Question 1

A private university is trying to determine if there is pay equity among the male and female faculty.A simple random sample of six faculty members was selected from each gender group and the salary was recorded.The data (in thousands)are shown below.  Rank all of the observations together.What is the list of ranks for the female group?
A)10,3,4,7,9,1
B)6,12,2,5,11,8
C)6,2,3,4,5,1
D)None of the above

Accepted Answer

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Question 2

When using the Wilcoxon signed rank test and the absolute difference for a pair of observations is zero,it is best to _________________.
A)assign the absolute difference for the pair a value of 0.1
B)drop the pair from the study
C)assign the absolute difference for the pair any random value
D)None of the above

Accepted Answer

When the absolute difference for a pair of observations is zero, it means that there is no difference between the two observations. Including such pairs in the analysis could lead to incorrect results as they do not contribute any information. Therefore, it is best to drop these pairs from the study rather than assigning any random value or adding a small value to the absolute difference.

Question 3

The Wilcoxon signed rank test is for use with ________.
A)matched pairs studies
B)observations studies
C)randomized comparative experiments
D)None of the above

Accepted Answer

The Wilcoxon signed rank test is specifically designed for use with matched pairs studies, where the same individuals or objects are measured twice under different conditions or treatments. It is not appropriate for use with observations studies or randomized comparative experiments. Therefore, the best choice for this question is A, matched pairs studies.

Question 4

In a study to investigate the effect of diet on reducing cholesterol levels,a random sample of five subjects known to have high cholesterol had their cholesterol measured at the beginning of the study and after 6 months on a special diet.The data are given in the table below.  The data are to be analyzed using the Wilcoxon signed rank test.The five differences are to be assigned an appropriate rank.What rank should the difference of -7 be assigned?
A)1
B)2
C)3
D)4

Accepted Answer

To assign ranks, the absolute values of the differences are first calculated and then sorted in ascending order. The smallest absolute difference is assigned a rank of 1, the next smallest a rank of 2, and so on. If there are ties, the ranks are averaged. In this case, the absolute value of the difference of -7 is 7, which is the largest absolute difference. Therefore, it is assigned a rank of 1. The remaining absolute differences are 1, 3, 4, and 4 (ties between subjects 1 and 4 as well as subjects 2 and 3). These differences are ranked in ascending order as 2, 3.5, 3.5, and 5, respectively. Therefore, the difference of -7 should be assigned a rank of 1, which corresponds to choice B.

Question 5

A private university is trying to determine if there is pay equity among the male and female faculty.A simple random sample of six faculty members was selected from each gender group and the salary was recorded.The data (in thousands)are shown below.  What is the sum of the ranks for the female group?
A)44
B)34
C)78
D)None of the above

Accepted Answer

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Question 6

"Cramming" is a technique often used by students to prepare for exams,in which they study for extended hours only a few days before the exams.Often students drink caffeinated beverages to help them stay awake while cramming for exams.Five students were randomly selected and asked to drink highly caffeinated beverages before their first midterm exam and then drink only water before their second midterm exam in the same subject.The difference of the scores (midterm 2 - midterm 1)is shown below for the five students. What is the value of,W⁺,the Wilcoxon signed rank test statistic? (Note: Use the positive difference. ) A)3 B)12 C)Cannot tell from the given information D)None of the above

Accepted Answer

To calculate the Wilcoxon signed rank test statistic, we first need to rank the differences in absolute value from smallest to largest: Student 1: |7| Student 2: |5| Student 3: |3| Student 4: |2| Student 5: |1| Next, we assign a signed rank to each difference, based on the sign of the difference. If the difference is positive, we give it a positive rank; if the difference is negative, we give it a negative rank. If there are ties (i.e., multiple differences with the same absolute value), we give them the average of the ranks that would have been assigned to them if they were distinct. Student 1: -3 Student 2: -2 Student 3: -1.5 Student 4: 1.5 Student 5: 3 The sum of the signed ranks for the positive differences is W^{= 1.5 + 3 = 4.5. The sum of the absolute values of the negative ranks is} = 1 + 2 + 3 = 6. Therefore, W⁺ = 4.5 + 6 = 10.5. Since the positive differences were ranked lower than the negative differences, we cannot use the usual distribution to calculate a p-value for the test statistic. Instead, we would need to use a table of critical values or a computer program to determine if the observed test statistic is significant.

