Question 1

The Mann-Whitney U test is always a one-tailed test.

Accepted Answer

The Mann-Whitney U test can be conducted as either a one-tailed or a two-tailed test, depending on the research hypothesis it is being used to test.

Question 2

In a Mann-Whitney U test, if the sample sizes are large then the test statistic can be approximated by the student's t-distribution.

Accepted Answer

The Mann-Whitney U test statistic is approximated by a normal distribution, not the student's t-distribution, when the sample sizes are large.

Question 3

In employing the Mann-Whitney U test, the sample data from the two populations are first combined and the ranks of the data are determined, but we keep track of which population each ranked item came from.

Accepted Answer

The Mann-Whitney U test involves combining the data from two samples, ranking all observations together regardless of their group, and then analyzing these ranks while keeping track of the group (population) each observation belongs to.

Question 4

The critical value for a one-tailed Mann-Whitney U test with sample sizes of n1 = 10 and n2 = 10 is 23 for a 0.05 level of significance.

Accepted Answer

The critical value for a one-tailed Mann-Whitney U test with sample sizes of n1 = 10 and n2 = 10 at a 0.05 level of significance is typically higher than 23. Exact critical values depend on tables or software calculations, but for these sample sizes, the value would generally be around 27 or 28, not 23.

Question 5

A claim was recently made that stated that the median income for male and female graduates is the same for those graduating with a degree in operations management. The following sample data were collected:  In employing the Mann-Whitney U test, the sum of the ranks for the males is 53.5

Accepted Answer

The answer of A claim was recently made that stated...

Question 6

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.  The appropriate null and alternative hypotheses are: H0 : 1 ≤ 2 H0 : 1 > 2

Accepted Answer

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

Question 7

One of the assumptions associated with the Wilcoxon Matched-Pairs Signed Rank test is that the distribution of the population differences is symmetric about their median.

Accepted Answer

The Wilcoxon Matched-Pairs Signed Rank test assumes that the differences between paired observations are symmetrically distributed around their median, which is crucial for the validity of the test.

Question 8

In conducting a Mann-Whitney U test when the sample size is greater than 20, the U test statistic can be assumed normally distributed.

Accepted Answer

For large sample sizes (typically n > 20), the Mann-Whitney U statistic can be approximated by a normal distribution due to the Central Limit Theorem, allowing for the use of z-scores in significance testing.

Question 9

If a decision maker wishes to test to determine whether the medians are equal for two populations the Mann-Whitney U test is appropriate for either independent or dependent sampling situations.

Accepted Answer

The Mann-Whitney U test is appropriate for independent samples, not dependent samples. For dependent samples, the Wilcoxon signed-rank test is typically used.

Question 10

A claim was recently made that stated that the median income for male and female graduates is the same for those graduating with a degree in operations management. The following sample data were collected:  In employing the Mann-Whitney U test, the U test statistic for the males is 43.5

Accepted Answer

The answer of A claim was recently made that stated...

Question 11

Recently, a study was done to determine whether the median speed on a section of highway is the same for cars versus trucks. A sample of 12 cars (n1 = 12) and 15 trucks (n2 = 15) was collected. If the Mann-Whitney U test is to be performed using an alpha = .05, the test critical U value is 49.

Accepted Answer

The critical value for the Mann-Whitney U test with n1 = 12 and n2 = 15 at alpha = .05 is 49.

Question 12

A claim was recently made that stated that the median income for male and female graduates is the same for those graduating with an MBA degree. In order to test this claim using the Mann-Whitney U test, it is not necessary to select an equal number of males and females.

Accepted Answer

The Mann-Whitney U test does not require equal sample sizes for the two groups being compared, making it suitable for comparing the median incomes of male and female MBA graduates regardless of the sample size of each group.

Question 13

The logic behind the Mann-Whitney U test is that if the hypothesis is true that the populations have equal central locations, then the sum of the ranks from each population will be approximately equal.

Accepted Answer

The Mann-Whitney U test is a non-parametric statistical test used to compare the central tendencies of two independent samples. The logic is that if the null hypothesis (that the two populations have equal central locations) is true, then the ranks of the observations from both groups should be evenly distributed throughout the combined set, leading to approximately equal sums of ranks for each group.

Question 14

One of the assumptions of the Mann-Whitney U test is that the population distributions are the same for shape and spread.

Accepted Answer

The Mann-Whitney U test assumes that the populations from which the samples are drawn have the same shape and spread, although it does not require them to follow a normal distribution. This is important for the validity of the test results.

