μ1 ≠ μ2 ≠ μ3 ≠ μ4 ≠ μ5 vs. the alternative that all the test means are equal D) H0 : μ1 = μ2 = μ3 = μ4 vs. the alternative that not all the catalyst means are equal E) H0 : μ1 = μ2 = μ3 = μ4 vs. the alternative that not all the test means are equal

Copyright © 2013 Pearson Education, Inc. 217

3)

4) A telemarketing company wants to compare the effectiveness of five of its employees by looking at the percentage of survey questions completed. Data from four past surveys are randomly chosen for each of the employees, and the percentage of completed questions is calculated.

A) H0 : μ1 = μ2 = μ3 = μ4 = μ5 vs. the alternative that not all employee means are equal

4)

B) H0 : μ1 ≠ μ2 ≠ μ3 ≠ μ4 vs. the alternative that all survey means are equal C) H0 : μ1 ≠ μ2 ≠ μ3 ≠ μ4 ≠ μ5 vs. the alternative that all employee means are equal D) H0 : μ1 = μ2 = μ3 = μ4 vs. the alternative that not all employee means are equal E) H0 : μ1 = μ2 = μ3 = μ4 vs. the alternative that not all survey means are equal Using the table, find the F-value for the numerator and denominator degrees of freedom. Use α = 0.05.

5) Using the table, find F-value for df1 = 3 and df2 = 12 for α = 0.05.

5)

A) 3.59 B) 3.29 C) 3.49 D) none of these E) 8.74 6) Using the table, find F-value for df1 = 6 and df2 = 20 for α = 0.05.

A) 2.74

B) 2.85

C) 2.63

D) 2.60

7) Using the table, find F-value for df1 = 12 and df2 = 15 for α = 0.05.

A) 2.13 B) 2.69 C) none of these D) 2.48 E) 2.53

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6) E) 2.47 7)

Use the MiniTab display.

8) A manager records the production output of three employees who each work on three different machines for three different days. The sample results are given below and the Minitab results follow.

I Machine II III

A 23, 27, 29 25, 26, 24 28, 25, 26

Employee B 30, 27, 25 24, 29, 26 25, 27, 23

8)

C 18, 20, 22 19, 16, 14 15, 11, 17

ANALYSIS OF VARIANCE ITEMS SOURCE MACHINE EMPLOYEE INTERACTION ERROR TOTAL

DF 2 2 4 18 26

SS 34.67 504.67 26.67 98.00 664.00

MS 17.33 252.33 6.67 5.44

Assume that the number of items produced is not affected by an interaction between employee and machine. Using a 0.05 significance level, test the claim that the choice of employee has no effect on the number of items produced. Calculate the F -statistic for this test. Round your answer to four decimal places.

B) 1.2261 C) 46.3842 D) 3.5500 E) 3.1857 A) 0.3538 9) A manager records the production output of three employees who each work on three different machines for three different days. The sample results are given below and the Minitab results follow.

Machine

I II III

A 23, 27, 29 25, 26, 24 28, 25, 26

Employee B 30, 27, 25 24, 29, 26 25, 27, 23

C 18, 20, 22 19, 16, 14 15, 11, 17

ANALYSIS OF VARIANCE ITEMS SOURCE DF 2 MACHINE EMPLOYEE 2 INTERACTION 4 ERROR 18 TOTAL 26

SS 34.67 504.67 26.67 98.00 664.00

MS 17.33 252.33 6.67 5.44

Using a 0.05 significance level, test the claim that the interaction between employee and machine has no effect on the number of items produced. State the null hypothesis.

A) Ha : There is an interaction effect.

B) Ha : There is no interaction effect.

C) None of these.

D) H0 : There is an interaction effect.

E) H0 : There is no interaction effect.

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9)

10) A manager records the production output of three employees who each work on three different machines for three different days. The sample results are given below and the Minitab results follow.

Machine

Employee A B 23, 27, 29 30, 27, 25 25, 26, 24 24, 29, 26 28, 25, 26 25, 27, 23

I II III

10)

C 18, 20, 22 19, 16, 14 15, 11, 17

ANALYSIS OF VARIANCE ITEMS SOURCE MACHINE EMPLOYEE INTERACTION ERROR TOTAL

DF 2 2 4 18 26

SS 34.67 504.67 26.67 98.00 664.00

MS 17.33 252.33 6.67 5.44

Assume that the number of items produced is not affected by an interaction between employee and machine. Using a 0.05 significance level, test the claim that the machine has no effect on the number of items produced. Calculate the F-statistic for this test. Round your answer to four decimal places.

B) 3.1857 C) 2.5982 D) 3.5500 E) 46.3842 A) 0.3538 11) A manager records the production output of three employees who each work on three different machines for three different days. The sample results are given below and the Minitab results follow.

Machine

I II III

A 31, 34, 32 19, 26, 22 21, 18, 26

Employee B 29, 23, 22 35, 33, 30 20, 23, 24

C 21, 20, 24 25, 19, 23 36, 37, 31

ANALYSIS OF VARIANCE ITEMS SOURCE MACHINE EMPLOYEE INTERACTION ERROR TOTAL

DF 2 2 4 18 26

SS 1.19 5.85 710.81 160.00 877.85

MS .59 2.93 177.70 8.89

Using a 0.05 significance level, test the claim that the interaction between employee and machine has no effect on the number of items produced. Calculate the F-statistic for this test. Round your answer to four decimal places.

