Deck 12: Chi-Square Tests and Nonparametric Tests

Question 1

TABLE 12-15
A perfume manufacturer is trying to choose between 2 magazine advertising layouts. An expensive layout would include a small package of the perfume. A cheaper layout would include a "scratch-and-sniff" sample of the product. The manufacturer would use the more expensive layout only if there is evidence that it would lead to a higher approval rate. The manufacturer presents the more expensive layout to 4 groups and determines the approval rating for each group. He presents the "scratch-and-sniff" layout to 5 groups and again determines the approval rating of the perfume for each group. The data are given below. Use this to test the appropriate hypotheses with the Wilcoxon Rank Sum Test with a level of significance of 0.05.
$$\begin{array}{l}\begin{array} { l l } \underline{\text { Package}} &\underline{\text { Scratch} }\\52 & 37 \\68 & 43 \\43 & 53 \\48 & 39 \\& 47\end{array}\end{array}$$

-Referring to Table 12-15, which hypotheses should be used?

A) $H_{0}: \mu_{1} \leq \mu_{2}$ versus $H_{1}: \mu_{1}>\mu_{2}$
B) $H_{0}: \mu_{1}=\mu_{2}$ versus $H_{1}: \mu_{1} \neq \mu_{2}$
C) $H_{0}: M_{1}=M_{2}$ versus $H_{1}: M_{1} \neq M_{2}$
D) $H_{0}: M_{1} \leq M_{2}$ versus $H_{1}: M_{1}>M_{2}$

Answer 1

$H_{0}: M_{1} \leq M_{2}$ versus $H_{1}: M_{1}>M_{2}$

Question 2

TABLE 12-11
Parents complain that children read too few storybooks and watch too much television nowadays. A survey of 1,000 children reveals the following information on average time spent watching TV and average time spent reading storybooks.
$$\begin{array}{l}\text { Average time spent reading story books }\\\begin{array} { | l | l | l | l | } \hline \text { Average time spent } \\ \text { watching TV }& { \begin{array} { c } \text { Less than } \\\text { 1 hour }\end{array} } & \begin{array} { l } \text { Between } \\1 \text { and 2 hours }\end{array} & \begin{array} { l } \text { More than } \\2 \text { hours }\end{array} \\\hline \text { Less than 2 hours } & 90 & 85& 130 \\\hline \text { More than 2 hours } & 655 & 32& 8 \\\hline\end{array}\end{array}$$

-Referring to Table 12-11, if the null hypothesis of no connection between time spent watching TV and time spent reading story books is true, how many children watching less than 2 hours of TV and reading no more than 2 hours of story books on average can we expect?

A) 227.23
B) 262.91
C) 969.75
D) 35.69

Answer 2

262.91

Question 3

TABLE 12-12
Recent studies have found that American children are more obese than in the past. The amount of time children spent watching television has received much of the blame. A survey of 100 ten-year-olds revealed the following with regards to weights and average number of hours a day spent watching television. We are interested in testing whether the average number of hours spent watching TV and weights are independent at 1% level of significance.
$$\begin{array} { l | c l l | r } &{ \text { TV Hours } } & \\\text { Weights } & 0 - 3 & 3 - 6 & 6 + & \text { Total } \\\hline \text { More than } 101 \mathrm { ls } \text {. overweight } & 1 & 9 & 20 & 30 \\\text { Within } 101 \mathrm { bs } \text {. of normal weight } & 20 & 15 & 15 & 50 \\\text { More than } 10 \mathrm { lbs } \text {. underweight } & 10 & 5 & 5 & 20 \\\hline \text { Total } & 31 & 29 & 40 & 100\end{array}$$

-Referring to Table 12-12, if there is no connection between weights and average number of hours spent watching TV, we should expect how many children to be spending 3-6 hours on average watching TV and are more than 10 lbs. underweight?

A) 5
B) 8
C) 5.8
D) 6.2

Answer 3

5.8

Question 4

To use the Wilcoxon Rank Sum Test as a test for location, we must assume that

A) both samples are randomly and independently drawn from their respective populations.
B) the obtained data are either ranks or numerical measurements that will be converted to combined ranks.
C) both underlying populations from which the samples were drawn are equivalent in shape and dispersion.
D) all of the above

Question 5

TABLE 12-12
Recent studies have found that American children are more obese than in the past. The amount of time children spent watching television has received much of the blame. A survey of 100 ten-year-olds revealed the following with regards to weights and average number of hours a day spent watching television. We are interested in testing whether the average number of hours spent watching TV and weights are independent at 1% level of significance.
$\begin{array}{l|ccc|r} & {\text { TV Hours }} & \\\text { Weights } & 0-3 & 3-6 & 6+ & \text { Total } \\\hline \text { More than 10 lbs. Overweight } & 1 & 9 & 20 & 30 \\\text { Within 10 lbs. of normal weight } & 20 & 15 & 15 & 50 \\\text { More than 10 lbs. underweight } & 10 & 5 & 5 & 20 \\\hline \text { Total } & 31 & 29 & 40 & 100\end{array}$


-Referring to Table 12-12, which of the following statements is correct?

A) We can reject the null for any level of significance greater than 0.005.
B) We can accept the null for any level of significance greater than 0.005.
C) We can accept the null for any level of significance smaller than 0.005
D) We can reject the null for any level of significance smaller than 0.005.

Question 6

TABLE 12-2
Many companies use well-known celebrities as spokespersons in their TV advertisements. A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent. Each in a sample of 300 female TV viewers was asked to identify a product advertised by a celebrity spokesperson. The gender of the spokesperson and whether or not the viewer could identify the product was recorded. The numbers in each category are given below.
$$\begin{array} { r l l } & \text { Male Celebrity } & \text { Female Celebrity } \\\text { Identified product } & 41 & 61 \\\text { Could notidentify } & 109 & 89\end{array}$$

-Referring to Table 12-2, which test would be used to properly analyze the data in this experiment?

A) ?² test for independence
B) Wilcoxon rank sum test for independent populations
C) ?² test for differences among more than two proportions
D) Wilcoxon signed ranks test for two related populations

Question 7

TABLE 12-8
The director of transportation of a large company is interested in the usage of the company's van pool program. She surveyed 129 of her employees on the usage of the program before and after a campaign to convince her employees to use the service and obtained the following:
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Before }$
$\begin{array}{l|l|c|c|l}\hline & &\text { Use }& \text { Do Not Use } & \text { Total } \\\hline \text { After } & \text { Use } & 27 &44 & 71 \\\hline & \text { Do Not Use } & 33 & 25 & 58 \\\hline & \text { Total } & 60 &69 & 129\end{array}$
She will use this information to perform test using a level of significance of 0.05.

-Referring to Table 12-8, the director now wants to know if the proportion of employees who use the service before the campaign and the proportion of employees who use the service after the campaign are the same. What should be her conclusion?

A) There is insufficient evidence that the proportion of employees who use the service before the campaign is not the same as the proportion of employees who use the service after the campaign.
B) There is insufficient evidence that the proportion of employees who use the service before the campaign is the same as the proportion of employees who use the service after the campaign.
C) There is sufficient evidence that the proportion of employees who use the service before the campaign is the same as the proportion of employees who use the service after the campaign.
D) There is sufficient evidence that the proportion of employees who use the service before the campaign is not the same as the proportion of employees who use the service after the campaign.

Question 8

TABLE 12-5
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let u₁ and u₂ represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.
Referring to Table 12-5, what is the critical value when testing whether population proportions are different if α = 0.10?

