Exam 17: Introduction to Nonparametric Statistics

Under what circumstances should the standard normal distribution be used when employing the Mann-Whitney U test?

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 a large sample Mann-Whitney U test in which the sample size from the first population is 30 and the sample size from the second population is 40, which of the following is the expected U value if the null hypothesis of equal median values is true?

Consider the situation in which a study was recently conducted to determine whether the median price of houses is the same in Seattle and Phoenix. The following data were collected. Given these data, if a Mann-Whitney U test is to be used, the U statistic for Phoenix is:

The Mann-Whitney U test can be used to test whether two independent populations have the same median so long as the data are measured on at least an ordinal scale.

A real estate broker claims that the median days that one of his listings stays on the market is 45 or less days. To test this, he has collected the following random sample of properties sold showing the days they were on the market prior to selling: The broker is unwilling to assume that the population data are normally distributed. a. What is the correct null and alternative hypothesis to be tested? b. What statistical test would you recommend be used to test this hypothesis? c. Conduct the test and indicate what conclusion should be reached if we test at an alpha = .05 level?

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

In the Wilcoxon signed rank test for testing about a single population median, if the sample size is large (n > 20), the test statistic can be approximated by the standard normal distribution.

A survey was recently conducted in which random samples of car owners of Chrysler, GM, and Ford cars were surveyed to determine their satisfaction. Each owner was asked to rate overall satisfaction on a scale of 1 (poor) to 1000 (excellent). The following data were recorded: If the analysts are not willing to assume that the population ratings are normally distributed and will use the Kruskal-Wallis test to determine if the three companies have different median ratings, what is the appropriate critical value if the test is to be conducted using an alpha = .05 level?

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

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

All Wilcoxon signed rank tests are two-tailed tests since we are testing whether the population median is the exact center of the population distribution.

The General Electric service department believes that the median time for a service call should be 30 or fewer minutes. To test this, the following random sample of service times was collected: Given that the managers do not wish to make the assumption that the population is normally distributed, the critical value for the test about median service times, using a .05 level of significance, is:

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.

Consider the situation in which a study was recently conducted to determine whether the median price of houses is the same in Seattle and Phoenix. The following data were collected. Given these data, if a Mann-Whitney U test is to be used, the sum of the ranks for Seattle is:

Which of the following tests would not be an example of nonparametric method?

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.

Assume that you are conducting a small sample Mann-Whitney U test where n1 = 14 and n2 = 16 and that U1 = 98. Assuming that U1 has been found correctly, what is the value of U2?

Under what conditions should a decision maker use a nonparametric statistical procedure?

Managers for a company that produces a weight loss product claim that the median weight lost over six weeks for people who use this product will be at least 20 pounds. The following data were collected from a sample of nine people who used the product. Based on these data, the test statistic is W = 12.