B) 0.2014 C) 2.9300 D) 0.0198 E) 19.9888 A) 4.4426

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11)

Provide an appropriate response.

12) A birdhunterʹs society is interested in knowing whether three different brands of turkey calls are equally effective in attracting gobblers. Each turkey call is randomly assigned to five hunters, and the order of each experiment is also randomized. An experiment consists of a hunter using one brand three times and waiting fifteen minutes. The number of gobblers attracted by the calls is counted. An ANOVA F-test rejected the hypothesis of equal means. Each pair of means were then compared, and the 95% confidence intervals are shown below:

12)

A) 1 vs. 2 (-2.620, -0.180) B) 1 vs. 3 (-0.661, 1.461) C) 2 vs. 3 (0.739, 2.861) Which tests show a significant difference between the means?

B) A C) C A) A,C

D) B

E) none

13) A printing company is interested in comparing the speed of four different desktop printers; four different documents are used for the experiment. Each test consists of randomly assigning one printer to one of the documents. The document is printed and the time to print in seconds is recorded. Each printer/document combination is tested. The F-value from an ANOVA is 6.173.

What is the F value having a P-value of 0.05?

B) 3.01 C) 3.59 D) 6.39 E) 3.24 A) 3.49

13)

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

14) Discuss the robustness of the ANOVA F test.

14)

15) Show how to construct a multiple regression model for the analysis of mean income over a three-way classification of gender (male, female), race (white, black), and type of job (blue-collar, white-collar, service). Interpret the parameters in the model. Assume that there is no interaction.

15)

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

16) In a one-factor ANOVA having three group levels with five observations in each group, the between group degrees of freedom is equal to A) 4 B) 15 C) 12 D) 10 E) 2

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16)

17) A golf organization wants to know which brand of golf ball goes the farthest when hit by a driver.

Three brands of golf balls are compared by using a well-known golf instructor to randomly hit each brand of ball five times. The total distance in yards is measured after each ball comes to rest.

Calculate the F-ratio. Can you reject H0 using α = 0.05? The ANOVA table is listed below.

17)

Analysis of Variance Source SS df MS F -ratio Brand 1405.375 2 702.688 Error 1467.556 12 122.296 Total 2872.931 A) F-Ratio = 0.174; Reject H0 B) F-Ratio = 0.958; Do not reject H0 C) F-Ratio = 5.746; Do not reject H0 D) F-Ratio = 5.746; Reject H0 E) F-Ratio = 0.174; Do not reject H0 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

18) The null hypothesis of equality of means for a factor is rejected in a two-way ANOVA. Does this imply that the hypothesis will be rejected in a one-way ANOVA F test, if the data are collapsed over the levels of the second variable? Explain.

18)

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

19) An industrial engineer wants to test the effect of three different ways of assembling a part on the total assembly time. Five people are randomly assigned to each of the three assembly methods, and the total assembly time (in seconds) is recorded. Calculate the F-ratio. Can you reject H0 using α = 0.05? The ANOVA table is listed below.

Analysis of Variance Source SS df MS Method 985535.907 2 492767.954 Error 276844.275 12 23070.356 Total 1262380.182 A) F-Ratio = 21.359; Reject H0

F -ratio

B) F-Ratio = 3.560; Reject H0 C) F-Ratio = 0.047; Don not reject H0 D) F-Ratio = 21.359; Do not reject H0 E) F-Ratio = 0.047; Reject H0

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19)

20) A chemist is interested in comparing four different catalysts by measuring reaction times. Each catalyst is tested five times, with each experiment randomly assigned one of the four catalysts.

Calculate the F-ratio. Can you reject H0 using α = 0.05? The ANOVA table is listed below.

20)

Analysis of Variance Source SS df MS F -ratio Catalyst 9.310 3 3.103 Error 79.320 16 4.958 Total 88.630 A) F-Ratio = 0.626; Do not reject H0 B) F-Ratio = 1.598; Reject H0 C) F-Ratio = 1.598; Do not reject H0 D) F-Ratio = 0.117; Do not reject H0 E) F-Ratio = 0.626; Reject H0 Select the most appropriate answer.

21) Which of the following are assumptions of the analysis of variance F test for comparing population means of several groups?

A) Each group has a normal population distribution.

B) Each group has the same standard deviation.

C) All of these.

D) The random samples drawn from each group are independent.

E) None of these.

21)

22) If the average crop yields are to be compared among 4 different varieties of seeds and 2 different irrigation techniques, which of the following methods of analysis seems most appropriate?

A) a factorial ANOVA B) a one-way ANOVA C) a logistic regression analysis D) a linear regression analysis E) a two-way ANOVA

22)

23) If the average weight losses are to be compared among 3 different diets, which of the following methods of analysis seems most appropriate?

A) a one-way ANOVA B) a three-way ANOVA C) a logistic regression analysis D) a two-way ANOVA E) a linear regression analysis

23)

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Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean.

24) 24) Source DF SS MS F p Factor 3 30 10.00 1.6 0.264 Error 8 50 6.25 Total 11 80 What can you conclude about the equality of the population means?