A) 2.706
B) ±1.645
C) 3.842
D) ±1.96

Question 9

TABLE 12-11
Parents complain that children read too few storybooks and watch too much television nowadays. A survey of 1,000 children reveals the following information on average time spent watching TV and average time spent reading storybooks.
$$\begin{array}{l}\text {\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad Average time spent reading story books }\\\begin{array} { | l | l | l | l | } \hline \text { Average time spent } &{ \begin{array} { c } \text { Less than } \\\text { 1 hour }\end{array} } & \begin{array} { l } \text { Between } \\1 \text { and 2 hours }\end{array} & \begin{array} { l } \text { More than } \\2 \text { hours }\end{array} \\\hline \text { watching TV } &{ 85 } & 130 \\\hline \text { Less than 2 hours } & 90 & 32 & 8 \\\hline \text { More than 2 hours } & 655 & 85 & 8 \\\hline\end{array}\end{array}$$

-Referring to Table 12-11, to test whether there is any relationship between average time spent watching TV and average time spent reading story books, the value of the measured test statistic is

A) -12.59.
B) 1,368.06.
C) 1.61.
D) 481.49.

Question 10

TABLE 12-5
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let u₁ and u₂ represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.

-Referring to Table 12-5, what is the critical value when performing a chi-square test on whether population proportions are different if ? = 0.05?

A) ±1.645
B) ±1.96
C) 2.706
D) 3.841

Question 11

When the normality assumption is not met in a randomized block design, which of the following tests should be used?

A) Wilcoxon rank sum test
B) Friedman rank test
C) Kruskal-Wallis test
D) Wilcoxon signed ranks test

Question 12

Which of the following is a "robust" test procedure against the violation of distribution assumptions?

A) ?²-test of independence
B) ?²-test for the differences among more than two proportions
C) Wilcoxon rank sum test for difference in medians
D) ?²-test of a variance

Question 13

TABLE 12-4
One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced. The quality control department wants to find out whether there is a relationship between years of experience and defect rate. Since the job is repetitious, after the initial training period any improvement due to a learning effect might be offset by a loss of motivation. A defect rate is calculated for each worker in a yearly evaluation. The results for 100 workers are given in the table below.
$$\begin{array}{l}\text {\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad Years Since Training Period }\\\begin{array} { r | r r c } & \text { < 1 Year } & 1 - 4 \text { Years } & 5 \text { - 9Years } \\\hline \text { High } & 6 & 9 & 9 \\\text { Defect Rate: Average } & 9 & 19 & 23 \\\text { Low } & 7 & 8 & 10\end{array}\end{array}$$

-Referring to Table 12-4, find the rejection region necessary for testing at the 0.05 level of significance whether there is a relationship between defect rate and years of experience.

A) Reject H₀ if ?² > 16.919
B) Reject H₀ if ?² > 9.488
C) Reject H₀ if ?² > 11.143
D) Reject H₀ if ?² > 15.507

Question 14

TABLE 12-3
A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of 5 memory locations. A check at the end of a day's transactions gave the counts shown in the table to each of the 5 memory locations, along with the number of reported errors.
$$\begin{array}{l}\begin{array} { l l l l l r } \hline \text { Memory Location: } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Number of Transactions: } & 82 & 100 & 74 & 92&102\end{array}\\\begin{array} { l l l l l l } \text { Number of Reported Errors: } & 11 & 12 & 6 & 9 & 10\end{array}\end{array}$$ The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ.

-Referring to Table 12-3, the critical value of the test statistic at 1% level of significance is

A) 7.7794.
B) 23.2093.
C) 13.2767.
D) 20.0902.

Question 15

A local real estate appraiser analyzed the sales prices of homes in 2 neighborhoods to the corresponding appraised values of the homes. The goal of the analysis was to compare the distribution of sale-to-appraised ratios from homes in the 2 neighborhoods. Random and independent samples were selected from the 2 neighborhoods from last year's homes sales, 8 from each of the 2 neighborhoods. Identify the nonparametric method that would be used to analyze the data.

A) the Wilcoxon Signed-Ranks Test, using the test statistic W
B) the Wilcoxon Rank Sum Test, using the test statistic Z
C) the Wilcoxon Signed-Ranks Test, using the test statistic Z
D) the Wilcoxon Rank Sum Test, using the test statistic T₁

Question 16

TABLE 12-13
According to an article in Marketing News, fewer checks are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by check among three consecutive years at a 0.05 level of significance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented below.
$$\text { Year }$$
$$\begin{array} { c | r | r | r } \text { Check Writter } & \text { Year } 1& \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\text { No } & 275 & 325 & 375\end{array}$$

-Referring to Table 12-13, what is the correct conclusion?

A) There is not enough evidence that at least two of the proportions are not equal.
B) There is enough evidence that the proportions are all different in the 3 years.
C) There is enough evidence that at least two of the proportions are not equal.
D) There is not enough evidence that the proportions are all different in the 3 years.

Question 17

TABLE 12-12
Recent studies have found that American children are more obese than in the past. The amount of time children spent watching television has received much of the blame. A survey of 100 ten-year-olds revealed the following with regards to weights and average number of hours a day spent watching television. We are interested in testing whether the average number of hours spent watching TV and weights are independent at 1% level of significance.
$$\begin{array} { l | c l l | r } & { \text { TV Hours } } & \\\text { Weights } & 0 - 3 & 3 - 6 & 6 + & \text { Total } \\\hline \text { More than } 101 \mathrm { ls } \text {. overweight } & 1 & 9 & 20 & 30 \\\text { Within } 101 \mathrm { bs } \text {. of normal weight } & 20 & 15 & 15 & 50 \\\text { More than } 10 \mathrm { lbs } \text {. underweight } & 10 & 5 & 5 & 20 \\\hline \text { Total } & 31 & 29 & 40 & 100\end{array}$$

-Referring to Table 12-12, if there is no connection between weights and average number of hours spent watching TV, we should expect how many children to be spending no more than 6 hours on average watching TV and are more than 10 lbs. underweight?

A) 12
B) 6.2
C) 8
D) 5.8

Question 18

$$\text { TABLE 12-8 }$$ The director of transportation of a large company is interested in the usage of the company's van pool program. She surveyed 129 of her employees on the usage of the program before and after a campaign to convince her employees to use the service and obtained the following:
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Before }$
$\begin{array}{l|l|c|c|l}\hline & & \text { Use } & \text { Do Not Use } & \text { Total } \\\hline \text { After } & \text { Use } & 27 & 44 & 71 \\\hline & \text { Do Not Use } & 33 & 25 & 58 \\\hline & \text { Total } & 60 & 69 & 129\end{array}$

She will use this information to perform test using a level of significance of 0.05.

-Referring to Table 12-8, the director now wants to know if the proportion of employees who use the service before the campaign and the proportion of employees who use the service after the campaign are the same. Which test should she use?

A) Wilcoxon rank sum test
B) Z-test for difference in proportions
C) ?²-test for difference in proportions
D) McNemar test for difference in proportions

Question 19

TABLE 12-4
One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced. The quality control department wants to find out whether there is a relationship between years of experience and defect rate. Since the job is repetitious, after the initial training period any improvement due to a learning effect might be offset by a loss of motivation. A defect rate is calculated for each worker in a yearly evaluation. The results for 100 workers are given in the table below.
$$\begin{array}{l}\text {\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad Years Since Training Period }\\\begin{array} { r | r r c } &< 1 \text { Year } & 1 - 4 \text { Years } & 5 \text { - 9Years } \\\hline \text { High } & 6 & 9 & 9 \\\text { Defect Rate: Average } & 9 & 19 & 23 \\\text { Low } & 7 & 8 & 10\end{array}\end{array}$$


-Referring to Table 12-4, of the cell for 1 to 4 years of training time and a high defect rate, what is the contribution to the overall ?² statistic for the independence test?

A) 0.36
B) 0.0144
C) 0.1296
D) 0.015

Question 20

$$\text { TABLE 12-2 }$$ Many companies use well-known celebrities as spokespersons in their TV advertisements. A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent. Each in a sample of 300 female TV viewers was asked to identify a product advertised by a celebrity spokesperson. The gender of the spokesperson and whether or not the viewer could identify the product was recorded. The numbers in each category are given below.
$\begin{array}{r|cc} & \text { Male Celebrity } & \text { Female Celebrity } \\\hline\text { Identified product } & 41 & 61 \\\text { Could notidentify } & 109 & 89\end{array}$


-Referring to Table 12-2, at 5% level of significance, the critical value of the test statistic is

A) 5.9914.
B) 9.4877.
C) 13.2767.
D) 3.8415.

Question 21

TABLE 12-4
One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced. The quality control department wants to find out whether there is a relationship between years of experience and defect rate. Since the job is repetitious, after the initial training period any improvement due to a learning effect might be offset by a loss of motivation. A defect rate is calculated for each worker in a yearly evaluation. The results for 100 workers are given in the table below.
$\quad$$\quad$ $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Years Since Training Period }$
$\begin{array}{r|rcc} & <1 \text { Year } & 1-4 \text { Years } & 5 \text { - } 9 \text { Years } \\\hline \text { High } & 6 & 9 & 9 \\\text { Defect Rate: Average } & 9 & 19 & 23 \\\text { Low } & 7 & 8 & 10\end{array}$


-Referring to Table 12-4, what is the expected number of employees with less than 1 year of training time and a high defect rate?

A) 4.60
B) 9.17
C) 5.28
D) 4.17

Question 22

TABLE 12-12
Recent studies have found that American children are more obese than in the past. The amount of time children spent watching television has received much of the blame. A survey of 100 ten-year-olds revealed the following with regards to weights and average number of hours a day spent watching television. We are interested in testing whether the average number of hours spent watching TV and weights are independent at 1% level of significance.
$\begin{array}{l|ccc|r} &{\text { TV Hours }} & \\\text { Weights } & 0-3 & 3-6 & 6+ & \text { Total } \\\hline \text { More than 10 lbs. Overweight } & 1 & 9 & 20 & 30 \\\text { Within 10 lbs. of normal weight } & 20 & 15 & 15 & 50 \\\text { More than 10 lbs. underweight } & 10 & 5 & 5 & 20 \\\hline \text { Total } & 31 & 29 & 40 & 100\end{array}$


-Referring to Table 12-12, what is the value of the test statistic?

A) 15.483
B) 69.744
C) 18.889
D) 8.532

Question 23

TABLE 12-3
A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of 5 memory locations. A check at the end of a day's transactions gave the counts shown in the table to each of the 5 memory locations, along with the number of reported errors.
$$\begin{array}{l}\begin{array} { l l l l l r } \hline \text { Memory Location: } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Number of Transactions: } & 82 & 100 & 74 & 92&102\end{array}\\\begin{array} { l l l l l l } \text { Number of Reported Errors: } & 11 & 12 & 6 & 9 & 10\end{array}\end{array}$$ The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ.

-Referring to Table 12-3, the calculated value of the test statistic is

A) -0.0185.
B) 1.4999.
C) 1.5190.
D) -0.1777.

Question 24

TABLE 12-4
One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced. The quality control department wants to find out whether there is a relationship between years of experience and defect rate. Since the job is repetitious, after the initial training period any improvement due to a learning effect might be offset by a loss of motivation. A defect rate is calculated for each worker in a yearly evaluation. The results for 100 workers are given in the table below.
$$\begin{array}{l}\text { \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad Years Since Training Period }\\\begin{array} { r | r r c } &< 1\text { Year } & 1 - 4 \text { Years } & 5 \text { - 9Years } \\\hline \text { High } & 6 & 9 & 9 \\\text { Defect Rate: Average } & 9 & 19 & 23 \\\text { Low } & 7 & 8 & 10\end{array}\end{array}$$

-Referring to Table 12-4, which test would be used to properly analyze the data in this experiment to determine whether there is a relationship between defect rate and years of experience?

A) ?² test for differences among more than two proportions
B) Wilcoxon rank sum test for independent populations
C) Wilcoxon signed ranks test for two related populations
D) ?² test for independence

Question 25

TABLE 12-16
A perfume manufacturer is trying to choose between 2 magazine advertising layouts. An expensive layout would include a small package of the perfume. A cheaper layout would include a "scratch-and-sniff" sample of the product. The manufacturer would use the more expensive layout only if there is evidence that it would lead to a higher approval rate. The manufacturer presents both layouts to 5 groups and determines the approval rating from each group on both layouts. The data are given below. Use this to test whether the median difference in approval rating is different from zero in favor of the more expensive layout with a level of significance of 0.05.
$$\begin{array} { l l } \text { Package } & \text { Scratch } \\\hline 52 & 37 \\68 & 43 \\43 & 53 \\48 & 39 \\56 & 47\end{array}$$

-Referring to Table 12-16, what is the right test to use?

A) Wilcoxon signed rank test for difference in median
B) Wilcoxon rank sum test for median difference
C) Wilcoxon rank sum test for difference in median
D) Wilcoxon signed rank test for median difference

Question 26

If we wish to determine whether there is evidence that the proportion of items of interest is the same in group 1 as in group 2, the appropriate test to use is

A) the Z test.
B) the ?² test.
C) both A and B
D) neither of A nor B

Question 27

TABLE 12-13
According to an article in Marketing News, fewer checks are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by check among three consecutive years at a 0.05 level of significance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented below.
$$\begin{array}{l}\text {\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad Year }\\\begin{array} { c | c | c | c } \hline \text { Check Written } & \text { Year 1 } & \text { Year 2}& \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\text { No } & 275 & 325 & 375 \end{array}\end{array}$$

-Referring to Table 12-13, what is the form of the alternative hypothesis?

A) $H_{0}: \pi_{1} \neq \pi_{2}=\pi_{3}$
B) $H_{0}: \pi_{1}=\pi_{2} \neq \pi_{3}$
C) $H_{1}:$ not all $\pi_{j}$ are the same
D) $H_{0}: \pi_{1} \neq \pi_{2} \neq \pi_{3}$

Question 28

When testing for independence in a contingency table with 3 rows and 4 columns, there are _____degrees of freedom.

A) 5
B) 12
C) 6
D) 7

Question 29

In testing for whether the median difference of two related populations is zero, the null hypothesis is

A) $H_{0}: M_{D} \neq 0$ .
B) $H_{0}: M_{1}-M_{2} \neq 0$ .
C) $H_{0}: M_{D}=0$ .
D) $H_{0}: M_{1}-M_{2}=0$ .

Question 30

TABLE 12-16
A perfume manufacturer is trying to choose between 2 magazine advertising layouts. An expensive layout would include a small package of the perfume. A cheaper layout would include a "scratch-and-sniff" sample of the product. The manufacturer would use the more expensive layout only if there is evidence that it would lead to a higher approval rate. The manufacturer presents both layouts to 5 groups and determines the approval rating from each group on both layouts. The data are given below. Use this to test whether the median difference in approval rating is different from zero in favor of the more expensive layout with a level of significance of 0.05.
$$\begin{array} { l l } \text { Package } & \text { Scratch } \\\hline 52 & 37 \\68 & 43 \\43 & 53 \\48 & 39 \\56 & 47\end{array}$$

-Referring to Table 12-16, the perfume manufacturer will

A) use the "scratch-and-sniff" layout because there is sufficient evidence to conclude that this is the best course of action.
B) use the package layout because there is insufficient evidence to do otherwise.
C) use the package layout because there is sufficient evidence to conclude that this is the best course of action.
D) use the "scratch-and-sniff" layout because there is insufficient evidence to do otherwise.

