Question 1

The sum of ranks in a Wilcoxon rank sum test must equal _______.
A) n(n + 1)/2
B) n(n - 1)/2
C) n(n - 2).
D) (n * n)/2.

Accepted Answer

In a Wilcoxon rank sum test, the sum of ranks should be equal to the sum of integers from 1 to n (the total number of observations). This can be calculated using the formula n(n + 1)/2. Therefore, the correct answer is A.

Question 2

Instruction 19-1 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: $$\begin{array} { | l | c | c | l | } \hline & \text { Male } & \text { Female } & \text { Total } \ \hline \text { Local } & 27 & 44 & 71 \ \hline \text { Non-Local } & 33 & 25 & 5 \ \hline \text { Total } & 60 & 69 & 129 \ \hline \end{array}$$ She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05. -Referring to Instruction 19-1,the director now wants to know if the proportion of users who are male and the proportion of users who use the local routes are the same.Which test should she use? A) Z-test for difference in proportions B) Wilcoxon rank sum test C) McNemar test for difference in proportions D) (?)²-test for difference in proportions

Accepted Answer

C

Question 3

Given two samples with sizes 20 and 14,respectively,for the Wilcoxon rank sum test the total sample size is _______.
A) 34
B) 35
C) 33
D) 32

Accepted Answer

The total sample size is the sum of the sizes of the two samples, which is 20 + 14 = 34.

Question 4

The McNemar test is approximately distributed as a standardised normal random variable.

Accepted Answer

The McNemar test is a non-parametric test that is used to compare the paired binary data. It is approximately distributed as a standardized normal random variable under the null hypothesis of no difference between the two groups.

Question 5

The McNemar test is used to determine whether there is evidence of a difference between the proportions of two related samples.

Accepted Answer

The McNemar test is specifically designed to analyze paired samples or dependent samples, and it compares the proportions of one characteristic between two groups. Therefore, the statement is true.

Question 6

For the Wilcoxon rank sum test,the quantity T₁ is defined as _______. A) the total sum of ranks minus B) the sum of ranks in the larger sample C) the total sum of ranks D) the sum of ranks of the values in the smaller sample

Accepted Answer

The Wilcoxon rank sum test's quantity T₁ represents the sum of ranks of the values in the smaller sample. This is a key component in calculating the test statistic for comparing two independent samples.

Question 7

Instruction 19-1
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:
 $$\begin{array} { | l | c | c | l | } 
\hline & \text { Male } & \text { Female } & \text { Total } \
\hline \text { Local } & 27 & 44 & 71 \
\hline \text { Non-Local } & 33 & 25 & 5 \
\hline \text { Total } & 60 & 69 & 129 \
\hline
\end{array}$$ She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.
-Referring to Instruction 19-1,the director now wants to know if the proportion of users who are male and the proportion of users who use the local routes are the same.What should be her conclusion?
A) There is insufficient evidence that the proportion of users who are male is not the same as the proportion of users who use the local routes.
B) There is sufficient evidence that the proportion of users who are male is not the same as the proportion of users who use the local routes.
C) There is insufficient evidence that the proportion of users who are male is the same as the proportion of users who use the local routes.
D) There is sufficient evidence that the proportion of users who are male is the same as the proportion of users who use the local routes.

Accepted Answer

The question as stated is not directly answerable with a chi-square test, which is designed to test for independence between categorical variables, not to compare proportions directly in the manner described. However, interpreting the intent behind the question, it seems to aim at understanding if there's a significant difference in the usage patterns between males and females regarding local routes, which indirectly addresses the proportion issue. Given the data provided, without the actual chi-square calculation shown, the correct choice relies on understanding that a chi-square test's outcome would indicate whether there's a significant association between gender and route preference (local vs. non-local), not directly compare the proportions of male users to the proportion of users who use local routes. Therefore, the statement about insufficient evidence is a cautious interpretation without the chi-square statistic and p-value provided.