A) Reject the null hypothesis since the p-value is greater than the significance level. We conclude that all of the factor means differ.

B) Do not reject the null hypothesis since the p-value is greater than the significance level. We conclude that the factor means are equal.

C) Do not reject the null hypothesis since the p-value is greater than the significance level.

There is not enough evidence to show that the factor means are unequal.

D) No conclusion can be made.

E) Reject the null hypothesis since the p-value is greater than the significance level. We conclude that at least two of the factor means differ.

Determine the degrees of freedom.

25) An independent research firm conducts a study to compare the taste of four new sports drinks.

Five people are randomly assigned to each of the four drinks. Each person tastes the drink and judges it on a scale from one to five. How many degrees of freedom (df1 ) does the group sum of squares have? How many degrees of freedom ( df2 ) for the error sum of squares?

A) df1 = 4; df2 = 17 B) df1 = 16; df2 = 3 C) df1 = 3; df2 = 16 D) df1 = 3; df2 = 17 E) df1 = 4; df2 = 16

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25)

Answer Key Testname: CHAPTER_14_EXAM_B

1) A 2) A 3) D 4) A 5) C 6) D 7) D 8) C 9) E 10) B 11) E 12) A 13) A 14) Since the ANOVA F test is robust to moderate breakdowns in the population normality and equal standard deviation assumptions, in practice it is used unless (i) graphical methods show extreme skew for the response variable or (ii) the largest group standard deviation is more than about double the smallest group standard deviation and the sample sizes are unequal.

15) a. We need 4 indicator variables to indicate the two genders, the two races, and the three types of jobs. The first indicator variable is x1 = 1 for female = 0 otherwise.

The second indicator variable is x2 = 1 for black = 0 otherwise.

The third indicator variable is x3 = 1 for white-collar = 0 otherwise.

The fourth indicator variable is x4 = 1 for service = 0 otherwise.

With these indicator variables, the multiple regression equation for the mean income is μy = α + β 1 x1 + β 2 x2 + β 3 x3 + β 4 x4 . α is the mean for male, white, blue collar workers; β 1 is added to the mean if the worker is female; β 2 is added to the mean if the worker is black; β 3 is added to the mean if the worker is white-collar and β 4 is added to the mean if the worker is a service worker.

16) E 17) D 18) No. Once the second factor is no longer controlled, the effect of the first factor on the response variable could change because the residual variation could change.

19) A 20) A 21) C 22) E 23) A 24) C 25) C

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Chapter 15 Exam A Name___________________________________

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

Provide an appropriate response.

1) SAT scores for students selected randomly from two different schools are shown below. Find W, the sum of the ranks for the larger sample, to test the claim that the scores for the two schools have the same distribution.

School B School A 550 480 670 460 580 620 400 700 520 380 680 570 540 740 560 660 500 480 360 560 650 600 550 A) 11.91 B) 131

C) 0.17

D) 12.08

1)

E) 145

Select the most appropriate answer.

2) A researcher wants to know if the time spent in prison for a particular type of crime was the same for men and women. A random sample of men and women were each asked to give the length of sentence received. The data, in years, are listed below. Which of the following tests can be used to test the claim that there is no difference in the sentence received by each sex if normality cannot be assumed?

2)

Men 10 22 16 18 19 26 Women 9 12 9 14 26 12 Men 14 22 12 19 23 24 Women 34 8 10 13 17 27 A) t-test B) Sign test C) Wilcoxon test D) Wilcoxon signed-rank test E) none of these Provide an appropriate response.

3) A local school district is concerned about the number of school days missed by its teachers due to illness. A random sample of 10 teachers is selected. The numbers of days absent in one year is listed below. An incentive program is offered in an attempt to decrease the number of days absent. The number of days absent in one year after the incentive program is listed below. Use the Wilcoxon signed-rank test to find the test statistic ws to test the claim that the incentive program cuts down on the number of days missed by teachers. Use α = 0.05. The difference is defined as the After Incentive-Before Incentive.

Teacher Days Absent Before Incentive Days Absent After Incentive A) -2

1

2

3

4

5

6

7

8

9

10

6

8

7

7

9

5

2

6

4

3

4

7 7 5 B) 2

8

3

0

7 2 C) 7

3 D) 1

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E) -3.16

3)

4) Verbal SAT scores for students randomly selected from two different schools are listed below. Use the Wilcoxon rank sum test to find W, the sum of the ranks for the larger sample, to test the claim that there is no difference in the scores from each school.

School 1 School 2 560 530 780 500 450 690 490 760 540 440 720 600 590 790 620 700 560 540 600 740 760 640 650 550 A) 3.58 B) 75.5

C) 60

D) 171.5

E) 128.5

5) Students in Statistics 102 were asked to report their final exam score (a 200 -point exam) in Statistics 101. These were then paired with the scores on record. The higher of the two scores is listed in the tables below (ʺRepʺ for reported and ʺRecʺ for recorded). At α = 0.05, determine the test statistic to support the claim that there is a difference between reported scores and recorded scores. Define p to be the population proportion who reported a larger score than was recorded.

