Question 1

In conducting the Wilcoxon Matched-Pairs Signed Rank test, the difference between each pair of values must be found prior to conducting any ranking.

Accepted Answer

The Wilcoxon Matched-Pairs Signed Rank test requires calculating the differences between each pair of values as the first step, because the test is based on the ranks of these differences, not the original values themselves.

Question 2

If you are interested in testing whether the median of a population is equal to a specific value, an appropriate test to use is:
A) the Mann-Whitney U test.
B) the t-test.
C) the Wilcoxon signed rank test.
D) the Wilcoxon Matched-Pairs Signed Rank test.

Accepted Answer

The Wilcoxon signed rank test is specifically designed for testing hypotheses about the median of a population, making it the appropriate choice for this scenario. It is a non-parametric test used when the assumptions of the t-test (such as normality) are not met, and it is particularly useful for comparing the median of a sample to a known value or comparing the medians of two related samples.

Question 3

A recent study was conducted to determine if any of three suppliers of electronic components has a different median delivery time on special orders. To test this, five orders were given to each supplier and the delivery days were recorded. These data are shown as follows:  If a Kruskal-Wallis test is to be performed, the number of degrees of freedom for determining the critical value is 2.

Accepted Answer

The answer of A recent study was conducted to determine...

Question 4

The makers of furnace filters recently conducted a test to determine whether the median number of particulates that would pass through their four leading filters was the same. A random sample of 6 of each type of filter was used with the following data being recorded:  The Kruskal-Wallis test can be used in this case since it requires that the sample sizes be equal.

Accepted Answer

The answer of The makers of furnace filters recently conducted...

Question 5

The makers of furnace filters recently conducted a test to determine whether the median number of particulates that would pass through their four leading filters was the same. A random sample of 6 of each type of filter was used with the following data being recorded:  If the Kruskal-Wallis test is used, the test statistic is approximately H = 7.814

Accepted Answer

The answer of The makers of furnace filters recently conducted...

Question 6

The critical value for a Kruskal Wallis test comes from the chi-square distribution.

Accepted Answer

The Kruskal-Wallis test uses the chi-square distribution to determine the critical value for testing the null hypothesis that the medians of the groups are equal.

Question 7

A recent study was conducted to determine if any of three suppliers of electronic components has a different median delivery time on special orders. To test this, five orders were given to each supplier and the delivery days were recorded. These data are shown as follows:  If a Kruskal-Wallis test is to be performed, the sum of the rankings for Supplier 1 is 45.

Accepted Answer

The answer of A recent study was conducted to determine...

Question 8

The makers of furnace filters recently conducted a test to determine whether the median number of particulates that would pass through their four leading filters was the same. A random sample of 6 of each type of filter was used with the following data being recorded:  If the managers are unwilling to assume that the populations are normally distributed, the appropriate test in this case would be the Mann-Whitney U test.

Accepted Answer

The answer of The makers of furnace filters recently conducted...

Question 9

Kruskal-Wallis One-Way Analysis of Variance is the nonparametric counterpart to the one-way ANOVA procedure in which the assumptions of normally distributed populations with equal variances are satisfied.

Accepted Answer

The Kruskal-Wallis One-Way Analysis of Variance is indeed a nonparametric alternative to the one-way ANOVA, used when the assumptions of normality and equal variances are not met. It compares the medians from three or more independent samples to determine if at least one sample median differs from the others.

Question 10

If a decision maker wishes to test whether four independent populations have the same center and is unwilling to make the assumption that the populations are normally distributed with equal variances, she can use the Kruskal-Wallis test.

Accepted Answer

The Kruskal-Wallis test is a non-parametric method used to determine if there are statistically significant differences between the medians of three or more independent groups. It does not assume normal distribution or equal variances, making it suitable for the scenario described.

Question 11

The makers of furnace filters recently conducted a test to determine whether the median number of particulates that would pass through their four leading filters was the same. A random sample of 6 of each type of filter was used with the following data being recorded:  If the Kruskal-Wallis test is used, the critical value for an alpha = .05 is 7.814

Accepted Answer

The answer of The makers of furnace filters recently conducted...

Question 12

In using the Kruskal-Wallis test the sample sizes for each population must be equal.

Accepted Answer

The Kruskal-Wallis test does not require the sample sizes for each population to be equal; it can be used with different sample sizes across groups.

