Deck 11: Chi-Square Tests

Question 1

If we use the $x ^ { 2 }$ method of analysis to test for the differences among 4 proportions, the degrees of freedom are equal to:

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

Answer 1

3

Question 2

The squared difference between the observed and theoretical frequencies should be large if there is no significant difference between the proportions.

Answer 2

False

Question 3

In testing a hypothesis using the $x ^ { 2 }$ test, the theoretical frequencies are based on the

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

Answer 3

null hypothesis.

Question 4

SCENARIO 12-2
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 Scenario 12-2, the value of the test statistic is _.

Question 5

SCENARIO 12-2
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 Scenario 12-2, the null hypothesis should be rejected.

Question 6

SCENARIO 12-1
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 $\pi$ 1 and $\pi$ 2 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 Scenario 12-1, what is the critical value when testing whether the population proportions are different if $\alpha$ = 0.10?

A) $\pm$ 1.645
B) $\pm$ 1.96
C)3.842
D)2.706

Question 7

SCENARIO 12-1
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 $\pi$ 1 and $\pi$ 2 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 Scenario 12-1, 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 changed 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 increased 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 8

SCENARIO 12-3
The director of transportation of a large company is interested in the usage of her van pool.She considers her routes to be divided into local and non-local.She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes.She takes a sample of a day's riders and finds the following: She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.
Referring to Scenario 12-3, the test will involve degree(s) of freedom.

Question 9

A test for the difference between two proportions can be performed using the chi- square distribution.

Question 10

SCENARIO 12-2
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 Scenario 12-2, the hypotheses the dean should use are:

Question 11

SCENARIO 12-3
The director of transportation of a large company is interested in the usage of her van pool.She considers her routes to be divided into local and non-local.She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes.She takes a sample of a day's riders and finds the following: She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.
Referring to Scenario 12-3, the overall or mean proportion of local riders is .

Question 12

SCENARIO 12-2
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 Scenario 12-2, the null hypothesis will be rejected if the test statistic is _.

Question 13

SCENARIO 12-1
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 $\pi$ 1 and $\pi$ 2 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 Scenario 12-1, what is the critical value when performing a chi-square test on whether the population proportions are different if $\alpha$ = 0.05?

A) $\pm$ 1.645
B) $\pm$ 1.96
C)3.841
D)2.706

Question 14

In testing the difference between two proportions using the normal distribution, we may use either a one-tail Chi-square test or two-tail Z test.

Question 15

SCENARIO 12-2
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 Scenario 12-2, the p-value of the test is _.

Question 16

SCENARIO 12-1
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 $\pi$ 1 and $\pi$ 2 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 Scenario 12-1, 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) $H _ { 0 } : \pi _ { 1 } - \pi _ { 2 } \neq 0$ versus $H _ { 1 } : \pi _ { 1 } - \pi _ { 2 } = 0$
c) $H _ { 0 } : \pi _ { 1 } - \pi _ { 2 } \leq 0$ versus $H _ { 1 } : \pi _ { 1 } - \pi _ { 2 } > 0$
d) $H _ { 0 } : \pi _ { 1 } - \pi _ { 2 } \geq 0$ versus $H _ { 1 } : \pi _ { 1 } - \pi _ { 2 } < 0$

Question 17

SCENARIO 12-2
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 Scenario 12-2, the same decision would be made with this test if the level of significance had been 0.01 rather than 0.05.

Question 18

A test for whether one proportion is higher than the other can be performed using the chi-square distribution.

Question 19

SCENARIO 12-2
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 Scenario 12-2, the same decision would be made with this test if the level of significance had been 0.10 rather than 0.05.

Question 20

SCENARIO 12-1
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 $\pi$ 1 and $\pi$ 2 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 Scenario 12-1, 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 $\alpha$ =0.10?

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

Question 21

SCENARIO 12-3
The director of transportation of a large company is interested in the usage of her van pool.She considers her routes to be divided into local and non-local.She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes.She takes a sample of a day's riders and finds the following: $$\begin{array} { l | | c c | c } & \text { Male } & \text { Female } & \text { Total } \\\hline \hline \text { Local } & 27 & 44 & 71 \\\text { Non-Local } & 33 & 25 & 58 \\\hline \hline \text { Total } & 60 & 69 & 129\end{array}$$ She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.

-Referring to Scenario 12-3, the null hypothesis will be rejected.