2 3 4 9 10 11 12 5 6 7 8 Student 1 Rep Rec Rep Rec Rep Rec Rec Rec Rep Rep Rep Same A) -1.508 B) 0 C) 8 D) 3

Swimming 2.9 3.2 3 2.7 2.7 2.6 B) 3.03

C) 3.5

D) 73.5

C) 95.5

D) 90

E) 8.61

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

8) List two cases when nonparametric methods are especially useful.

Copyright © 2013 Pearson Education, Inc. 227

6)

E) 12.25

7) A teacher uses two different CAI programs to remediate students. Results for each group on a standardized test are listed in a table below. Use the Wilcoxon rank sum test to find W, the sum of the ranks for the smaller sample, to test the claim that there is no difference in the results from each program.

Program I Program II 60 75 61 63 66 89 68 77 86 69 64 70 84 80 81 87 72 82 59 78 73 91 93 94 95 A) 235 B) 143

5)

E) -1.732

6) The grade point averages of students participating in sports at a college are to be compared. The data are listed below. Find the average rank for the tennis GPAs to be used in the Kruskal -Wallis test for testing the claim that there is no difference in the distributions of the populations.

Tennis Golf 3.4 2 2.8 2.3 3.5 2.7 3.7 2.1 3.3 2.5 2.3 2.2 A) 4.08

4)

8)

7)

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

9) A person who commutes to work is choosing between two different routes. He tries the first route 11 times and the second route 12 times and records the time of each trip. The results (in minutes) are shown below. Find W, the difference between sample mean ranks for the two groups, to test the claim that the times for both routes have the same distribution.

Route 1 Route 2 35 42 41 41 46 38 33 48 40 49 53 36 39 50 46 51 57 53 36 40 45 50 55 A) 15.17 B) 182 C) 8.55 D) 94 E) -6.62

9)

10) A researcher wishes to determine whether there is a difference in the average age of elementary school, high school, and community college teachers. Teachers are randomly selected. Their ages are recorded below. Find the mean rank for high school teachers that are used in the Kruskal-Wallis test.

10)

Elementary School High School Community College Teachers Teachers Teachers 37 40 24 29 42 46 28 39 37 53 48 62 38 43 46 26 32 36 A) 40.2 B) 63.5 C) 10.58

D) 381

E) 36

11) 11 female employees and 11 male employees are randomly selected from one company and their weekly salaries are recorded. The salaries (in dollars) are shown below. Software reports a small-sample one-sided P-value of 0.008. Interpret.

Female Male 350 420 470 410 460 650 385 675 520 545 720 810 540 400 550 660 500 880 450 640 700 750 A) The probability that a randomly selected female earns the same as a randomly selected male is 0.008. There is strong evidence that the average male salary is higher.

B) If there were no difference in weekly salaries among men and women, the probability of obtaining a sample as extreme as that observed is 0.008. There is strong evidence that the average male salary is higher.

C) If there were no difference in weekly salaries among men and women, the probability of obtaining a sample as extreme as that observed is 0.008. There is strong evidence that the average salaries differ.

D) The probability of obtaining a sample where the average female salary is greater than or equal to the average male salary is 0.008. There is strong evidence that the average male salary is higher.

E) The probability that a randomly selected male earns more than a randomly selected female is 0.008. There is strong evidence that the average male salary is higher.

Copyright © 2013 Pearson Education, Inc. 228

11)

Select the most appropriate answer.

12) If the P-value of the Kruskal-Wallis test is small, to find out which pairs of groups significantly differ the Kruskal-Wallis test should be followed up by

12)

I. the Wilcoxon test to compare each pair of groups.

II. constructing a confidence interval for the difference between the population medians for each pair of groups.

III. constructing a confidence interval for the difference between the population means for each pair of groups.

A) I only B) II only C) both I and II D) III only E) both I and III Answer true or false.

13) The Wilcoxon signed-rank test improves on the sign test by taking into account the sizes of the differences and not merely their sign.

A) True B) False SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

14) To compare the length of stay (in days) in the hospital (H) for patients with the same diagnosis at two different hospitals, the following data were collected.

H #1 H #2

21 86

10 27

32 10

60 68

8 87

44 76

29 125

5 60

13 35

26 73

33 96

44

14)

238

a. Why might a t test not be very useful in this case? b. Explain how to find the ranks for the Wilcoxon test by showing which of the 24 observations get ranks 1, 2, 23, and 24. c. The test statistic for the Wilcoxon test is W = 83.5 and the P-value = 0.0019 (adjusted for ties), interpret.

Copyright © 2013 Pearson Education, Inc. 229

13)

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

15) 11 female employees and 11 male employees are randomly selected from one company and their weekly salaries are recorded. The salaries (in dollars) are shown below. Find W, the sum of the ranks for the smaller sample, to test the claim that salaries for female and male employees of the company have the same distribution.

Male Female 350 420 470 410 460 650 385 675 520 545 720 810 540 400 550 660 500 880 450 640 700 750 A) 163 B) 14.82 C) 90 D) -6.64 E) 8.18

15)

16) Nine students took the SAT test. Their scores are listed below. Later on, they took a test preparation course and retook the SAT. Their new scores are listed below. Use the Wilcoxon signed-ranks test to find the test statistic ws to test the claim that the test preparation had no effect

16)

on their scores. Use α = 0.05. The difference is defined as the before score-after score.

Student 1 2 3 4 5 6 Before Score 1040 1070 1000 1080 1170 910 After Score 1060 1070 990 1120 1200 920 A) -4 B) 15 C) -32

7 830 820

8 930 970

9 870 890 D) 32

E) 4

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

Fill in the blank.

17) The t test for comparing two means is to the one -way ANOVA F test as the ____________________ test is to the Kruskal -Wallis test.

17)

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

Provide an appropriate response.

18) A weight-lifting coach claims that a weight-lifter can increase strength by taking vitamin E. To test the theory, the coach randomly selects 9 athletes and gives them a strength test using a bench press. Thirty days later, after regular training supplemented by vitamin E, they are tested again.

The table below lists whether the athlete was stronger before or after taking vitamin E. Using the sign test for the claim that the vitamin E supplement is effective in increasing the athleteʹs strength, find the p-value.

5 6 7 8 9 2 3 4 Athlete 1 After After Same Before After After After Before After A) 0.289 B) 0.157 C) 0.164 D) 0.05

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E) 0.145

18)

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

19) The data below represent the number of computer units sold per week by a random sample of 8 salespersons before and after a bonus plan was introduced. The difference is defined as after minus before. A paired t-test to determine whether the bonus plan had significantly increased sales on average yielded a P-value of 0.03.

54 53 -1

Before After Difference

25 30 5

80 79 -1

76 79 3

63 70 7

82 90 8

94 92 -2

19)

72 81 9

a. Suppose the assumption of normality for the differences was not valid and conduct a Wilcoxon signed-rank test. b. Does the test in part (a) agree with the paired t-test? If not, which result is more reliable?

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

20) Nine students took the SAT test. Later on, they took a test preparation course and retook the SAT. Their new scores are listed below. For each of the nine students, the table below lists which test had the higher score, before the preparation test or after. Using the sign test for the claim that the test preparation had no effect on their scores, find the p-value.

5 6 7 8 9 Student 1 2 3 4 After Same Before After After After Before After After A) 0.157 B) 0.289 C) 0.085 D) 0.145

E) 0.05

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

21) To study whether the sport of a college athlete is associated with college GPA, the following data were collected.

The following represents the MINITAB output for the Kruskal-Wallis test on these data.

Interpret these results.

Kruskal-Wallis Test: gpa versus sport sport N golf 6 swimming 6 tennis 6 H = 5.13

DF = 2

Median 2.550 3.100 3.350 P = 0.077

Rank 5.6 10.7 12.3 (adjusted for ties)

Copyright © 2013 Pearson Education, Inc. 231

21)

20)

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

22) A teacher uses two different CAI programs to remediate students. Results for each group on a standardized test are listed in a table below. Software reports a small -sample two-sided P-value of 0.003. Interpret.

22)

Program I Program II 60 75 61 63 66 89 68 77 86 69 64 70 84 80 81 87 72 82 59 78 73 91 93 94 95 A) If there were no difference between programs, the probability of obtaining a sample as extreme as that observed would be 0.003. We conclude that Program II gives better results.

B) The probability that the programs give different results is 0.003. There is strong evidence that the programs give the same results.

C) The probability that the programs give the same results is 0.003. We conclude that Program II gives better results.

D) If there were no difference between programs, the probability of obtaining a sample as extreme as that observed would be 0.003. There is strong evidence that the programs give different results.

E) The probability that the programs give the same results is 0.003. There is strong evidence that the programs give different results.

Select the most appropriate answer.

23) The nonparametric test for comparing mean ranks of several groups with independent random samples is the A) Kruskal-Wallis test B) t-test C) Wilcoxon test D) Wilcoxon signed-rank test E) Sign test 24) Which of the following is a nonparametric test for comparing two groups with matched -pairs data when the difference can be ranked?

A) Bonferroni test B) sign test C) Wilcoxon signed-rank test D) Wilcoxon test E) Kruskal-Wallis test Provide an appropriate response.

25) A pharmaceutical company wishes to test a new drug with the expectation of lowering cholesterol levels. Ten subjects are randomly selected and their cholesterol levels are recorded. The subjects were placed on the drug for a period of 6 months, after which their cholesterol levels were tested again. The table below lists whether the subjectʹs cholesterol was lower before or after taking the drug. Using the sign test for the companyʹs claim that the drug lowers cholesterol levels, find the test statistic.

7 8 9 10 Subject 1 2 3 4 5 6 After After Before After After Same After After After After A) 2.33 B) 0.11 C) 1 D) 8

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E) 1.90

23)

24)

25)

Answer Key Testname: CHAPTER_15_EXAM_A

1) E 2) C 3) B 4) D 5) A 6) E 7) D 8) 1) When the data are ranks for the subjects rather than quantitative measurements; 2) When itʹs inappropriate to assume normality and the ordinary statistical method is not robust when the normality assumption is violated.

9) E 10) C 11) B 12) C 13) A 14) a. The box plots above do not show any substantial skew, but there is an extreme outlier for the H #2 group. One patient in that group had a very long stay, 238 days. The Wilcoxon test is not affected by an outlier; b. Rank 1 goes to the shortest stay, so the value 5 gets rank 1. The second shortest stay is 8, which gets rank 2. The longest stay is 238, which gets rank 24. The next longest stay is 125, which gets rank 23; c. The P -value shows strong evidence against the null hypothesis that the distribution of stay times is identical for the two hospitals. The stay times tend to be longer for patients staying at hospital #2.

15) C 16) E 17) Wilcoxon 18) E 19) a. 1) Assumptions: Random sample of matched pairs for which the differences of observations have a symmetric population distribution and can be ranked; 2) H0 : Population median of difference scores is 0 and Ha : Population median of difference scores is greater than 0; 3) test statistic = 30; 4) P-value = 0.054; 5) Since the P-value > 0.05, there is not sufficient evidence that the bonus plan had significantly increased sales on average; b. No, the parametric test rejects the null hypothesis in favor of the alternative which states that the number of computer units sold per week increased after the bonus plan was introduced. The nonparametric test did not find sufficient evidence to reject the null hypothesis of no difference. Assuming the assumption of normality is not met, the non parametric test is more reliable.

20) B 21) If H0 : identical population distributions for the three groups were true, the Kruskal Wallis test statistic would have an approximate chi-squared distribution with df = 2. The test statistic is H = 5.13. The P-value, the right-tail probability above 5.13, is 0.077. At a usual 0.05 level of significance, it is plausible that GPA is independent of sport. The sample median GPAs are not very different.

22) D 23) A 24) C 25) A

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Chapter 15 Exam B Name___________________________________

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

Select the most appropriate answer.

1) A researcher wants to know if the time spent in prison for a particular type of crime was the same for men and women. A random sample of men and women were each asked to give the length of sentence received. The data, in years, are listed below. Which of the following tests can be used to test the claim that there is no difference in the sentence received by each sex if normality cannot be assumed?

1)

Men 10 22 16 18 19 26 Women 9 12 9 14 26 12 Men 14 22 12 19 23 24 Women 34 8 10 13 17 27 A) none of these B) t-test C) Sign test D) Wilcoxon test E) Wilcoxon signed-rank test 2) The nonparametric test for comparing mean ranks of several groups with independent random samples is the A) Kruskal-Wallis test B) Wilcoxon test C) Sign test D) Wilcoxon signed-rank test E) t-test

2)

3) Which of the following is a nonparametric test for comparing two groups with matched -pairs data when the difference can be ranked?

A) Wilcoxon signed-rank test B) Kruskal-Wallis test C) Bonferroni test D) sign test E) Wilcoxon test

3)

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4) If the P-value of the Kruskal-Wallis test is small, to find out which pairs of groups significantly differ the Kruskal-Wallis test should be followed up by

4)

I. the Wilcoxon test to compare each pair of groups.

II. constructing a confidence interval for the difference between the population medians for each pair of groups.

III. constructing a confidence interval for the difference between the population means for each pair of groups.

A) III only B) both I and II C) both I and III D) I only E) II only Provide an appropriate response.

5) Nine students took the SAT test. Their scores are listed below. Later on, they took a test preparation course and retook the SAT. Their new scores are listed below. Use the Wilcoxon signed-ranks test to find the test statistic ws to test the claim that the test preparation had no effect

5)

on their scores. Use α = 0.05. The difference is defined as the before score-after score.

Student 1 2 3 4 5 6 Before Score 1040 1070 1000 1080 1170 910 After Score 1060 1070 990 1120 1200 920 A) -32 B) -4 C) 32

7 830 820

8 930 970

9 870 890 D) 4

E) 15

6) The grade point averages of students participating in sports at a college are to be compared. The data are listed below. Find the average rank for the tennis GPAs to be used in the Kruskal -Wallis test for testing the claim that there is no difference in the distributions of the populations.

Tennis Golf 3.4 2 2.8 2.3 3.5 2.7 3.7 2.1 3.3 2.5 2.3 2.2 A) 73.5

Swimming 2.9 3.2 3 2.7 2.7 2.6 B) 3.5

C) 3.03

D) 12.25

E) 4.08

7) A local school district is concerned about the number of school days missed by its teachers due to illness. A random sample of 10 teachers is selected. The numbers of days absent in one year is listed below. An incentive program is offered in an attempt to decrease the number of days absent. The number of days absent in one year after the incentive program is listed below. Use the Wilcoxon signed-rank test to find the test statistic ws to test the claim that the incentive program cuts down on the number of days missed by teachers. Use α = 0.05. The difference is defined as the After Incentive-Before Incentive.

Teacher Days Absent Before Incentive Days Absent After Incentive A) 7

1

2

3

4

5

6

7

8

9

10

6

8

7

7

9

5

2

6

4

3

4

7 7 5 B) 2

8

3

0

7 2 C) 1

3 D) -3.16

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6)

E) -2

7)

8) A teacher uses two different CAI programs to remediate students. Results for each group on a standardized test are listed in a table below. Use the Wilcoxon rank sum test to find W, the sum of the ranks for the smaller sample, to test the claim that there is no difference in the results from each program.