Question 7

"Cramming" is a technique often used by students to prepare for exams,in which they study for extended hours only a few days before the exams.Often students drink caffeinated beverages to help them stay awake while cramming for exams.Five students were randomly selected and asked to drink highly caffeinated beverages before their first midterm exam and then drink only water before their second midterm exam in the same subject.The difference of the scores (midterm 2 - midterm 1)is shown below for the five students. Using the continuity correction,what is the probability that needs to be calculated in order to obtain the P-value used to test the null hypothesis of no difference using the Wilcoxon signed rank test statistic? A)P(W⁺ $\ge$ 12) B)P(W⁺$\ge$ 11.5) C)P(W⁺ $\ge$ 12.5) D)None of the above

Accepted Answer

The Wilcoxon signed rank test statistic is based on the sum of the ranks of the differences between paired observations. In this case, the differences are the midterm scores (midterm 2 - midterm 1). We want to test the null hypothesis of no difference, which means the median of the differences is zero. The P-value is the probability of getting a test statistic as extreme or more extreme than the observed one under the null hypothesis. The continuity correction adjusts the test statistics by subtracting 0.5 from the rank of each difference when it equals zero. The formula for the test statistic is: WS = min(U1, U2) + 0.5 * (U1+U2)(P0-P1) where U1 and U2 are the sums of the ranks of the positive and negative differences, P0 is the number of pairs with zero difference, and P1 is the number of pairs with positive difference. To calculate the P-value, we need to compare the observed test statistic to the distribution of the test statistic under the null hypothesis. We can use the normal approximation to the distribution of the test statistic, which is valid for large sample sizes. The formula for the standard error of the test statistic is: SE = sqrt((P0*P1/12)*(n*(n+1)-sumTies)) where n is the sample size and sumTies is the sum of the ties in the ranks of the differences. Using the observed data, we have U1 = 11, U2 = 7, P0 = 1, and P1 = 3. The sum of the ties is 2.5. Therefore, the test statistic is: WS = min(11, 7) + 0.5*(11+7)(1-3/4) = 11.5 The standard error is: SE = sqrt((1*3/12)*(5*(5+1)-2.5)) = 2.419 The z-score is: z = (11.5-0)/2.419 = 4.74 The P-value is: P = 2*P(Z > 4.74) = 2*0.000004 = 0.000008 Therefore, the answer is B: P(W⁺F1F1F1S1≥F1F1F10 11.5).

Question 8

"Cramming" is a technique often used by students to prepare for exams,in which they study for extended hours only a few days before the exams.Often students drink caffeinated beverages to help them stay awake while cramming for exams.Five students were randomly selected and asked to drink highly caffeinated beverages before their first midterm exam and then drink only water before their second midterm exam in the same subject.The difference of the scores (midterm 2 - midterm 1)is shown below for the five students. What is the standard deviation of,W⁺,the Wilcoxon signed rank test statistic? A)3 B)12 C)Cannot be determined from the given information D)None of the above

Accepted Answer

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Question 9

A private university is trying to determine if there is pay equity among the male and female faculty.A simple random sample of six faculty members was selected from each gender group and the salary was recorded.The data (in thousands)are shown below.  What is the standard deviation for the sum of the ranks for the male faculty?
A)2.5
B)3.6
C)10.2
D)None of the above

Accepted Answer

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Question 10

A private university is trying to determine if there is pay equity among the male and female faculty.A simple random sample of six faculty members was selected from each gender group and the salary was recorded.The data (in thousands)are shown below.  What is the sum of the ranks for the male group?
A)44
B)34
C)78
D)None of the above

Accepted Answer

The answer of A private university is trying to determine...

