Exam 17: Introduction to Nonparametric Statistics

When employing a small sample Mann-Whitney U test for a two-tailed test,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 Kruskal-Wallis test is used,the critical value for an alpha = .05 is 7.814.

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

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.

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

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 Seattle is:

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 Mann-Whitney U test,if the sample sizes are large then the test statistic can be approximated by the student's t-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,which company has the smallest sum of ranks?

The critical value for a Kruskal Wallis test is an F value from the F-distribution.

If we wish to test whether two related populations have equal medians,an appropriate nonparametric test to use is:

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.In order to test this claim using the Mann-Whitney U test,the same number of males and females must be selected.

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.

The Wilcoxon signed rank test is always a one-tail test with the rejection region in the upper tail.

If a decision maker believes that the population is normally distributed and the data are known to be ratio level,then the either the t-test or the Wilcoxon signed rank test can be used to test null hypotheses about a single population mean.

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.

If we are interested in testing to determine whether the center of three or more populations is equal when the data in the samples are ordinal,what is the appropriate test to conduct?

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.

The Kruskal-Wallis test is usually limited to comparing sample values from ________ or more populations.

A restaurant has three separate dining areas: the patio,the alcove,and the main hall.At question is whether the median dollar amount per customer is the same or different between these three restaurant locations.To test this,the manager has randomly selected samples from each location.These data are shown as follows: a.If the manager is unwilling to make the assumption that the bill amounts are normally distributed at all three locations,what statistical technique would you suggest to test whether the median bill amounts are the same or different? b.State the appropriate null and alternative hypotheses. c.Using an alpha level equal to .05,test the null hypothesis and state your conclusion.