Question 22

SCENARIO 12-4
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.
$\begin{array} { |l |l |l |l |l |l | } \hline \quad\quad\quad&\quad&\quad&\quad&\quad&\quad\\\hline \quad\quad\quad&\quad&\quad&\quad&\quad&\quad\\\hline \quad\quad\quad&\quad&\quad&\quad&\quad&\quad\\\hline \end{array}$
$$\begin{array} { | l | l | l | l | l | l | } \hline \text { MemorvLocation: } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Number of Transactions: } & 82 & 100 & 74 & 92 & 102 \\\hline \text { Number of Reported Errors } & 11 & 12 & 6 & 9 & 10 \\\hline\end{array}$$ The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ.

-Referring to Scenario 12-4, the critical value of the test statistic at 1% level of significance is

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

Question 23

SCENARIO 12-3
The director of transportation of a large company is interested in the usage of her van pool.She considers her routes to be divided into local and non-local.She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes.She takes a sample of a day's riders and finds the following: She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.
Referring to Scenario 12-3, the expected cell frequency in the Female/Non-Local cell is.

Question 24

SCENARIO 12-5
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:
Referring to Scenario 12-5, the overall or mean proportion of clear operations is .

Question 25

SCENARIO 12-3
The director of transportation of a large company is interested in the usage of her van pool.She considers her routes to be divided into local and non-local.She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes.She takes a sample of a day's riders and finds the following: She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.
Referring to Scenario 12-3, the expected cell frequency in the Male/Local cell is .

Question 26

SCENARIO 12-4
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.
$\begin{array} { |l |l |l |l |l |l | } \hline \quad\quad\quad&\quad&\quad&\quad&\quad&\quad\\\hline \quad\quad\quad&\quad&\quad&\quad&\quad&\quad\\\hline \quad\quad\quad&\quad&\quad&\quad&\quad&\quad\\\hline \end{array}$
$$\begin{array} { | l | l | l | l | l | l | } \hline \text { MemorvLocation: } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Number of Transactions: } & 82 & 100 & 74 & 92 & 102 \\\hline \text { Number of Reported Errors } & 11 & 12 & 6 & 9 & 10 \\\hline\end{array}$$ The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ.

-Referring to Scenario 12-4, which test would be used to properly analyze the data in this experiment?

A) $x ^ { 2 }$ test of independence
B) $x ^ { 2 }$ test for difference among more than two proportions
C)Wilcoxon rank sum test
D)Kruskal-Wallis rank Test

Question 27

SCENARIO 12-3
The director of transportation of a large company is interested in the usage of her van pool.She considers her routes to be divided into local and non-local.She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes.She takes a sample of a day's riders and finds the following: She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.
Referring to Scenario 12-3, the critical value of the test is .

Question 28

SCENARIO 12-5
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:
Referring to Scenario 12-5, the expected cell frequency for the Procedure D/Return cell is.

Question 29

SCENARIO 12-4
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.
$\begin{array} { |l |l |l |l |l |l | } \hline \quad\quad\quad&\quad&\quad&\quad&\quad&\quad\\\hline \quad\quad\quad&\quad&\quad&\quad&\quad&\quad\\\hline \quad\quad\quad&\quad&\quad&\quad&\quad&\quad\\\hline \end{array}$
$$\begin{array} { | l | l | l | l | l | l | } \hline \text { MemorvLocation: } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Number of Transactions: } & 82 & 100 & 74 & 92 & 102 \\\hline \text { Number of Reported Errors } & 11 & 12 & 6 & 9 & 10 \\\hline\end{array}$$ The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ.

-Referring to Scenario 12-4, at 1% level of significance

A)there is sufficient evidence to conclude that the proportions of errors in transactions assigned to each of the 5 memory locations are all different.
B)there is insufficient evidence to conclude that the proportions of errors in transactions assigned to each of the 5 memory locations are all different.
C)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.
D)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.

Question 30

SCENARIO 12-5
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:
Referring to Scenario 12-5, the value of the test statistic is .

Question 31

SCENARIO 12-5
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: $$\begin{array} { c | | c c c c | | c } &&{ \text { Procedure } }\\&A&B&C&D & { \text { Total } } \\\hline \hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \hline \text { Total } & 38 & 56 & 30 & 18 & 142\end{array}$$

-Referring to Scenario 12-5, the decision made suggests that the 4 procedures do not all have the same proportion of clear operations.

Question 32

SCENARIO 12-5
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:
Referring to Scenario 12-5, the critical value of the test is .

Question 33

SCENARIO 12-5
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:
Referring to Scenario 12-5, the test will involve degrees of freedom.