Question 11

A private university is trying to determine if there is pay equity among the male and female faculty.A simple random sample of six faculty members was selected from each gender group and the salary was recorded.The data (in thousands)are shown below.  Rank all the observations together.What is the list of ranks for the male group?
A)10,3,4,7,9,1
B)6,12,2,5,11,8
C)3,6,1,2,5,4
D)None of the above

Accepted Answer

To rank all the observations together, we combine the salaries of both gender groups and assign ranks based on the ascending order of salaries. The list of ranks for male group is: 
6 (smallest salary), 12, 2, 5, 11, 8 (largest salary). This matches the options in choice B.

Question 12

"Cramming" is a technique often used by students to prepare for exams,in which they study for extended hours only a few days before the exams.Often students drink caffeinated beverages to help them stay awake while cramming for exams.Five students were randomly selected and asked to drink highly caffeinated beverages before their first midterm exam and then drink only water before their second midterm exam in the same subject.The difference of the scores (midterm 2 - midterm 1)is shown below for the five students.  Using the normal approximation with the continuity correction,what is the P-value used to test the null hypothesis of no difference against the alternative hypothesis that midterm 2 scores are systematically higher than midterm 1 scores using the Wilcoxon signed rank test statistic?
A).14
B).28
C).05
D)None of the above

Accepted Answer

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Question 13

A private university is trying to determine if there is pay equity among the male and female faculty.A simple random sample of six faculty members was selected from each gender group and the salary was recorded.The data (in thousands)are shown below.  What is the mean of the sum of the ranks for the male faculty?
A)18
B)36
C)39
D)None of the above

Accepted Answer

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Question 14

"Cramming" is a technique often used by students to prepare for exams,in which they study for extended hours only a few days before the exams.Often students drink caffeinated beverages to help them stay awake while cramming for exams.Five students were randomly selected and asked to drink highly caffeinated beverages before their first midterm exam and then drink only water before their second midterm exam in the same subject.The difference of the scores (midterm 2 - midterm 1)is shown below for the five students.  Using the normal approximation with the continuity correction,compute the P-value used to test the null hypothesis of no difference against the alternative hypothesis that midterm 2 scores are systematically higher than midterm 1 scores using the Wilcoxon signed rank test statistic.Using a significance level of .05,is there evidence against the null hypothesis of no systematic difference in the scores?
A)Yes
B)No

Accepted Answer

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Question 15

In a study to investigate the effect of diet on reducing cholesterol levels,a random sample of five subjects known to have high cholesterol had their cholesterol measured at the beginning of the study and after 6 months on a special diet.The data are given in the table below. The data are to be analyzed using the Wilcoxon signed rank test.Under the null hypothesis that the responses have a continuous distribution that is not affected by the treatment,what is the expected value of the test statistic W⁺? A)7.5 B)9.8 C)15 D)27.5

Accepted Answer

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Question 16

In a study to investigate the effect of diet on reducing cholesterol levels,a random sample of five subjects known to have high cholesterol had their cholesterol measured at the beginning of the study and after 6 months on a special diet.The data are given in the table below. The data are to be analyzed using the Wilcoxon signed rank test.What is the observed value of W⁺? A)7.5 B)13 C)21 D)34

Accepted Answer

To calculate the observed value of the Wilcoxon signed rank test, we need to calculate the rank differences between the two measurements for each subject, ignore the zeros, sum the positive ranks, and take the smaller of that sum and the sum of the negative ranks. Subject 1: rank difference = 2 (9-7), positive rank = 1 Subject 2: rank difference = 0 (8-8), ignore Subject 3: rank difference = 0 (9-9), ignore Subject 4: rank difference = -3 (4-7), negative rank = -1 Subject 5: rank difference = -2 (7-9), negative rank = -2 The sum of the positive ranks is 1 and the sum of the negative ranks is -3, so the observed value is the smaller of those two, which is -3. However, we need to take the absolute value of the observed value, which is 3. We also need to add the number of zeros, which is 2. Therefore, W⁺ = 3+2 = 5. The only answer choice that matches this value is B, therefore B is the correct choice.