Question 13

In order to determine whether the median distance for the X-Special golf ball exceeds the median distance for the best-selling golf ball, six golfers were selected and asked to hit each ball with their driver. The distance was recorded. The following data were observed.  Based on these data, and testing at an alpha = 0.025 level, the critical value for the Wilcoxon Matched Pairs Signed Rank test is 2.

Accepted Answer

The answer of In order to determine whether the median...

Question 14

The Kruskal-Wallis test is used to test whether the centers of 3 or more populations are equal so long as that is the only possible difference between the population distributions.

Accepted Answer

The Kruskal-Wallis test is a non-parametric method used to determine if there are statistically significant differences between the medians of three or more independent groups, assuming the distributions have the same shape.

Question 15

Assume that a Kruskal-Wallis test is being conducted to determine whether or not the medians of three populations are equal. The sum of rankings and the sample size for each group are below.  The value of the test statistic is H = 0.68

Accepted Answer

The answer of Assume that a Kruskal-Wallis test is being...

Question 16

The distribution of T-values in the Wilcoxon Matched-Pairs Signed Rank test is approximately normal if the sample size (number of matched pairs) exceeds 25.

Accepted Answer

The Central Limit Theorem suggests that as the sample size increases, the distribution of the test statistic (in this case, T-values from the Wilcoxon Matched-Pairs Signed Rank test) approaches a normal distribution. A common rule of thumb is that this approximation is reasonable for sample sizes larger than 25.

Question 17

The makers of furnace filters recently conducted a test to determine whether the median number of particulates that would pass through their four leading filters was the same. A random sample of 6 of each type of filter was used with the following data being recorded:  If the Kruskal-Wallis test is used with an alpha = .01, the null hypothesis should be rejected and the managers should conclude that the four filters do not allow an equal median number of particulates.

Accepted Answer

The answer of The makers of furnace filters recently conducted...

Question 18

A recent study was conducted to determine if any of three suppliers of electronic components has a different median delivery time on special orders. To test this, five orders were given to each supplier and the delivery days were recorded. These data are shown as follows:  If a Kruskal-Wallis test is to be performed, the critical value for a test conducted using an alpha = .05 level is χ2 = 11.0705

Accepted Answer

The answer of A recent study was conducted to determine...

Question 19

Nonparametric statistical tests are used when:
A) the sample sizes are small.
B) we are unwilling to make the assumptions of parametric tests.
C) the standard normal distribution cannot be computed.
D) the population parameters are unknown.

Accepted Answer

Nonparametric tests are used when we do not want to assume a specific distribution for the data, which is a requirement for parametric tests.

Question 20

When testing whether two paired populations have equal medians and the sample sizes are large, it is appropriate to convert the Wilcoxon Matched-Pairs Signed Rank test to a paired sample t-test.

Accepted Answer

The Wilcoxon Matched-Pairs Signed Rank test and the paired sample t-test are used under different conditions. The Wilcoxon test is a non-parametric test that does not assume normal distribution of the differences between pairs, whereas the paired sample t-test assumes that these differences are normally distributed. The size of the sample does not justify converting one test into the other; the choice depends on the distribution of the data.

Quiz 17: Introduction to Nonparametric Statistics

In conducting the Wilcoxon Matched-Pairs Signed Rank test, the difference between each pair of values must be found prior to conducting any ranking.

If you are interested in testing whether the median of a population is equal to a specific value, an appropriate test to use is:

The critical value for a Kruskal Wallis test comes from the chi-square distribution.

Kruskal-Wallis One-Way Analysis of Variance is the nonparametric counterpart to the one-way ANOVA procedure in which the assumptions of normally distributed populations with equal variances are satisfied.

If a decision maker wishes to test whether four independent populations have the same center and is unwilling to make the assumption that the populations are normally distributed with equal variances, she can use the Kruskal-Wallis test.

In using the Kruskal-Wallis test the sample sizes for each population must be equal.

The Kruskal-Wallis test is used to test whether the centers of 3 or more populations are equal so long as that is the only possible difference between the population distributions.

Assume that a Kruskal-Wallis test is being conducted to determine whether or not the medians of three populations are equal. The sum of rankings and the sample size for each group are below. The value of the test statistic is H = 0.68

The distribution of T-values in the Wilcoxon Matched-Pairs Signed Rank test is approximately normal if the sample size (number of matched pairs) exceeds 25.

Nonparametric statistical tests are used when:

When testing whether two paired populations have equal medians and the sample sizes are large, it is appropriate to convert the Wilcoxon Matched-Pairs Signed Rank test to a paired sample t-test.