Program I Program II 60 75 61 63 66 89 68 77 86 69 64 70 84 80 81 87 72 82 59 78 73 91 93 94 95 A) 95.5 B) 143

C) 235

D) 8.61

E) 90

9) A researcher wishes to determine whether there is a difference in the average age of elementary school, high school, and community college teachers. Teachers are randomly selected. Their ages are recorded below. Find the mean rank for high school teachers that are used in the Kruskal-Wallis test.

Elementary School High School Community College Teachers Teachers Teachers 37 40 24 29 42 46 28 39 37 53 48 62 38 43 46 26 32 36 A) 381 B) 10.58 C) 36

D) 40.2

8)

9)

E) 63.5

10) A person who commutes to work is choosing between two different routes. He tries the first route 11 times and the second route 12 times and records the time of each trip. The results (in minutes) are shown below. Find W, the difference between sample mean ranks for the two groups, to test the claim that the times for both routes have the same distribution.

Route 1 Route 2 35 42 41 41 46 38 33 48 40 49 53 36 39 50 46 51 57 53 36 40 45 50 55 A) 94 B) 8.55 C) 182 D) 15.17 E) -6.62

10)

11) 11 female employees and 11 male employees are randomly selected from one company and their weekly salaries are recorded. The salaries (in dollars) are shown below. Find W, the sum of the ranks for the smaller sample, to test the claim that salaries for female and male employees of the company have the same distribution.

Male Female 350 420 470 410 460 650 385 675 520 545 720 810 540 400 550 660 500 880 450 640 700 750 A) 8.18 B) 163 C) 14.82 D) -6.64 E) 90

11)

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

12) List two cases when nonparametric methods are especially useful.

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12)

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

13) A teacher uses two different CAI programs to remediate students. Results for each group on a standardized test are listed in a table below. Software reports a small -sample two-sided P-value of 0.003. Interpret.

13)

Program I Program II 60 75 61 63 66 89 68 77 86 69 64 70 84 80 81 87 72 82 59 78 73 91 93 94 95 A) The probability that the programs give the same results is 0.003. We conclude that Program II gives better results.

B) The probability that the programs give the same results is 0.003. There is strong evidence that the programs give different results.

C) If there were no difference between programs, the probability of obtaining a sample as extreme as that observed would be 0.003. There is strong evidence that the programs give different results.

D) If there were no difference between programs, the probability of obtaining a sample as extreme as that observed would be 0.003. We conclude that Program II gives better results.

E) The probability that the programs give different results is 0.003. There is strong evidence that the programs give the same results.

14) A pharmaceutical company wishes to test a new drug with the expectation of lowering cholesterol levels. Ten subjects are randomly selected and their cholesterol levels are recorded. The subjects were placed on the drug for a period of 6 months, after which their cholesterol levels were tested again. The table below lists whether the subjectʹs cholesterol was lower before or after taking the drug. Using the sign test for the companyʹs claim that the drug lowers cholesterol levels, find the test statistic.

2 3 4 5 6 7 8 9 10 Subject 1 After After Before After After Same After After After After A) 8 B) 2.33 C) 1 D) 1.90

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E) 0.11

14)

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

15) To study whether the sport of a college athlete is associated with college GPA, the following data were collected.

15)

The following represents the MINITAB output for the Kruskal-Wallis test on these data.

Interpret these results.

Kruskal-Wallis Test: gpa versus sport sport N golf 6 swimming 6 tennis 6 H = 5.13

DF = 2

Median 2.550 3.100 3.350 P = 0.077

Rank 5.6 10.7 12.3 (adjusted for ties)

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

16) A weight-lifting coach claims that a weight-lifter can increase strength by taking vitamin E. To test the theory, the coach randomly selects 9 athletes and gives them a strength test using a bench press. Thirty days later, after regular training supplemented by vitamin E, they are tested again.

The table below lists whether the athlete was stronger before or after taking vitamin E. Using the sign test for the claim that the vitamin E supplement is effective in increasing the athleteʹs strength, find the p-value.

Athlete 1 2 3 4 5 6 7 8 9 After After Same Before After After After Before After A) 0.05 B) 0.157 C) 0.145 D) 0.289

E) 0.164

17) Verbal SAT scores for students randomly selected from two different schools are listed below. Use the Wilcoxon rank sum test to find W, the sum of the ranks for the larger sample, to test the claim that there is no difference in the scores from each school.

School 1 School 2 560 530 780 500 450 690 490 760 540 440 720 600 590 790 620 700 560 540 600 740 760 640 650 550 A) 128.5 B) 60

C) 171.5

D) 3.58

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16)

E) 75.5

17)

18) 11 female employees and 11 male employees are randomly selected from one company and their weekly salaries are recorded. The salaries (in dollars) are shown below. Software reports a small-sample one-sided P-value of 0.008. Interpret.

Female Male 350 420 470 410 460 650 385 675 520 545 720 810 540 400 550 660 500 880 450 640 700 750 A) If there were no difference in weekly salaries among men and women, the probability of obtaining a sample as extreme as that observed is 0.008. There is strong evidence that the average salaries differ.

B) If there were no difference in weekly salaries among men and women, the probability of obtaining a sample as extreme as that observed is 0.008. There is strong evidence that the average male salary is higher.

C) The probability that a randomly selected female earns the same as a randomly selected male is 0.008. There is strong evidence that the average male salary is higher.