Question 34

SCENARIO 12-4
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.
$\begin{array} { |l |l |l |l |l |l | } \hline \quad\quad\quad&\quad&\quad&\quad&\quad&\quad\\\hline \quad\quad\quad&\quad&\quad&\quad&\quad&\quad\\\hline \quad\quad\quad&\quad&\quad&\quad&\quad&\quad\\\hline \end{array}$
$$\begin{array} { | l | l | l | l | l | l | } \hline \text { MemorvLocation: } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Number of Transactions: } & 82 & 100 & 74 & 92 & 102 \\\hline \text { Number of Reported Errors } & 11 & 12 & 6 & 9 & 10 \\\hline\end{array}$$ The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ.

-Referring to Scenario 12-4, the calculated value of the test statistic is

A)-0.1777
B)-0.0185
C)1.2068
D)1.5190

Question 35

SCENARIO 12-3
The director of transportation of a large company is interested in the usage of her van pool.She considers her routes to be divided into local and non-local.She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes.She takes a sample of a day's riders and finds the following: She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.
Referring to Scenario 12-3, the value of the test statistic is .

Question 36

SCENARIO 12-3
The director of transportation of a large company is interested in the usage of her van pool.She considers her routes to be divided into local and non-local.She is particularly interested in learning if there is a difference in the proportion of males and females who use the local routes.She takes a sample of a day's riders and finds the following: $$\begin{array} { l | | c c | c } & \text { Male } & \text { Female } & \text { Total } \\\hline \hline \text { Local } & 27 & 44 & 71 \\\text { Non-Local } & 33 & 25 & 58 \\\hline \hline \text { Total } & 60 & 69 & 129\end{array}$$ She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.

-Referring to Scenario 12-3, the decision made suggests that there is a difference between the proportion of males and females who ride local versus non-local routes.

Question 37

SCENARIO 12-5
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: $$\begin{array} { c | | c c c c | | c } &&{ \text { Procedure } }\\&A&B&C&D & { \text { Total } } \\\hline \hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \hline \text { Total } & 38 & 56 & 30 & 18 & 142\end{array}$$

-Referring to Scenario 12-5, the decision made suggests that the 4 procedures all have different proportions of clear operations.

Question 38

SCENARIO 12-5
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:
Referring to Scenario 12-5, the expected cell frequency for the Procedure A/Clear cell is.

Question 39

SCENARIO 12-4
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.
$\begin{array} { |l |l |l |l |l |l | } \hline \quad\quad\quad&\quad&\quad&\quad&\quad&\quad\\\hline \quad\quad\quad&\quad&\quad&\quad&\quad&\quad\\\hline \quad\quad\quad&\quad&\quad&\quad&\quad&\quad\\\hline \end{array}$
$$\begin{array} { | l | l | l | l | l | l | } \hline \text { MemorvLocation: } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Number of Transactions: } & 82 & 100 & 74 & 92 & 102 \\\hline \text { Number of Reported Errors } & 11 & 12 & 6 & 9 & 10 \\\hline\end{array}$$ The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ.

-Referring to Scenario 12-4, the degrees of freedom of the test statistic is

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

Question 40

SCENARIO 12-5
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: $$\begin{array} { c | | c c c c | | c } &&{ \text { Procedure } }\\&A&B&C&D & { \text { Total } } \\\hline \hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \hline \text { Total } & 38 & 56 & 30 & 18 & 142\end{array}$$

-Referring to Scenario 12-5, the null hypothesis will be rejected.

Question 41

SCENARIO 12-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout 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. $$\begin{array} { | l | c | c | c | } \hline & & { \text { Year } } \\\hline \text { Check Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\hline \text { No } & 275 & 325 & 375 \\\hline\end{array}$$

-Referring to Scenario 12-6, the assumptions needed to perform the test are satisfied.

Question 42

SCENARIO 12-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout 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 Scenario 12-6, what is the value of the test statistic?

Question 43

SCENARIO 12-5
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:
Referring to Scenario 12-5, what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between procedure B and procedure C using a 0.05 level of significance?

Question 44

SCENARIO 12-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout 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 Scenario 12-6, what is the form of the null hypothesis?

Question 45

SCENARIO 12-5
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: $$\begin{array} { c | | c c c c | | c } &&{ \text { Procedure } }\\&A&B&C&D & { \text { Total } } \\\hline \hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \hline \text { Total } & 38 & 56 & 30 & 18 & 142\end{array}$$

-Referring to Scenario 12-5, there is sufficient evidence to conclude that the proportions between procedure C and procedure D are different at a 0.05 level of significance.