Question 15

Recently, a study was done to determine whether the median speed on a section of highway is the same for cars versus trucks. A sample of 12 cars (n1 = 12) and 15 trucks (n2 = 15) was collected. If the Mann-Whitney U test is to be performed using an alpha = .05 and if the U test statistic is calculated to be 68, the null hypothesis should be rejected.

Accepted Answer

The Mann-Whitney U test is a non-parametric test used to compare the medians of two independent samples. The null hypothesis for the Mann-Whitney U test is that the medians of the two samples are equal. If the U test statistic is less than or equal to the critical value, the null hypothesis is rejected. In this case, the U test statistic is 68, which is greater than the critical value of 67 for alpha = .05. Therefore, the null hypothesis should be rejected.

Question 16

A large sample Mann-Whitney U test should be used when the sample sizes exceed 20.

Accepted Answer

The Mann-Whitney U test is a non-parametric test used to compare differences between two independent groups. For large samples (typically n > 20), the test statistic approximates a normal distribution, allowing for the use of a normal approximation to calculate p-values.

Question 17

In a Mann-Whitney U test, the test statistic will be equal to the sum of the ranks from sample one, or sample two, whichever is larger.

Accepted Answer

The Mann-Whitney U test statistic is calculated separately for each sample and is not simply the sum of the ranks of one of the samples. It involves calculating the sum of ranks for each sample and then using these sums to calculate two U values, one for each sample. The smaller of these two U values is often used as the test statistic.

Question 18

A claim was recently made that stated that the median income for male and female graduates is the same for those graduating with a degree in operations management. The following sample data were collected:  In employing the Mann-Whitney U test, the U test statistic is 25.5

Accepted Answer

The answer of A claim was recently made that stated...

Question 19

The Wilcoxon Matched-Pairs Signed rank test is an alternative to the paired sample t-test when we are unwilling to assume that the populations are normally distributed.

Accepted Answer

The Wilcoxon Matched-Pairs Signed Rank Test is a non-parametric alternative to the paired sample t-test and is used when the normality assumption required for the t-test cannot be met. It is suitable for comparing two related samples or repeated measurements on a single sample to assess whether their population mean ranks differ.

Question 20

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, the appropriate test is the Kruskal-Wallis one-way analysis of variance.

Accepted Answer

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

Quiz 17: Introduction to Nonparametric Statistics

The Mann-Whitney U test is always a one-tailed test.

In a Mann-Whitney U test, if the sample sizes are large then the test statistic can be approximated by the student's t-distribution.

In employing the Mann-Whitney U test, the sample data from the two populations are first combined and the ranks of the data are determined, but we keep track of which population each ranked item came from.

The critical value for a one-tailed Mann-Whitney U test with sample sizes of n1 = 10 and n2 = 10 is 23 for a 0.05 level of significance.

A claim was recently made that stated that the median income for male and female graduates is the same for those graduating with a degree in operations management. The following sample data were collected: In employing the Mann-Whitney U test, the sum of the ranks for the males is 53.5

One of the assumptions associated with the Wilcoxon Matched-Pairs Signed Rank test is that the distribution of the population differences is symmetric about their median.

In conducting a Mann-Whitney U test when the sample size is greater than 20, the U test statistic can be assumed normally distributed.

If a decision maker wishes to test to determine whether the medians are equal for two populations the Mann-Whitney U test is appropriate for either independent or dependent sampling situations.

A claim was recently made that stated that the median income for male and female graduates is the same for those graduating with a degree in operations management. The following sample data were collected: In employing the Mann-Whitney U test, the U test statistic for the males is 43.5

Recently, a study was done to determine whether the median speed on a section of highway is the same for cars versus trucks. A sample of 12 cars (n1 = 12) and 15 trucks (n2 = 15) was collected. If the Mann-Whitney U test is to be performed using an alpha = .05, the test critical U value is 49.

A claim was recently made that stated that the median income for male and female graduates is the same for those graduating with an MBA degree. In order to test this claim using the Mann-Whitney U test, it is not necessary to select an equal number of males and females.

The logic behind the Mann-Whitney U test is that if the hypothesis is true that the populations have equal central locations, then the sum of the ranks from each population will be approximately equal.

One of the assumptions of the Mann-Whitney U test is that the population distributions are the same for shape and spread.

A large sample Mann-Whitney U test should be used when the sample sizes exceed 20.

In a Mann-Whitney U test, the test statistic will be equal to the sum of the ranks from sample one, or sample two, whichever is larger.

A claim was recently made that stated that the median income for male and female graduates is the same for those graduating with a degree in operations management. The following sample data were collected: In employing the Mann-Whitney U test, the U test statistic is 25.5

The Wilcoxon Matched-Pairs Signed rank test is an alternative to the paired sample t-test when we are unwilling to assume that the populations are normally distributed.