Question 8

One reason for using the Wilcoxon rank sum test rather than the t test is if you cannot assume that the populations from which the samples came are normally distributed.

Accepted Answer

The Wilcoxon rank sum test is a nonparametric test that can be used when assuming normality of the populations is not reasonable or when the sample size is small. In contrast, the t test assumes normally distributed populations and is typically used for larger sample sizes.

Question 9

Instruction 19-1 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: $$\begin{array} { | l | c | c | l | } \hline & \text { Male } & \text { Female } & \text { Total } \ \hline \text { Local } & 27 & 44 & 71 \ \hline \text { Non-Local } & 33 & 25 & 5 \ \hline \text { Total } & 60 & 69 & 129 \ \hline \end{array}$$ She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05. -Referring to Instruction 19-1,the director now wants to know if the proportion of users who are female and the proportion of users who use the local routes are the same.Which test should she use? A) McNemar test for difference in proportions B) (?)²-test for difference in proportions C) Z-test for difference in proportions D) Wilcoxon rank sum test

Accepted Answer

The answer of Instruction 19-1
The director of transportation of a...

Question 10

The McNemar test is approximately chi-square distributed.

Accepted Answer

The answer of The McNemar test is approximately chi-square distributed....

Question 11

Instruction 19-1
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:
 $$\begin{array} { | l | c | c | l | } 
\hline & \text { Male } & \text { Female } & \text { Total } \
\hline \text { Local } & 27 & 44 & 71 \
\hline \text { Non-Local } & 33 & 25 & 5 \
\hline \text { Total } & 60 & 69 & 129 \
\hline
\end{array}$$ She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.
-Referring to Instruction 19-1,the director now wants to know if the proportion of users who are male and the proportion of users who use the local routes are the same.What is the p-value of the test statistic using a 5% level of significance?

Accepted Answer

The answer of Instruction 19-1
The director of transportation of a...

Question 12

Instruction 19-1
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:
 $$\begin{array} { | l | c | c | l | } 
\hline & \text { Male } & \text { Female } & \text { Total } \
\hline \text { Local } & 27 & 44 & 71 \
\hline \text { Non-Local } & 33 & 25 & 5 \
\hline \text { Total } & 60 & 69 & 129 \
\hline
\end{array}$$ She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.
-Referring to Instruction 19-1,the director now wants to know if the proportion of users who are male and the proportion of users who use the local routes are the same.She should reject the null hypothesis using a 5% level of significance.

Accepted Answer

The information provided does not include the results of the chi-square test or the critical value needed to determine whether to reject the null hypothesis. Without this information or a calculation of the chi-square statistic and its comparison to the critical value, we cannot conclude whether the null hypothesis should be rejected.

Question 13

The McNemar test is approximately distributed as a chi-square random variable.

Accepted Answer

The answer of The McNemar test is approximately distributed as...

Question 14

One disadvantage of the Wilcoxon rank sum test,as compared to the t test,is that Wilcoxon rank sum test is much less powerful.

Accepted Answer

The Wilcoxon rank sum test can be more powerful than the t-test when the assumptions of the t-test are not met, particularly when the data are not normally distributed or when there are outliers, as it is a non-parametric test that does not assume normal distribution of the data.

Question 15

Instruction 19-1
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:
 $$\begin{array} { | l | c | c | l | } 
\hline & \text { Male } & \text { Female } & \text { Total } \
\hline \text { Local } & 27 & 44 & 71 \
\hline \text { Non-Local } & 33 & 25 & 5 \
\hline \text { Total } & 60 & 69 & 129 \
\hline
\end{array}$$ She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.
-Referring to Instruction 19-1,the director now wants to know if the proportion of users who are male and the proportion of users who use the local routes are the same.She should reject the null hypothesis using a 5% level of significance.

Accepted Answer

The question does not provide data on the proportions of males and females who use the local routes, so it is impossible to compare them. The statement in the question about rejecting the null hypothesis is not supported by any analysis. Therefore, we cannot determine whether the null hypothesis should be rejected or not.

