Question 1

The z-test approximation to the Wilcoxon signed rank sum test is used whenever the number of non-zeros differences is at least 50.

Accepted Answer

The z-test approximation to the Wilcoxon signed rank sum test is used when the sample size is at least 50, not necessarily the number of non-zeros differences.

Question 2

Which of the following tests employs matched-pairs sampling?

Accepted Answer

The Wilcoxon signed-rank test employs matched-pairs sampling, as it compares the difference between two related samples. The other tests listed do not involve matched-pairs sampling.

Question 3

The significance level for a Wilcoxon signed rank test is 0.05. The alternative hypothesis is stated as: The location of population 1 is to the left of the location of population 2. The appropriate critical value for a sample of size 20 (that is the number of nonzero differences) is:

Accepted Answer

The answer of The significance level for a Wilcoxon signed...

Question 4

A paired sample, two-sample t-test, corresponds to:

Accepted Answer

A paired sample, two-sample t-test, corresponds to a Wilcoxon signed rank test for paired samples, as they both compare the means of two dependent samples.

Question 5

In a normal approximation to the Wilcoxon signed rank test, the test statistic is calculated as z = 1.36. For a two-tail test, the p-value is:

Accepted Answer

The p-value for a two-tail test with a test statistic of z = 1.36 is 0.1738.

Question 6

In a Wilcoxon signed rank test for matched pairs with n = 32, the rank sums of the positive and negative differences are 367.5 and 160.5, respectively. The value of the standardized test statistic z is:

Accepted Answer

To find the standardized test statistic z, we use the formula:

z = (T - μT) / σT

where T is the smaller of the rank sums of the positive and negative differences (in this case, 160.5), μT is the mean of the rank sums under the null hypothesis (which is n(n+1)/4 = 16(17)/4 = 68) and σT is the standard deviation of the rank sums under the null hypothesis (which is sqrt(n(n+1)(2n+1)/24) = sqrt(32*33*65/24) ≈ 16.246).

Substituting these values, we get:

z = (160.5 - 68) / 16.246 ≈ 1.935

Therefore, the answer is D.

Question 7

The Wilcoxon Signed-Rank test may be more appropriate than the paired-difference t-test if:

Accepted Answer

The Wilcoxon Signed-Rank test does not require the population of differences to be normal, making it more appropriate if the assumption of normality is violated.

Question 8

The Wilcoxon signed rank test statistic is approximately normally distributed whenever the sample sizes are larger than or equal to:

Accepted Answer

The Wilcoxon signed rank test statistic is approximately normally distributed when the sample sizes are larger than or equal to 25.

Question 9

The significance level for a Wilcoxon signed rank sum test is 0.05. The alternative hypothesis is stated as: The location of population 1 is different from the location of population 2. The appropriate critical value for a sample of size 20 (that is the number of nonzero differences is 20) is:

Accepted Answer

To find the appropriate critical value, we need to refer to the Wilcoxon signed rank sum critical values table.

First, we identify the sample size, which is 20. Then, we locate the significance level of 0.05 in the table. Going down the column, we find the critical value closest to the number of nonzero differences, which is 20 in this case.

The closest critical value is 52, which is therefore the appropriate choice. So, the answer is C.

Question 10

Which of the following tests employs matched-pairs sampling?

Accepted Answer

The Wilcoxon signed-rank test employs matched-pairs sampling as it compares two sets of paired data to determine if there is a significant difference between them.

Question 11

Suppose you wish to detect a difference in the locations of two population distributions based on a paired-difference experiment consisting of n = 35 pairs. Use the Wilcoxon Signed-Rank test. [NOTE:  = n(n+ 1) / 2.]
If  = 339, what are your conclusions?
Give the test statistic.
T = ______________
Give the rejection region for the test for  = 0.05.
Reject  if T  ______________.
Conclude: ______________
There is ______________ of a difference between the two distributions.
Conduct the test using the large-sample z-test.
Compute the z-statistic: ______________
Reject  if the z-statistic  ______________.
Conclude: ______________
There is ______________ of a difference between the two distributions.
Compare your results with the nonparametric test results above.
______________

Accepted Answer

The answer of Suppose you wish to detect a difference...

Question 12

The Wilcoxon Signed-Rank test:

Accepted Answer

The Wilcoxon Signed-Rank test makes use of the sign and the magnitude of the rank of the differences between pairs of measurements. This test is used to compare paired samples, where the data is not normally distributed. It is appropriate for both continuous and ordinal data types.

Question 13

A nonparametric method to compare two populations, when the samples are matched pairs and the data are interval, and where the normality requirement necessary to perform the parametric test is unsatisfied, is the:

Accepted Answer

The Wilcoxon signed rank test is a nonparametric test that can be used to compare two populations when the samples are matched pairs and the normality assumption is not met. It is suitable for interval data and has the advantage of being more robust than the matched pairs t-test. The sign test is another nonparametric option for comparing paired samples, but it is less powerful than the Wilcoxon signed rank test. The matched pairs t-test and matched pairs z-test are both parametric tests that require normality, so they are not appropriate in this scenario.