Question 31

The Journal of Business Venturing reported on the activities of entrepreneurs during the organization creation process. As part of a designed study, a total of 71 entrepreneurs were interviewed and divided into 3 groups: those that were successful in founding a new firm (n₁ = 34), those still actively trying to establish a firm (n₂ = 21), and those who tried to start a new firm but eventually gave up (n₃ = 16). The total number of activities undertaken (e.g., developed a business plan, sought funding, looked for facilities) by each group over a specified time period during organization creation was measured. The objective is to compare the mean number of activities of the 3 groups of entrepreneurs. Because of concerns over necessary assumption of the parametric analysis, it was decided to use a nonparametric analysis. Identify the nonparametric method that would be used to analyze the data.

A) Wilcoxon Rank Sums Test
B) Kruskal-Wallis Rank Test
C) Wilcoxon Signed Rank Test
D) one-way ANOVA F test

Question 32

TABLE 12-5
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let u₁ and u₂ represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.
Referring to Table 12-5, what is the value of the test statistic to use in evaluating the alternative hypothesis that there is a difference in the two population proportions using α = 0.10?

A) 1.194
B) 0.274
C) 2.706
D) 4.335

Question 33

TABLE 12-1
A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles depends on ethnic status in San Diego County. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) ethnic status (Hispanic or non-Hispanic) and
(2) seat belt usage (worn or not worn) during the accident. The number of children in each category is given in the table below.
$$\begin{array} { l| c c } &\text {Hispanic }&\text {Non-Hispanic}\\\hline\text { Seat belta worn } & 31 & 148 \\\text { Seat belta not worn } & 273 & 377\end{array}$$

-Referring to Table 12-1, which test would be used to properly analyze the data in this experiment?

A) Wilcoxon signed ranks test for two related populations
B) Wilcoxon rank sum test for independent populations
C) ?² test for independence
D) ?² test for differences among more than two proportions

Question 34

If the assumptions of the one-way ANOVA F test are not met, which of the following test could be used?

A) McNemar test
B) Marascuilo procedure
C) Kruskal-Wallis test
D) none of the above

Question 35

In testing a hypothesis using the ?² test, the theoretical frequencies are based on the

A) alternative hypothesis.
B) normal distribution.
C) null hypothesis.
D) none of the above

Question 36

Suppose there is interest in comparing the median response time for three independent groups learning a specific task. The appropriate nonparametric procedure is

A) Friedman rank test.
B) Kruskal-Wallis Rank Test.
C) Wilcoxon Rank Sums Test.
D) Wilcoxon Signed Rank Test.

Question 37

TABLE 12-11
Parents complain that children read too few storybooks and watch too much television nowadays. A survey of 1,000 children reveals the following information on average time spent watching TV and average time spent reading storybooks.
$\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\text { Average time spent reading story books }$
$\begin{array}{|l|l|l|l|}\hline \begin{array}{l}\text { Average time spent } \\\text { watching TV }\end{array} &{\begin{array}{c}\text { Less than } \\\text { 1 hour }\end{array}} & \begin{array}{l}\text { Between } \\1 \text { and 2 hours }\end{array} & \begin{array}{l}\text { More than } \\\text { 2 hours }\end{array} \\\hline \text { Less than 2 hours } & 90 & 85 & 130 \\\hline \text { More than 2 hours } & 655 & 32 & 8\\\hline \end{array}$


-Referring to Table 12-11, how many children in the survey spent less than 2 hours watching TV and more than 2 hours reading story books on average?

A) 687
B) 130
C) 8
D) 175

Question 38

TABLE 12-3
A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of 5 memory locations. A check at the end of a day's transactions gave the counts shown in the table to each of the 5 memory locations, along with the number of reported errors.
$$\begin{array}{l}\begin{array} { l l l l l r } \hline \text { Memory Location: } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Number of Transactions: } & 82 & 100 & 74 & 92&102\end{array}\\\begin{array} { l l l l l l } \text { Number of Reported Errors: } & 11 & 12 & 6 & 9 & 10\end{array}\end{array}$$ The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ.

-Referring to Table 12-3, which test would be used to properly analyze the data in this experiment?

A) McNemar test for the difference among more than two proportions
B) McNemar test for the difference between two proportions
C) ?² test for difference among more than two proportions
D) ?² test of independence

Question 39

TABLE 12-12
Recent studies have found that American children are more obese than in the past. The amount of time children spent watching television has received much of the blame. A survey of 100 ten-year-olds revealed the following with regards to weights and average number of hours a day spent watching television. We are interested in testing whether the average number of hours spent watching TV and weights are independent at 1% level of significance.
$\begin{array}{l|ccc|r} &{\text { TV Hours }} & \\\text { Weights } & 0-3 & 3-6 & 6+ & \text { Total } \\\hline \text { More than 10 lbs. Overweight } & 1 & 9 & 20 & 30 \\\text { Within 10 lbs. of normal weight } & 20 & 15 & 15 & 50 \\\text { More than 10 lbs. underweight } & 10 & 5 & 5 & 20 \\\hline \text { Total } & 31 & 29 & 40 & 100\end{array}$


-Referring to Table 12-12, the degrees of freedom of the test statistic are

A) 2.
B) 4.
C) 1.
D) 9.

Question 40

TABLE 12-6
The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors. In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors
had job offers. If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2," perform the appropriate hypothesis test using a level of significance of 0.05.

-Referring to Table 12-6, which hypotheses should the dean use?

A) $H_{0}: \pi_{1}-\pi_{2} \neq 0$ versus $H_{1}: \pi_{1}-\pi_{2}=0$
B) $H_{0}: \pi_{1}-\pi_{2} \leq 0$ versus $H_{1}: \pi_{1}-\pi_{2}>0$
C) $H_{0}: \pi_{1}-\pi_{2} \geq 0$ versus $H_{1}: \pi_{1}-\pi_{2}<0$
D) $H_{0}: \pi_{1}-\pi_{2}=0$ versus $H_{1}: \pi_{1}-\pi_{2} \neq 0$

Question 41

TABLE 12-11
Parents complain that children read too few storybooks and watch too much television nowadays. A survey of 1,000 children reveals the following information on average time spent watching TV and average time spent reading storybooks.
$\begin{array}{l}\text {\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad Average time spent reading story books }\\\begin{array}{|l|l|l|l|}\hline \begin{array}{l}\text { Aver age time spent } \\\text { watching TV }\end{array} & {\begin{array}{l}\text { Less than } \\1 \text { hour }\end{array}} & \begin{array}{l}\text { Between } \\1 \text { and 2 hours }\end{array} & \begin{array}{l}\text { More than } \\2 \text { hours }\end{array} \\\hline \text { Less than 2 hours } & 90 & 85 & 130 \\\hline \text { More than 2 hours } & 655 & 32 & 8 \\\hline\end{array}\end{array}$

-Referring to Table 12-11, if the null hypothesis of no connection between time spent watching TV and time spent reading story books is true, how many children watching less than 2 hours of TV and reading more than 2 hours of story books on average can we expect?

A) 42.09
B) 987.75
C) 155.25
D) 262.92

Question 42

TABLE 12-2
Many companies use well-known celebrities as spokespersons in their TV advertisements. A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent. Each in a sample of 300 female TV viewers was asked to identify a product advertised by a celebrity spokesperson. The gender of the spokesperson and whether or not the viewer could identify the product was recorded. The numbers in each category are given below.
$$\begin{array} { l| c c } & \text { Male Celebrity } & \text { Female Celebrity } \\\hline\text { Identified product } & 41 & 61 \\\text { Could notidentify } & 109 & 89\end{array}$$

-Referring to Table 12-2, the degrees of freedom of the test statistic are

A) 299.
B) 1.
C) 2.
D) 4.

