Exam 17: Introduction to Nonparametric Statistics

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 correct conclusion if the test is to be conducted using an alpha = .05 level?

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.

The basic logic of the Wilcoxon signed rank test is that if about half the data values fall above the hypothesized median,and about half fall below,the null hypothesis should not be rejected.

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.As long as the data are considered interval or ratio level,the t-test can be used to test MLB's claim.

When the Mann-Whitney U test is performed,which of the following 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 test statistic is:

Which of the following is not an assumption of the Kruskal-Wallis one-way analysis of variance?

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

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.

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.

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

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.

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.

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?

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 correct test statistic for these data?

Which of the following is not an assumption of the Mann-Whitney U test?

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

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.

Assume you are conducting a two-tailed Mann Whitney U test for a small sample and have found that U₁ = 58 and U₂ = 86.What is the value of the test statistic?

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?