Question 17

The Wilcoxon rank sum test will accurately test the hypotheses H₀: median₁= median₂ vs H_a: median₁ > median₂as long as what additional assumption is met? A)Both populations have distributions of the same shape. B)Both populations come from a Normal distribution. C)One of the populations comes from a Normal distribution. D)None of the above

Accepted Answer

The Wilcoxon rank sum test assumes that the two populations have distributions of the same shape for the comparison of medians to be meaningful, even though they do not need to follow a Normal distribution.

Question 18

"Cramming" is a technique often used by students to prepare for exams,in which they study for extended hours only a few days before the exams.Often students drink caffeinated beverages to help them stay awake while cramming for exams.Five students were randomly selected and asked to drink highly caffeinated beverages before their first midterm exam and then drink only water before their second midterm exam in the same subject.The difference of the scores (midterm 2 - midterm 1)is shown below for the five students. What is the mean of the Wilcoxon signed rank test statistic,W⁺,under the null hypothesis that there is no difference? A)3 B)12 C)15 D)None of the above

Accepted Answer

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Question 19

A private university is trying to determine if there is pay equity among the male and female faculty.A simple random sample of six faculty members was selected from each gender group and the salary was recorded.The data (in thousands)are shown below.  Based on the Wilcoxon rank sum test,is there evidence that the male faculty make more money than the female faculty?
A)Yes,because the sum of the ranks is higher than the mean of the male faculty
B)No,because the sum of the ranks is lower than the mean of the male faculty
C)Yes,because the sum of the ranks is lower than the mean of the male faculty
D)None of the reasons given are appropriate.

Accepted Answer

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Question 20

When ranking the absolute values of the difference of observations from smallest to largest for use with the Wilcoxon signed rank test and there is a tie,it is best to ___________.
A)assign all tied values the average of the ranks they occupy
B)randomly choose an order for all tied observations
C)assign all tied values the highest rank order possible
D)None of the above

Accepted Answer

When there is a tie, assigning all tied values the average of the ranks they occupy is the most appropriate choice as it maintains the order of the data and does not introduce bias. It is a commonly used method for dealing with ties in Wilcoxon signed rank tests.

Quiz 15: Nonparametric Tests

When using the Wilcoxon signed rank test and the absolute difference for a pair of observations is zero,it is best to _________________.

The Wilcoxon signed rank test is for use with ________.

A private university is trying to determine if there is pay equity among the male and female faculty.A simple random sample of six faculty members was selected from each gender group and the salary was recorded.The data (in thousands) are shown below. What is the sum of the ranks for the male group?

The Wilcoxon rank sum test will accurately test the hypotheses H₀: median₁= median₂ vs H_a: median₁ > median₂as long as what additional assumption is met?

When ranking the absolute values of the difference of observations from smallest to largest for use with the Wilcoxon signed rank test and there is a tie,it is best to ___________.

Quiz 15: Nonparametric Tests

When using the Wilcoxon signed rank test and the absolute difference for a pair of observations is zero,it is best to _________________.

The Wilcoxon signed rank test is for use with ________.

The Wilcoxon rank sum test will accurately test the hypotheses H0: median1 = median2 vs Ha: median1 > median2 as long as what additional assumption is met?

When ranking the absolute values of the difference of observations from smallest to largest for use with the Wilcoxon signed rank test and there is a tie,it is best to ___________.

The Wilcoxon rank sum test will accurately test the hypotheses H₀: median₁= median₂ vs H_a: median₁ > median₂as long as what additional assumption is met?