Question 43

TABLE 12-11
Parents complain that children read too few storybooks and watch too much television nowadays. A survey of 1,000 children reveals the following information on average time spent watching TV and average time spent reading storybooks.
$$\begin{array}{l}\text { \quad\quad\quad\quad\quad\quad\quad\quad\quad Average time spent reading story books }\\\begin{array} { | l | l | l | l | } \hline \begin{array} { l } \text { Average time spent } \\\text { watching TV }\end{array} & { \begin{array} { c } \text { Less than } \\\text { 1 hour }\end{array} } & \begin{array} { l } \text { Between } \\1 \text { and 2 hours }\end{array} & \begin{array} { l } \text { More than } \\\text { 2hours }\end{array} \\\hline \text { Less than 2 hours } & 90 & 85 & 130 \\\hline \text { More than 2 hours } & 655 & 32 & 8 \\\hline\end{array}\end{array}$$

-Referring to Table 12-11, suppose we want to constrain the probability of committing a Type I error to 5% when testing whether there is any relationship between average time spent watching TV and average time spent reading story books, the critical value will be

A) 14.449.
B) 12.592.
C) 7.378.
D) 5.991.

Question 44

TABLE 12-3
A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of 5 memory locations. A check at the end of a day's transactions gave the counts shown in the table to each of the 5 memory locations, along with the number of reported errors.
$$\begin{array}{l}\begin{array} { l l l l l r } \hline \text { Memory Location: } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Number of Transactions: } & 82 & 100 & 74 & 92&102\\\text { Number of Reported Errors: } & 11 & 12 & 6 & 9 & 10\end{array}\end{array}$$
The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ.

-Referring to Table 12-3, at 1% level of significance

A) there is sufficient evidence to conclude that the proportion of errors in transactions assigned to each of the 5 memory locations are not all the same.
B) there is insufficient evidence to conclude that the proportion of errors in transactions assigned to each of the 5 memory locations are not all the same.
C) there is insufficient evidence to conclude that the proportions of errors in transactions assigned to each of the 5 memory locations are all different.
D) there is sufficient evidence to conclude that the proportions of errors in transactions assigned to each of the 5 memory locations are all different.

Question 45

TABLE 12-4
One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced. The quality control department wants to find out whether there is a relationship between years of experience and defect rate. Since the job is repetitious, after the initial training period any improvement due to a learning effect might be offset by a loss of motivation. A defect rate is calculated for each worker in a yearly evaluation. The results for 100 workers are given in the table below.
$$\begin{array}{l}\text { \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad \quad Years Since Training Period }\\\begin{array} { r | r c c } & < 1 \text { Year } & 1 - 4 \text { Years } & 5 - 9 \text { Years } \\\hline \text { High } & 6 & 9 & 9 \\\text { Defect Rate: Average } & 9 & 19 & 23 \\\text { Low } & 7 & 8 & 10\end{array}\end{array}$$

-Referring to Table 12-4, a test was conducted to determine if a relationship exists between defect rate and years of experience. Which of the following p-values would indicate that defect rate and years of experience are dependent? Assume you are testing at ? = 0.05.

A) 0.080
B) 0.055
C) 0.074
D) 0.045

Question 46

TABLE 12-11
Parents complain that children read too few storybooks and watch too much television nowadays. A survey of 1,000 children reveals the following information on average time spent watching TV and average time spent reading storybooks.
$\begin{array}{l}\text { Average time spent reading story books }\\\begin{array}{|l|l|l|l|}\hline \begin{array}{l}\text { Aver age time spent } \\\text { watching TV }\end{array} & {\begin{array}{l}\text { Less than } \\1 \text { hour }\end{array}} & \begin{array}{l}\text { Between } \\1 \text { and 2 hours }\end{array} & \begin{array}{l}\text { More than } \\2 \text { hours }\end{array} \\\hline \text { Less than 2 hours } & 90 & 85 & 130 \\\hline \text { More than 2 hours } & 655 & 32 & 8 \\\hline\end{array}\end{array}$


-Referring to Table 12-11, we want to test whether there is any relationship between average time spent watching TV and average time spent reading storybooks. Suppose the value of the test statistic was 164 (which is not the correct answer) and the critical value was 19.00 (which is not the correct answer), then we could conclude that

A) more time spent reading storybooks leads to less time spent watching TV.
B) there is connection between time spent reading storybooks and time spent watching TV.
C) more time spent watching TV leads to less time spent reading storybooks.
D) there is no connection between time spent reading storybooks and time spent watching TV.

Question 47

In testing for differences between the median of two independent populations, the null hypothesis is

A) H₀ : M₁ - M₂ = 0.
B) H₀ : M₁ - M₂ ? 0.
C) H₀ : M_D = 0.
D) H₀ : M_D ? 0.

Question 48

TABLE 12-2
Many companies use well-known celebrities as spokespersons in their TV advertisements. A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent. Each in a sample of 300 female TV viewers was asked to identify a product advertised by a celebrity spokesperson. The gender of the spokesperson and whether or not the viewer could identify the product was recorded. The numbers in each category are given below.
$$\begin{array} { l| c c } & \text { Male Celebrity } & \text { Female Celebrity } \\\hline\text { Identified product } & 41 & 61 \\\text { Could notidentify } & 109 & 89\end{array}$$

-The Kruskal-Wallis Rank Test for differences in more than two medians is a nonparametric alternative to

A) Student's t test for independent samples.
B) Student's t test for related samples.
C) ANOVA F test for completely randomized experiments.
D) Wilcoxon's Rank Sum Test for differences in two medians.

Question 49

TABLE 12-12
Recent studies have found that American children are more obese than in the past. The amount of time children spent watching television has received much of the blame. A survey of 100 ten-year-olds revealed the following with regards to weights and average number of hours a day spent watching television. We are interested in testing whether the average number of hours spent watching TV and weights are independent at 1% level of significance.
$\begin{array}{l|ccc|r} &{\text { TV Hours }} & \\\text { Weights } & 0-3 & 3-6 & 6+ & \text { Total } \\\hline \text { More than 10 lbs. Overweight } & 1 & 9 & 20 & 30 \\\text { Within 10 lbs. of normal weight } & 20 & 15 & 15 & 50 \\\text { More than 10 lbs. underweight } & 10 & 5 & 5 & 20 \\\hline \text { Total } & 31 & 29 & 40 & 100\end{array}$


-Referring to Table 12-12, the critical value of the test will be

A) 21.666.
B) 14.860.
C) 6.635.
D) 13.277.

Question 50

TABLE 12-15
A perfume manufacturer is trying to choose between 2 magazine advertising layouts. An expensive layout would include a small package of the perfume. A cheaper layout would include a "scratch-and-sniff" sample of the product. The manufacturer would use the more expensive layout only if there is evidence that it would lead to a higher approval rate. The manufacturer presents the more expensive layout to 4 groups and determines the approval rating for each group. He presents the "scratch-and-sniff" layout to 5 groups and again determines the approval rating of the perfume for each group. The data are given below. Use this to test the appropriate hypotheses with the Wilcoxon Rank Sum Test with a level of significance of 0.05.
$$\begin{array}{l}\begin{array} { l l } \text { Package}& \text { Scratch }\\52 & 37 \\68 & 43 \\43 & 53 \\48 & 39 \\& 47\end{array}\end{array}$$

-Referring to Table 12-15, the perfume manufacturer will

A) use the "scratch-and-sniff" layout because there is sufficient evidence to conclude that this is the best course of action.
B) use the package layout because there is sufficient evidence to conclude that this is the best course of action.
C) use the package layout because there is insufficient evidence to do otherwise.
D) use the "scratch-and-sniff" layout because there is insufficient evidence to do otherwise.

