Exam 17: Introduction to Nonparametric Statistics

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.

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.

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

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

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?

The procedure of the Wilcoxon signed rank test is the same for either small or large sample sizes.

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.

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.

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.

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.

Assume that 4 populations are to be compared using a Kruskal-Wallis one-way analysis of variance.What is the critical value using a 0.05 level of significance?

In the Wilcoxon signed rank test using either small or large sample sizes,any value that equals the hypothesized median is discarded from the analysis.

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.

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: Days 50 30 70 20 30 40 60 80 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?

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:

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.

A recent study was conducted to determine if any of three suppliers of electronic components has a different median delivery time on special orders.To test this,five orders were given to each supplier and the delivery days were recorded.These data are shown as follows: If a Kruskal-Wallis test is to be performed,the critical value for a test conducted using an alpha = .05 level is χ² = 11.0705

Nonparametric statistical tests are used when:

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 critical value is t = 1.9432.