Question 46

SCENARIO 12-5
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: $$\begin{array} { c | | c c c c | | c } &&{ \text { Procedure } }\\&A&B&C&D & { \text { Total } } \\\hline \hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \hline \text { Total } & 38 & 56 & 30 & 18 & 142\end{array}$$

-Referring to Scenario 12-5, there is sufficient evidence to conclude that the proportions between procedure B and procedure C are different at a 0.05 level of significance.

Question 47

SCENARIO 12-5
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:
Referring to Scenario 12-5, what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between procedure B and procedure D using a 0.05 level of significance?

Question 48

SCENARIO 12-5
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:
Referring to Scenario 12-5, 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 49

SCENARIO 12-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout 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 Scenario 12-6, what is the expected number of shoppers who do not pay by check in year 3 if there is no difference in the proportion of shoppers who pay by check among the three years?

Question 50

SCENARIO 12-5
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:
Referring to Scenario 12-5, what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between procedure C and procedure D using a 0.05 level of significance?

Question 51

SCENARIO 12-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout 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 Scenario 12-6, 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 52

SCENARIO 12-5
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: $$\begin{array} { c | | c c c c | | c } &&{ \text { Procedure } }\\&A&B&C&D & { \text { Total } } \\\hline \hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \hline \text { Total } & 38 & 56 & 30 & 18 & 142\end{array}$$

-Referring to Scenario 12-5, there is sufficient evidence to conclude that the proportions between procedure A and procedure D are different at a 0.05 level of significance.

Question 53

SCENARIO 12-5
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: $$\begin{array} { c | | c c c c | | c } &&{ \text { Procedure } }\\&A&B&C&D & { \text { Total } } \\\hline \hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \hline \text { Total } & 38 & 56 & 30 & 18 & 142\end{array}$$

-Referring to Scenario 12-5, there is sufficient evidence to conclude that the proportions between procedure A and procedure B are different at a 0.05 level of significance.

Question 54

SCENARIO 12-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout 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 Scenario 12-6, what is the form of the alternative hypothesis?

Question 55

SCENARIO 12-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout 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 Scenario 12-6, what are the degrees of freedom of the test statistic?

Question 56

SCENARIO 12-5
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:
Referring to Scenario 12-5, what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between procedure A and procedure C using a 0.05 level of significance?

Question 57

SCENARIO 12-5
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: $$\begin{array} { c | | c c c c | | c } &&{ \text { Procedure } }\\&A&B&C&D & { \text { Total } } \\\hline \hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \hline \text { Total } & 38 & 56 & 30 & 18 & 142\end{array}$$

-Referring to Scenario 12-5, there is sufficient evidence to conclude that the proportions between procedure A and procedure C are different at a 0.05 level of significance.

Question 58

SCENARIO 12-5
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: $$\begin{array} { c | | c c c c | | c } &&{ \text { Procedure } }\\&A&B&C&D & { \text { Total } } \\\hline \hline \text { Clear } & 27 & 41 & 21 & 7 & 96 \\\text { Return } & 11 & 15 & 9 & 11 & 46 \\\hline \hline \text { Total } & 38 & 56 & 30 & 18 & 142\end{array}$$

-Referring to Scenario 12-5, there is sufficient evidence to conclude that the proportions between procedure B and procedure D are different at a 0.05 level of significance.

Question 59

SCENARIO 12-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout 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 Scenario 12-6, what is the critical value?

Question 60

SCENARIO 12-5
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:
Referring to Scenario 12-5, 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?

Question 61

SCENARIO 12-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout 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. $$\begin{array} { | l | c | c | c | } \hline & & { \text { Year } } \\\hline \text { Check Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\hline \text { No } & 275 & 325 & 375 \\\hline\end{array}$$

-Referring to Scenario 12-6, the null hypothesis cannot be rejected.

Question 62

SCENARIO 12-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout 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 Scenario 12-6, what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between year 1 and year 2 using a 0.05 level of significance?

Question 63

SCENARIO 12-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout 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 Scenario 12-6, what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between year 1 and year 3 using a 0.05 level of significance?

Question 64

SCENARIO 12-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout 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. $$\begin{array} { | l | c | c | c | } \hline & & { \text { Year } } \\\hline \text { Check Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\hline \text { No } & 275 & 325 & 375 \\\hline\end{array}$$

-Referring to Scenario 12-6, there is sufficient evidence to conclude that the proportions between year 2 and year 3 are different at a 0.05 level of significance.