Question 51

TABLE 12-11
Parents complain that children read too few storybooks and watch too much television nowadays. A survey of 1,000 children reveals the following information on average time spent watching TV and average time spent reading storybooks.
$\begin{array}{l}\text { Average time spent reading story books }\\\begin{array}{|l|l|l|l|}\hline \begin{array}{l}\text { Aver age time spent } \\\text { watching TV }\end{array} & {\begin{array}{l}\text { Less than } \\1 \text { hour }\end{array}} & \begin{array}{l}\text { Between } \\1 \text { and 2 hours }\end{array} & \begin{array}{l}\text { More than } \\2 \text { hours }\end{array} \\\hline \text { Less than 2 hours } & 90 & 85 & 130 \\\hline \text { More than 2 hours } & 655 & 32 & 8 \\\hline\end{array}\end{array}$


-Referring to Table 12-11, how many children in the survey spent less than 2 hours watching TV and no more than 2 hours reading storybooks on average?

A) 175
B) 8
C) 130
D) 687

Question 52

TABLE 12-19
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants all 3 varieties of the seeds on each of 5 different patches of fields. She then measures the crop yield in bushels per acre. Treating this as a randomized block design, the results are presented in the table that follows.
$$\begin{array} { l l l l } \underline{\text { Fields }} & \underline{\text { Smith} } &\underline{ \text { Walsh }} & \underline{\text { Trevor} } \\1 & 11.1 & 19.0 & 14.6 \\2 & 13.5 & 18.0 & 15.7 \\3 & 15.3 & 19.8 & 16.8 \\4 & 14.6 & 19.6 & 16.7 \\5 & 9.8 & 16.6 & 15.2\end{array}$$ Below is the Minitab output of the Friedman rank test:
Friedman Test: Yield versus Varieties, Fields
$\text { Friedman test for Yield by Varieties blocked by Fields }$

$\mathrm{S}=10.00 \quad \mathrm{DF}=2 \quad \mathrm{P}=0.007$
$\begin{array}{lrccc} & & \text { Est } & \text { Sum of } & \\\text { Varieties } & \mathrm{N} & \text { Median } & \text { Ranks } \\\text { Smith } & 5 & 13.500 & 5.0 \\\text { Trevor } & 5 & 15.667 & 10.0 \\\text { Walsh } & 5 & 18.533 & 15.0 \\\\{\text { Grand median }=} & 15.900\end{array}$

-Referring to Table 12-19, what is the null hypothesis for the Friedman rank test?

A) H₀: µField1 = µField2 = µField3 = µField4 = µField5
B) H₀: MSmith = MWalsh = MTrevor
C) H₀: µSmith = µWalsh = µTrevor
D) H₀: MField1 = MField2 = MField3 = MField4 = MField5

Question 53

TABLE 12-1
A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles depends on ethnic status in San Diego County. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) ethnic status (Hispanic or non-Hispanic) and
(2) seat belt usage (worn or not worn) during the accident. The number of children in each category is given in the table below.
$$\begin{array}{l}\begin{array} { l |r l } &\text {Hispanic }&\text {Non Hispanic }\\\hline \text { Seat belts worn } & 31 & 148 \\\text { Seat belts not worn } & 283 & 330\end{array}\end{array}$$

-Referring to Table 12-1, at 5% level of significance, there is sufficient evidence to conclude that

A) use of seat belts in motor vehicles depends on ethnic status in San Diego County.
B) use of seat belts in motor vehicles is associated with ethnic status in San Diego County.
C) use of seat belts in motor vehicles is related to ethnic status in San Diego County.
D) all of the above

Question 54

TABLE 12-2
Many companies use well-known celebrities as spokespersons in their TV advertisements. A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent. Each in a sample of 300 female TV viewers was asked to identify a product advertised by a celebrity spokesperson. The gender of the spokesperson and whether or not the viewer could identify the product was recorded. The numbers in each category are given below.
$$\begin{array} { l| c c } & \text { Male Celebrity } & \text { Female Celebrity } \\\hline\text { Identified product } & 41 & 61 \\\text { Could notidentify } & 109 & 89\end{array}$$

-Referring to Table 12-2, at 5% level of significance, the conclusion is that

A) brand awareness of female TV viewers and the gender of the spokesperson are independent.
B) brand awareness of female TV viewers and the gender of the spokesperson are not independent.
C) brand awareness of female TV viewers and the gender of the spokesperson are related.
D) both B and C

Question 55

TABLE 12-17
The director of the MBA program of a state university wanted to know if a one week orientation would change the proportion among potential incoming students who would perceive the program as being good. Given below is the result from 215 students' view of the program before and after the orientation.
$$\begin{array}{l}\text {\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad After the Orientation }\\\begin{array} { l c c r } \text { Before the Orientation } & \text { Good } & \text { NotGood } & \text { Total } \\\hline\text { Good } & 93 & 37 & 130 \\\text { Not Good } & 71 & 14 & 85 \\\text { Total } & 164 & 51 & 215\end{array}\end{array}$$

-Referring to Table 12-17, what should be the director's conclusion?

A) There is insufficient evidence that the proportion of potential incoming students who perceive the program as being good is not the same before and after the orientation.
B) There is sufficient evidence that the proportion of potential incoming students who perceive the program as being good is not the same before and after the orientation.
C) There is sufficient evidence that the proportion of potential incoming students who perceive the program as being good is the same before and after the orientation.
D) There is insufficient evidence that the proportion of potential incoming students who perceive the program as being good is the same before and after the orientation.

Question 56

TABLE 12-11
Parents complain that children read too few storybooks and watch too much television nowadays. A survey of 1,000 children reveals the following information on average time spent watching TV and average time spent reading storybooks.
$\begin{array}{l}\text { Average time spent reading story books }\\\begin{array}{|l|l|l|l|}\hline \begin{array}{l}\text { Aver age time spent } \\\text { watching TV }\end{array} & {\begin{array}{l}\text { Less than } \\1 \text { hour }\end{array}} & \begin{array}{l}\text { Between } \\1 \text { and 2 hours }\end{array} & \begin{array}{l}\text { More than } \\2 \text { hours }\end{array} \\\hline \text { Less than 2 hours } & 90 & 85 & 130 \\\hline \text { More than 2 hours } & 655 & 32 & 8 \\\hline\end{array}\end{array}$


-Referring to Table 12-12, how many children in the survey spend more than 6 hours watching TV and are more than 10 lbs. overweight?

A) 9
B) 20
C) 1
D) 40

Question 57

TABLE 12-12
Recent studies have found that American children are more obese than in the past. The amount of time children spent watching television has received much of the blame. A survey of 100 ten-year-olds revealed the following with regards to weights and average number of hours a day spent watching television. We are interested in testing whether the average number of hours spent watching TV and weights are independent at 1% level of significance.
$$\begin{array} { l | c l l | r } & { \text { TV Hours } } & \\\text { Weights } & 0 - 3 & 3 - 6 & 6 + & \text { Total } \\\hline \text { More than } 101 \mathrm { ls } \text {. overweight } & 1 & 9 & 20 & 30 \\\text { Within } 101 \mathrm { bs } \text {. of normal weight } & 20 & 15 & 15 & 50 \\\text { More than } 10 \mathrm { lbs } \text {. underweight } & 10 & 5 & 5 & 20 \\\hline \text { Total } & 31 & 29 & 40 & 100\end{array}$$

-Referring to Table 12-12, suppose the value of the test statistic was 30.00 (which is not the correct value) and the critical value at 1% level of significance was 10.00 (which is not the correct value), which of the following conclusions would be correct?

