Exam 17: Introduction to Nonparametric Statistics

In a Kruskal-Wallis test when ties occur, each observation is given the ________ for which it is tied.

In the finding the critical value for the Wilcoxon signed rank test, what does "n" represent?

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, which company has the smallest sum of ranks?

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.

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.

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.

When the Mann-Whitney U test is performed, which of the following is true?

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.

The Mann-Whitney U test is a nonparametric test that is used to test whether two related populations have the same median.

Consider the situation in which a human resources manager wishes to determine whether the median number of days of sick leave per year is the same for female employees as for male employees. The following data represent random samples of males and females: If the manager is unwilling to assume that the populations are normally distributed, which of the following would be the appropriate null hypothesis to be tested?

Recently, Major League Baseball officials stated that the median cost for a family of four to attend a baseball game including, parking, tickets, food, and drinks did not exceed $125.00. The following sample data were collected: Assuming that the test of the owners' claim is going to be conducted using an alpha = .05 level, the null hypothesis that the median cost does not exceed $125 should not be rejected.

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 test statistic for the Wilcoxon signed rank sum test is:

The Wilcoxon matched-pairs signed rank test assumes that the two samples are:

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

Consider the situation in which a human resources manager wishes to determine whether the median number of days of sick leave per year is greater for female employees than for male employees. The following data represent random samples of males and females: If the manager is unwilling to assume that the populations are normally distributed, which of the following is the correct conclusion to reach if the test is conducted using a .05 level of significance?

A paint manufacturer is interested in determining whether there is a difference in the median time it takes for two different brands of paint to dry once they have been applied to a wall surface. To test this, the company has selected a random sample of 5 walls and applied brand 1 and another 5 walls and applied brand 2. The following data reflect the actual drying time in hours: a. If you are unwilling to make the assumptions necessary to use a t-test, what test would you recommend in this situation? b. What would be the appropriate null and alternative hypothesis? c. Using an alpha level equal to .05, conduct the hypothesis test and state the conclusion.

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

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. In order to test the manager's claim, they will need to assume that the population is normally distributed.

Recently, a legislative committee commissioned a study of incomes in a western state. At issue was whether the ratings of the legislature's performance differed between rural citizens and city residents. A random sample of 25 city residents and 35 rural residents was asked to rate the performance of the legislature on a scale of 1 to 100. The analysts believe that the population distribution of ratings would be highly skewed so they decided to use the Mann-Whiney U test to test whether there is a difference in median ratings by the two groups. Given this information, which of the following is the correct critical value if the test is to be conducted at the .10 level of significance?