D) The probability that a randomly selected male earns more than a randomly selected female is 0.008. There is strong evidence that the average male salary is higher.

E) The probability of obtaining a sample where the average female salary is greater than or equal to the average male salary is 0.008. There is strong evidence that the average male salary is higher.

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18)

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

19) To compare the length of stay (in days) in the hospital (H) for patients with the same diagnosis at two different hospitals, the following data were collected.

H #1 H #2

21 86

10 27

32 10

60 68

8 87

44 76

29 125

5 60

13 35

26 73

33 96

44

19)

238

a. Why might a t test not be very useful in this case? b. Explain how to find the ranks for the Wilcoxon test by showing which of the 24 observations get ranks 1, 2, 23, and 24. c. The test statistic for the Wilcoxon test is W = 83.5 and the P-value = 0.0019 (adjusted for ties), interpret.

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

20) Nine students took the SAT test. Later on, they took a test preparation course and retook the SAT. Their new scores are listed below. For each of the nine students, the table below lists which test had the higher score, before the preparation test or after. Using the sign test for the claim that the test preparation had no effect on their scores, find the p-value.

2 3 4 5 6 7 8 9 Student 1 After Same Before After After After Before After After A) 0.145 B) 0.157 C) 0.05 D) 0.289

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E) 0.085

20)

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

21) The data below represent the number of computer units sold per week by a random sample of 8 salespersons before and after a bonus plan was introduced. The difference is defined as after minus before. A paired t-test to determine whether the bonus plan had significantly increased sales on average yielded a P-value of 0.03.

Before After Difference

54 53 -1

25 30 5

80 79 -1

76 79 3

63 70 7

82 90 8

94 92 -2

21)

72 81 9

a. Suppose the assumption of normality for the differences was not valid and conduct a Wilcoxon signed-rank test. b. Does the test in part (a) agree with the paired t-test? If not, which result is more reliable?

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

22) Students in Statistics 102 were asked to report their final exam score (a 200 -point exam) in Statistics 101. These were then paired with the scores on record. The higher of the two scores is listed in the tables below (ʺRepʺ for reported and ʺRecʺ for recorded). At α = 0.05, determine the test statistic to support the claim that there is a difference between reported scores and recorded scores. Define p to be the population proportion who reported a larger score than was recorded.

9 10 11 12 Student 1 2 3 4 5 6 7 8 Rep Rec Rep Rec Rep Rec Rec Rec Rep Rep Rep Same A) 3 B) 8 C) 0 D) -1.732

E) -1.508

23) SAT scores for students selected randomly from two different schools are shown below. Find W, the sum of the ranks for the larger sample, to test the claim that the scores for the two schools have the same distribution.

School A School B 550 480 670 460 580 620 400 700 520 380 680 570 540 740 560 660 500 480 360 560 650 600 550 A) 145 B) 131

C) 11.91

D) 12.08

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

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23)

E) 0.17

Answer true or false.

24) The Wilcoxon signed-rank test improves on the sign test by taking into account the sizes of the differences and not merely their sign.

A) True B) False

Fill in the blank.

25) The t test for comparing two means is to the one -way ANOVA F test as the ____________________ test is to the Kruskal -Wallis test.

22)

25)

24)

Answer Key Testname: CHAPTER_15_EXAM_B

1) D 2) A 3) A 4) B 5) D 6) D 7) B 8) E 9) B 10) E 11) E 12) 1) When the data are ranks for the subjects rather than quantitative measurements; 2) When itʹs inappropriate to assume normality and the ordinary statistical method is not robust when the normality assumption is violated.

13) C 14) B 15) If H0 : identical population distributions for the three groups were true, the Kruskal Wallis test statistic would have an approximate chi-squared distribution with df = 2. The test statistic is H = 5.13. The P-value, the right-tail probability above 5.13, is 0.077. At a usual 0.05 level of significance, it is plausible that GPA is independent of sport. The sample median GPAs are not very different.

16) C 17) C 18) B 19) a. The box plots above do not show any substantial skew, but there is an extreme outlier for the H #2 group. One patient in that group had a very long stay, 238 days. The Wilcoxon test is not affected by an outlier; b. Rank 1 goes to the shortest stay, so the value 5 gets rank 1. The second shortest stay is 8, which gets rank 2. The longest stay is 238, which gets rank 24. The next longest stay is 125, which gets rank 23; c. The P -value shows strong evidence against the null hypothesis that the distribution of stay times is identical for the two hospitals. The stay times tend to be longer for patients staying at hospital #2.

20) D 21) a. 1) Assumptions: Random sample of matched pairs for which the differences of observations have a symmetric population distribution and can be ranked; 2) H0 : Population median of difference scores is 0 and Ha : Population median of difference scores is greater than 0; 3) test statistic = 30; 4) P-value = 0.054; 5) Since the P-value > 0.05, there is not sufficient evidence that the bonus plan had significantly increased sales on average; b. No, the parametric test rejects the null hypothesis in favor of the alternative which states that the number of computer units sold per week increased after the bonus plan was introduced. The nonparametric test did not find sufficient evidence to reject the null hypothesis of no difference. Assuming the assumption of normality is not met, the non parametric test is more reliable.

22) E 23) A 24) A 25) Wilcoxon

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