A) We will reject the null and conclude that average number of hours spent watching TV and weights are independent.
B) We will accept the null and conclude that average number of hours spent watching TV and weights are not independent.
C) We will reject the null and conclude that average number of hours spent watching TV and weights are not independent.
D) We will accept the null and conclude that average number of hours spent watching TV and weights are independent.

Question 58

TABLE 12-2
Many companies use well-known celebrities as spokespersons in their TV advertisements. A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent. Each in a sample of 300 female TV viewers was asked to identify a product advertised by a celebrity spokesperson. The gender of the spokesperson and whether or not the viewer could identify the product was recorded. The numbers in each category are given below.
$$\begin{array} { l |c c } & \text { Male Celebrity } & \text { Female Celebrity } \\\hline\text { Identified product } & 41 & 61 \\\text { Could notidentify } & 109 & 89\end{array}$$

-Referring to Table 12-2, the calculated test statistic is

A) 5.9418.
B) 6.1194.
C) -0.1006.
D) 0.00.

Question 59

TABLE 12-16
A perfume manufacturer is trying to choose between 2 magazine advertising layouts. An expensive layout would include a small package of the perfume. A cheaper layout would include a "scratch-and-sniff" sample of the product. The manufacturer would use the more expensive layout only if there is evidence that it would lead to a higher approval rate. The manufacturer presents both layouts to 5 groups and determines the approval rating from each group on both layouts. The data are given below. Use this to test whether the median difference in approval rating is different from zero in favor of the more expensive layout with a level of significance of 0.05.
$$\begin{array} { l l } \text { Package } & \text { Scratch } \\\hline 52 & 37 \\68 & 43 \\43 & 53 \\48 & 39 \\56 & 47\end{array}$$

-Referring to Table 12-16, which hypotheses should be used?

A) $H_{0}: M_{D} \leq 0$ versus $H_{1}: M_{D}>0$
B) $H_{0}: M_{1}=M_{2}$ versus $H_{1}: M_{1} \neq M_{2}$
C) $H_{0}: M_{D}=0$ versus $H_{1}: M_{D} \neq 0$
D) $H_{0}: M_{1} \leq M_{2}$ versus $H_{1}: M_{1}>M_{2}$

Question 60

TABLE 12-17
The director of the MBA program of a state university wanted to know if a one week orientation would change the proportion among potential incoming students who would perceive the program as being good. Given below is the result from 215 students' view of the program before and after the orientation.
$$\begin{array}{l}\text {\quad\quad\quad\quad\quad\quad\quad\quad\quad After the Orientation }\\\begin{array} { l c c r } \text { Before the Orientation } & \text { Good } & \text { NotGood } & \text { Total } \\\hline\text { Good } & 93 & 37 & 130 \\\text { Not Good } & 71 & 14 & 85 \\\text { Total } & 164 & 51 & 215\end{array}\end{array}$$

-Referring to Table 12-17, which test should she use?

A)?²-test for difference in proportions
B) McNemar test for difference in proportions
C) Wilcoxon rank sum test
D) Z-test for difference in proportions

Question 61

TABLE 12-13
According to an article in Marketing News, fewer checks are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by check among three consecutive years at a 0.05 level of significance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented below.

Referring to Table 12-13, what is the p-value of the test statistic?

Question 62

TABLE 12-9
Four surgical procedures currently are used to install pacemakers. If the patient does not need to return for follow-up surgery the operation is called a "clear" operation. A heart center wants to compare the proportion of clear operations for the 4 procedures, and collects the following numbers of patients from their own records:
$$\begin{array}{l}\text {\quad\quad\quad\quad\quad\quad\quad Procedure }\\\begin{array} { l | r r r r | r } & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142\end{array}\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a level of significance of 0.05.

-Referring to Table 12-9, the expected cell frequency for the Procedure D/Return cell is_____

Question 63

TABLE 12-4
One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per 1,000 parts produced. The quality control department wants to find out whether there is a relationship between years of experience and defect rate. Since the job is repetitious, after the initial training period any improvement due to a learning effect might be offset by a loss of motivation. A defect rate is calculated for each worker in a yearly evaluation. The results for 100 workers are given in the table below.
$$\begin{array}{l}\text {\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad Years Since Training Period }\\\begin{array} { r | r r c } &< 1 \text { Year } & 1 - 4 \text { Years } & 5 \text { - 9Years } \\\hline \text { High } & 6 & 9 & 9 \\\text { Defect Rate: Average } & 9 & 19 & 23 \\\text { Low } & 7 & 8 & 10\end{array}\end{array}$$

-Referring to Table 12-4, what is the expected number of employees with 1 to 4 years of training time and a high defect rate?

A) 8.64
B) 12.00
C) 6.67
D) 6.00

Question 64

TABLE 12-14
A filling machine at a local soft drinks company is calibrated to fill the cans at an average amount of 12 fluid ounces and a standard deviation of 0.5 ounces. The company wants to test whether the standard deviation of the amount filled by the machine is indeed 0.5 ounces. A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces.

-Referring to Table 12-14, what type of test should be performed?

A) two-tailed test
B) upper-tailed test
C) lower-tailed test
D) none of the above

Question 65

TABLE 12-19
An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants all 3 varieties of the seeds on each of 5 different patches of fields. She then measures the crop yield in bushels per acre. Treating this as a randomized block design, the results are presented in the table that follows.
$$\begin{array} { l l l l } \underline{\text { Fields} } & \underline{\text { Smith} } &\underline{ \text { Walsh }} &\underline{ \text { Trevor } }\\1 & 11.1 & 19.0 & 14.6 \\2 & 13.5 & 18.0 & 15.7 \\3 & 15.3 & 19.8 & 16.8 \\4 & 14.6 & 19.6 & 16.7 \\5 & 9.8 & 16.6 & 15.2\end{array}$$ Below is the Minitab output of the Friedman rank test:
Friedman Test: Yield versus Varieties, Fields
Friedman test for Yield by Varieties blocked by Fields
$\mathrm{s}= 10.00$ $\quad$$\mathrm{DF}=2 \quad \mathrm{P}=0.007$

$\begin{array}{llcc} & \text { Est } & \text { Sum of } \\ \text { Varieties } & \text { N } & \text { Median } & \text { Ranks } \\ \text { Smith } & 5 & 13.500 & 5.0 \\ \text { Trevor } & 5 & 15.667 & 10.0 \\ \text { Walsh } & 5 & 18.533 & 15.0 \\\\ \text { Grand median= } & 15.900\end{array}$


-Referring to Table 12-19, what is the critical value of the Friedman rank test for the difference in the medians at a level of significance of 0.01?

Question 66

TABLE 12-9
Four surgical procedures currently are used to install pacemakers. If the patient does not need to return for follow-up surgery the operation is called a "clear" operation. A heart center wants to compare the proportion of clear operations for the 4 procedures, and collects the following numbers of patients from their own records:
$$\begin{array}{l}\text {\quad\quad\quad\quad\quad\quad\quad Procedure }\\\begin{array} { l | r r r r | r } & \text { A } & \text { B } & \text { C } & \text { D } & \text { Total } \\\hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \text { Total } & 38 & 56 & 30 & 18 & 142\end{array}\end{array}$$ They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a level of significance of 0.05.

-Referring to Table 12-9, what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between procedure A and procedure D using a 0.05 level of significance?

Question 67

TABLE 12-13
According to an article in Marketing News, fewer checks are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by check among three consecutive years at a 0.05 level of significance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented below.
$$\begin{array}{l}\text { \quad\quad\quad\quad \quad\quad\quad\quad\quad\quad\quad\quad Year }\\\begin{array} { c | c | c | c } \text { Check Written } & \text { Year 1 } & \text { Year 2} & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\text { No } & 275 & 325 & 375\end{array}\end{array}$$

-Referring to Table 12-13, what is the expected number of shoppers who pay by check in year 1 if there is no difference in the proportion of shoppers who pay by check among the three years?

