Exam 17: Introduction to Nonparametric Statistics

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.

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 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.

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.

The Wilcoxon signed rank test is used for testing hypotheses about a population median if the data are at nominal level.

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.

In conducting the Wilcoxon signed rank test, after collecting the sample data the next step is to find the sample median and subtract this value from each data value to obtain the deviations.

Which of the following is not a step involved in the Wilcoxon signed rank test?

If a decision maker wishes to test to determine whether the medians are equal for two populations the Mann-Whitney U test is appropriate for either independent or dependent sampling situations.

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.

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 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 data, and testing at an alpha = 0.025 level, the critical value for the Wilcoxon Matched Pairs Signed Rank test is 2.

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

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

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

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

If a Mann-Whitney U test was performed and U1 = 50 and U2 = 40, if the sample from population 1 was 10, the sample size from population 2 was:

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 number of degrees of freedom for determining the critical value is 2.

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

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.