Exam 17: Introduction to Nonparametric Statistics

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The Wilcoxon Matched-Pairs Signed rank test is an alternative to the paired sample t-test when we are unwilling to assume that the populations are normally distributed.

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

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A large sample Mann-Whitney U test should be used when the sample sizes exceed 20.

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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. 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: Given these data,if a Mann-Whitney U test is to be used,the U statistic for Phoenix is:

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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: 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: 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:

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

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In a large sample test about a single population median,it is appropriate to employ the standard normal distribution so long as the population is also normally distributed.

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The Mann-Whitney U test assumes that the 2 samples are:

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Assume that you are conducting a Mann-Whitney U test and have found the following after ranking the data for the two groups: Assume that you are conducting a Mann-Whitney U test and have found the following after ranking the data for the two groups:   Then the U<sub>1</sub> statistic is 77. Then the U1 statistic is 77.

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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.

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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,the test critical U value is 49.

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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: 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 sum of the rankings for Supplier 1 is 45. If a Kruskal-Wallis test is to be performed,the sum of the rankings for Supplier 1 is 45.

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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.

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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: 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 is 25.5. In employing the Mann-Whitney U test,the U test statistic is 25.5.

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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: 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 χ<sup>2</sup> = 11.0705. 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.

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In conducting a Mann-Whitney U test when the sample size is greater than 20,the U test statistic can be assumed normally distributed.

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If a two-tailed Wilcoxon Matched-Pairs Signed Rank test is conducted for a sample of n = 8 and an alpha level equal to .05,the critical value is:

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In conducting a Kruskal-Wallis one-way analysis of variance,the test statistic is assumed have approximately which distribution when the null hypothesis is true?

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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: 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. 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.

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Kruskal-Wallis One-Way Analysis of Variance is the nonparametric counterpart to the one-way ANOVA procedure in which the assumptions of normally distributed populations with equal variances are satisfied.

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