Question 68

TABLE 12-1
A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles depends on ethnic status in San Diego County. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) ethnic status (Hispanic or non-Hispanic) and
1() seat belt usage (worn or not worn) during the accident. The number of children in each category is given in the table below.
$$\begin{array}{l}\begin{array} { l |r r } &\text {Hispanic}&\text { Non- Hispanic }\\\hline \text { Seat belts worn } & 31 & 148 \\\text { Seat belts not worn } & 283 & 330\end{array}\end{array}$$

-Referring to Table 12-1, at 5% level of significance, the critical value of the test statistic is

A) 13.2767.
B) 5.9914.
C) 9.4877.
D) 3.8415.

Question 69

TABLE 12-6
The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors. In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors
had job offers. If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2," perform the appropriate hypothesis test using a level of significance of 0.05.

-Referring to Table 12-6, the value of the test statistic is _____ .

Question 70

TABLE 12-14
A filling machine at a local soft drinks company is calibrated to fill the cans at an average amount of 12 fluid ounces and a standard deviation of 0.5 ounces. The company wants to test whether the standard deviation of the amount filled by the machine is indeed 0.5 ounces. A random sample of 15 cans filled by the machine reveals a standard deviation of 0.67 ounces.

-Referring to Table 12-14, which is the appropriate test to use?

A) ?²-test of population variance
B) Wilcoxon rank sum test
C) Wilcoxon signed ranks test
D)?²-test of independence

Question 71

The Kruskal-Wallis test is an extension of which of the following for two independent samples?

A) Wilcoxon signed ranks test
B) Wilcoxon rank sum test
C) pooled-variance t test
D) paired-sample t test

Question 72

TABLE 12-5
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let u₁ and u₂ represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.

-Referring to Table 12-5, the company tests to determine at the 0.05 level whether the population proportion has changed from the previous study. Which of the following is most correct?

A) Reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has increased over the intervening 10 years.
B) Do not reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has not changed over the intervening 10 years.
C) Reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has changed over the intervening 10 years.
D) Do not reject the null hypothesis and conclude that the proportion of employees who are interested in a self-improvement course has increased over the intervening 10 years.

Question 73

TABLE 12-1
A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles depends on ethnic status in San Diego County. A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained, and each child was classified according to (1) ethnic status (Hispanic or non-Hispanic) and
1() seat belt usage (worn or not worn) during the accident. The number of children in each category is given in the table below.
$$\begin{array}{l}\begin{array} { l |r r } &\text {Hispanic}&\text { Non- Hispanic }\\\hline \text { Seat belts worn } & 31 & 148 \\\text { Seat belts not worn } & 283 & 330\end{array}\end{array}$$

-Referring to Table 12-1, the calculated test statistic is

A) -0.9991.
B) -0.1368.
C) 72.8063.
D) 48.1849.

Question 74

TABLE 12-16
A perfume manufacturer is trying to choose between 2 magazine advertising layouts. An expensive layout would include a small package of the perfume. A cheaper layout would include a "scratch-and-sniff" sample of the product. The manufacturer would use the more expensive layout only if there is evidence that it would lead to a higher approval rate. The manufacturer presents both layouts to 5 groups and determines the approval rating from each group on both layouts. The data are given below. Use this to test whether the median difference in approval rating is different from zero in favor of the more expensive layout with a level of significance of 0.05.

Referring to Table 12-16, which pair(s) of observations has a negative signed rank?

Question 75

TABLE 12-13
According to an article in Marketing News, fewer checks are being written at grocery store checkout stands than in the past. To determine whether there is a difference in the proportion of shoppers who pay by check among three consecutive years at a 0.05 level of significance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented below.
$$\begin{array}{l}\text { \quad\quad\quad\quad\quad\quad\quad\quad\quad \quad\quad\quad Year }\\\begin{array} { c | c | c | c } \text { Check Written } & \text { Year 1 } & \text { Year 2 } & \text {Year3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\text { No } & 275 & 325 & 375\end{array}\end{array}$$

-Referring to Table 12-13, what is the form of the null hypothesis?

A) $H_{0}: \pi_{1} \neq \pi_{2} \neq \pi_{3}$
B) $H_{0}: \pi_{1} \neq \pi_{2}=\pi_{3}$
C) $H_{0}: \pi_{1}=\pi_{2}=\pi_{3}$
D) $H_{0}: \pi_{1}=\pi_{2} \neq \pi_{3}$

Question 76

TABLE 12-5
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let u₁ and u₂ represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.

-Referring to Table 12-5, if the firm wanted to test whether this proportion has changed from the previous study, which represents the relevant hypotheses?

A) $H_{0}: \pi_{1}-\pi_{2}=0$ versus $H_{1}: \pi_{1}-\pi_{2} \neq 0$
B) $H_{0}: \pi_{1}-\pi_{2} \leq 0$ versus $H_{1}: \pi_{1}-\pi_{2}>0$
C) $H_{0}: \pi_{1}-\pi_{2} \geq 0$ versus $H_{1}: \pi_{1}-\pi_{2}<0$
D) $H_{0}: \pi_{1}-\pi_{2} \neq 0$ versus $H_{1}: \pi_{1}-\pi_{2}=0$

Question 77

If we use the ?² method of analysis to test for the differences among 4 proportions, the degrees of freedom are equal to

A) 3.
B) 1.
C) 4.
D) 5.

Question 78

TABLE 12-12
Recent studies have found that American children are more obese than in the past. The amount of time children spent watching television has received much of the blame. A survey of 100 ten-year-olds revealed the following with regards to weights and average number of hours a day spent watching television. We are interested in testing whether the average number of hours spent watching TV and weights are independent at 1% level of significance.
$$\begin{array} { l | c l l | r } & { \text { TV Hours } } & \\\text { Weights } & 0 - 3 & 3 - 6 & 6 + & \text { Total } \\\hline \text { More than } 101 \mathrm { ls } \text {. overweight } & 1 & 9 & 20 & 30 \\\text { Within } 101 \mathrm { bs } \text {. of normal weight } & 20 & 15 & 15 & 50 \\\text { More than } 10 \mathrm { lbs } \text {. underweight } & 10 & 5 & 5 & 20 \\\hline \text { Total } & 31 & 29 & 40 & 100\end{array}$$

-Referring to Table 12-12, how many children in the survey spend no more than 6 hours watching TV and are more than 10 lbs. underweight?

A) 20
B) 15
C) 10
D) 5

Question 79

TABLE 12-3
A computer used by a 24-hour banking service is supposed to randomly assign each transaction to one of 5 memory locations. A check at the end of a day's transactions gave the counts shown in the table to each of the 5 memory locations, along with the number of reported errors.
$$\begin{array}{l}\begin{array} { l l l l l r } \hline \text { Memory Location: } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Number of Transactions: } & 82 & 100 & 74 & 92&102\\\text { Number of Reported Errors: } & 11 & 12 & 6 & 9 & 10\end{array}\\\begin{array} { l l l l l l } \end{array}\end{array}$$ The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ.

-Referring to Table 12-3, the degrees of freedom of the test statistic is

A) 10.
B) 4.
C) 8.
D) 448.

Question 80

TABLE 12-9
Four surgical procedures currently are used to install pacemakers. If the patient does not need to return for follow-up surgery the operation is called a "clear" operation. A heart center wants to compare the proportion of clear operations for the 4 procedures, and collects the following numbers of patients from their own records:
They will use this information to test for a difference among the proportion of clear operations using a chi-square test with a level of significance of 0.05.
Referring to Table 12-9, what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between procedure A and procedure B using a 0.05 level of significance?