Question 16

The Wilcoxon rank sum test is a non-parametric test for testing the difference between two ____from independent samples.

Accepted Answer

The answer of The Wilcoxon rank sum test is a...

Question 17

Instruction 19-1
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:
 $$\begin{array} { | l | c | c | l | } 
\hline & \text { Male } & \text { Female } & \text { Total } \
\hline \text { Local } & 27 & 44 & 71 \
\hline \text { Non-Local } & 33 & 25 & 5 \
\hline \text { Total } & 60 & 69 & 129 \
\hline
\end{array}$$ She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.
-Referring to Instruction 19-1,the director now wants to know if the proportion of users who are female and the proportion of users who use the local routes are the same.What is the value of the test statistic using a 5% level of significance?

Accepted Answer

The answer of Instruction 19-1
The director of transportation of a...

Question 18

Instruction 19-1
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:
 $$\begin{array} { | l | c | c | l | } 
\hline & \text { Male } & \text { Female } & \text { Total } \
\hline \text { Local } & 27 & 44 & 71 \
\hline \text { Non-Local } & 33 & 25 & 5 \
\hline \text { Total } & 60 & 69 & 129 \
\hline
\end{array}$$ She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.
-Referring to Instruction 19-1,the director now wants to know if the proportion of users who are male and the proportion of users who use the local routes are the same.What is the p-value of the test statistic using a 5% level of significance?

Accepted Answer

The answer of Instruction 19-1
The director of transportation of a...

Question 19

Instruction 19-2
The director of a university's MBA program 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.
After the Orientation
 $$\begin{array} { | c | c | c | c | } 
\hline \text { Before the Orientation } & \text { Good } & \text { Not Good } & \text { Total } \
\hline \text { Good } & 93 & 37 & 130 \
\hline \text { Not Good } & 71 & 14 & 85 \
\hline \text { Total } & 164 & 51 & 215 \
\hline
\end{array}$$
-Referring to Instruction 19-2,the director should reject the null hypothesis using a 1% level of significance.

Accepted Answer

We cannot see the data or the null hypothesis, but based on the given information, the conclusion is that the director should reject the null hypothesis, which means there is significant evidence that the orientation changed the proportion of potential students who perceived the program as being good. The decision is made at a 1% level of significance, which means the director is quite confident in this conclusion.

Question 20

Instruction 19-1
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:
 $$\begin{array} { | l | c | c | l | } 
\hline & \text { Male } & \text { Female } & \text { Total } \
\hline \text { Local } & 27 & 44 & 71 \
\hline \text { Non-Local } & 33 & 25 & 5 \
\hline \text { Total } & 60 & 69 & 129 \
\hline
\end{array}$$ She will use this information to perform a chi-square hypothesis test using a level of significance of 0.05.
-Referring to Instruction 19-1,the director now wants to know if the proportion of users who are male and the proportion of users who use the local routes are the same.What is the value of the test statistic using a 5% level of significance?

Accepted Answer

The answer of Instruction 19-1
The director of transportation of a...

Quiz 19: Further Non-Parametric Tests

The sum of ranks in a Wilcoxon rank sum test must equal _______.

Given two samples with sizes 20 and 14,respectively,for the Wilcoxon rank sum test the total sample size is _______.

The McNemar test is approximately distributed as a standardised normal random variable.

The McNemar test is used to determine whether there is evidence of a difference between the proportions of two related samples.

For the Wilcoxon rank sum test,the quantity T1 is defined as _______.

One reason for using the Wilcoxon rank sum test rather than the t test is if you cannot assume that the populations from which the samples came are normally distributed.

The McNemar test is approximately chi-square distributed.

The McNemar test is approximately distributed as a chi-square random variable.

One disadvantage of the Wilcoxon rank sum test,as compared to the t test,is that Wilcoxon rank sum test is much less powerful.

The Wilcoxon rank sum test is a non-parametric test for testing the difference between two ____from independent samples.

For the Wilcoxon rank sum test,the quantity T₁ is defined as _______.