Question 65

SCENARIO 12-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout 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. $$\begin{array} { | l | c | c | c | } \hline & & { \text { Year } } \\\hline \text { Check Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\hline \text { No } & 275 & 325 & 375 \\\hline\end{array}$$

-Referring to Scenario 12-6, what is the correct conclusion?

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

Question 66

SCENARIO 12-7
Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below. At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.
Referring to Scenario 12-7, the test will involve degrees of freedom.

Question 67

SCENARIO 12-7
Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below. At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.
Referring to Scenario 12-7, the expected cell frequency for the Hong Kong/Yes cell is.

Question 68

SCENARIO 12-7
Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below. $$\begin{array} { c | | c c c } & \text { Hong Kong } & \text { New York } & \text { Paris } \\\hline \hline \text { Yes } & 86 \% & 76 \% & 78 \% \\\text { No } & 14 \% & 24 \% & 22 \%\end{array}$$ At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.

-Referring to Scenario 12-7, the null hypothesis will be rejected.

Question 69

SCENARIO 12-7
Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below. $$\begin{array} { c | | c c c } & \text { Hong Kong } & \text { New York } & \text { Paris } \\\hline \hline \text { Yes } & 86 \% & 76 \% & 78 \% \\\text { No } & 14 \% & 24 \% & 22 \%\end{array}$$ At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.

-Referring to Scenario 12-7, the decision made suggests that the 3 cities do not all have the same proportion of hotels that correctly post minibar charges.

Question 70

SCENARIO 12-7
Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below. $$\begin{array} { c | | c c c } & \text { Hong Kong } & \text { New York } & \text { Paris } \\\hline \hline \text { Yes } & 86 \% & 76 \% & 78 \% \\\text { No } & 14 \% & 24 \% & 22 \%\end{array}$$ At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.

-Referring to Scenario 12-7, the decision made suggests that the 3 cities all have different proportions of hotels that correctly post minibar charges.

Question 71

SCENARIO 12-7
Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below. At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.
Referring to Scenario 12-7, what are the values of the absolute difference and the critical range for the Marascuilo procedure to test for the difference in proportions between Hong Kong and New York using a 0.05 level of significance?

Question 72

SCENARIO 12-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout 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. $$\begin{array} { | l | c | c | c | } \hline & & { \text { Year } } \\\hline \text { Check Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\hline \text { No } & 275 & 325 & 375 \\\hline\end{array}$$

-Referring to Scenario 12-6, there is insufficient evidence to conclude that the proportions between year 1 and year 3 are different at a 0.05 level of significance.

Question 73

SCENARIO 12-7
Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below. $$\begin{array} { c | | c c c } & \text { Hong Kong } & \text { New York } & \text { Paris } \\\hline \hline \text { Yes } & 86 \% & 76 \% & 78 \% \\\text { No } & 14 \% & 24 \% & 22 \%\end{array}$$ At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.

-Referring to Scenario 12-7, there is sufficient evidence to conclude that the proportions between Hong Kong and New York are different at a 0.05 level of significance.

Question 74

SCENARIO 12-7
Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below. At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.
Referring to Scenario 12-7, the critical value of the test is .

Question 75

SCENARIO 12-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout 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. $$\begin{array} { | l | c | c | c | } \hline & & { \text { Year } } \\\hline \text { Check Written } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } \\\hline \text { Yes } & 225 & 175 & 125 \\\hline \text { No } & 275 & 325 & 375 \\\hline\end{array}$$

-Referring to Scenario 12-6, there is sufficient evidence to conclude that the proportions between year 1 and year 2 are different at a 0.05 level of significance.

Question 76

SCENARIO 12-7
Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below. At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.
Referring to Scenario 12-7, the expected cell frequency for the Paris/No cell is .

Question 77

SCENARIO 12-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout 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 Scenario 12-6, what is the p-value of the test statistic?

Question 78

SCENARIO 12-7
Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below. At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.
Referring to Scenario 12-7, the value of the test statistic is .

Question 79

SCENARIO 12-7
Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below. At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.
Referring to Scenario 12-7, what are the values of the absolute difference and the critical range for the Marascuilo procedure to test for the difference in proportions between Hong Kong and Paris using a 0.05 level of significance?

Question 80

SCENARIO 12-6
According to an article in Marketing News, fewer checks are being written at the grocery store checkout 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 Scenario 12-6, what is the value of the critical range for the Marascuilo procedure to test for the difference in proportions between year 2 and year 3 using a 0.05 level of significance?