Question 14

In a Wilcoxon signed rank test, the test statistic is calculated as T = 75. If there are n = 15 observations for which the difference is not zero, and a two-tailed test is performed at the 5% significance level, then:

Accepted Answer

The critical value for a two-tailed Wilcoxon signed rank test with n = 15 at the 5% significance level is greater than 75, so we do not reject the null hypothesis.

Question 15

In the Wilcoxon Signed-Rank test, if two or more measurements have the same nonzero difference, signs ignored, then:

Accepted Answer

The Wilcoxon Signed-Rank test handles ties by assigning the average of the ranks that the tied values would have occupied. This ensures that the ranking system remains fair and consistent, even when multiple measurements have the same difference.

Question 16

Two aptitude tests are currently being used to screen applicants for a certain position within a company. The question arose as to whether the two tests are comparable, i.e., whether they yield the same results. Six applicants were selected at random to take both tests (in a random order). The following scores were recorded:  Use the Wilcoxon signed-rank test to determine whether there is a difference in scores between the two tests. Use  = 0.10.
What is the test statistic?
______________
What is the critical value for the test statistic?
______________
Conclude:
______________
We ______________ conclude there is a difference in the frequency distributions of scores for the two aptitude tests.

Accepted Answer

The answer of Two aptitude tests are currently being used...

Question 17

The Wilcoxon signed-rank sum test involves:

Accepted Answer

The Wilcoxon signed-rank sum test involves all of these steps. First, the difference between the sample data for each matched pair is calculated and pairs with zero differences are eliminated. Then, the absolute values of the remaining nonzero differences are ranked from smallest to largest. The sign of each rank is then designated based on the corresponding original difference, and the sum of these signed ranks is calculated as the test statistic, T.

Question 18

The nonparametric counterpart of the parametric t-test of  for matched pairs is the:

Accepted Answer

The Wilcoxon signed rank test is the nonparametric counterpart of the parametric t-test for matched pairs, as it is used to compare two related or matched groups. The Friedman and Kruskal-Wallis tests are nonparametric tests for independent groups, while the Wilcoxon rank sum test is a nonparametric test for independent groups without a matched or related design. The chi-square test is used for categorical data. Therefore, choice C is the best option.

Question 19

In a Wilcoxon signed rank test for matched pairs with n = 35, the rank sums of the positive and negative differences are 380 and 225, respectively. The value of the standardized test statistic z is:

Accepted Answer

The answer of In a Wilcoxon signed rank test for...

Question 20

The significance level for a Wilcoxon signed rank test is 0.05. The alternative hypothesis is stated as: The location of population 1 is to the left of the location of population 2. The appropriate critical value for a sample of size 25 (that is, the number of nonzero differences is 25) is:

Accepted Answer

The answer of The significance level for a Wilcoxon signed...

Quiz 15: Nonparametric Statistics

The z-test approximation to the Wilcoxon signed rank sum test is used whenever the number of non-zeros differences is at least 50.

Which of the following tests employs matched-pairs sampling?

The significance level for a Wilcoxon signed rank test is 0.05. The alternative hypothesis is stated as: The location of population 1 is to the left of the location of population 2. The appropriate critical value for a sample of size 20 (that is the number of nonzero differences) is:

A paired sample, two-sample t-test, corresponds to:

In a normal approximation to the Wilcoxon signed rank test, the test statistic is calculated as z = 1.36. For a two-tail test, the p-value is:

In a Wilcoxon signed rank test for matched pairs with n = 32, the rank sums of the positive and negative differences are 367.5 and 160.5, respectively. The value of the standardized test statistic z is:

The Wilcoxon Signed-Rank test may be more appropriate than the paired-difference t-test if:

The Wilcoxon signed rank test statistic is approximately normally distributed whenever the sample sizes are larger than or equal to:

The significance level for a Wilcoxon signed rank sum test is 0.05. The alternative hypothesis is stated as: The location of population 1 is different from the location of population 2. The appropriate critical value for a sample of size 20 (that is the number of nonzero differences is 20) is:

Which of the following tests employs matched-pairs sampling?

The Wilcoxon Signed-Rank test:

A nonparametric method to compare two populations, when the samples are matched pairs and the data are interval, and where the normality requirement necessary to perform the parametric test is unsatisfied, is the:

In a Wilcoxon signed rank test, the test statistic is calculated as T = 75. If there are n = 15 observations for which the difference is not zero, and a two-tailed test is performed at the 5% significance level, then:

In the Wilcoxon Signed-Rank test, if two or more measurements have the same nonzero difference, signs ignored, then:

The Wilcoxon signed-rank sum test involves:

The nonparametric counterpart of the parametric t-test of for matched pairs is the:

In a Wilcoxon signed rank test for matched pairs with n = 35, the rank sums of the positive and negative differences are 380 and 225, respectively. The value of the standardized test statistic z is:

The significance level for a Wilcoxon signed rank test is 0.05. The alternative hypothesis is stated as: The location of population 1 is to the left of the location of population 2. The appropriate critical value for a sample of size 25 (that is, the number of nonzero differences is 25) is: