Exam 14: Nonparametric Statistics

A physician claims that a person's diastolic blood pressure can be lowered, if, instead of taking a drug, the person listens to a relaxation tape each evening. Ten subjects are randomly selected. Their blood pressures, measured in millimeters of mercury, are listed below. The 10 patients are given the tapes and told to listen to them each evening for one month. At the end of the month, their blood pressures are taken again. The data are listed below. Use the Wilcoxon signed rank test to test the physician's claim. Use α = .05. Patient 1 2 3 4 5 6 7 8 9 10 Before 86 97 83 96 95 98 80 99 93 89 After 83 91 83 88 89 87 83 89 89 73

The median household income of a community is reported to be $62,000. A random sample of six households in the community yielded the following incomes. \ 42,000 \ 57,000 \ 65,000 \ 69,000 \ 75,000 \ 150,000 Does the sample provide sufficient evidence to refute the reported median household income? Perform a sign test using α = .10.

The sign test can not be used when an outlier is present.

When applying the Wilcoxon signed rank test, the number of ties should be small relative to the number of observations to ensure the validity of the test.

A researcher wants to know if the time spent in prison for a particular type of crime is the same for men and women. A random sample of men and women were each asked to give the length of sentence received. The data, in years, are listed below. Use the Wilcoxon rank sum procedure to test the claim that there is no difference in the sentence received by each gender. Use α = .05. Men 35 47 41 43 44 51 Women 34 37 34 39 51 37 Men 39 47 37 44 48 49 Women 59 33 35 38 42 52

Specify the rejection region for the Wilcoxon signed rank test in the following situation. n = 35, α = .10 H0: Two probability distributions, 1 and 2, are identical Ha: Probability distribution of population 1 is shifted to the right or left of the probability distribution for population 2

Which of the following is unknown, in general?

The results of independent random samples from two populations are shown below. Sample A: 35, 38, 42, 43, 45, 47, 49, 58 Sample B: 36, 41, 44, 53, 57 Calculate the rank sum for each sample. Which would be used as the test statistic in a Wilcoxon rank sum test?

Consider the data set shown below. Find the rejection region for determining if the Spearman's Rank Correlation between the variables x and y exceeds 0. Use α = 0.025. 0 4 2 3 8 10 11 -2 0 2 4 6 8 10 A) $r > 0.886$ B) $r > 0.714$ C) $r > 0.786$ D) $r > 0.893$

The drama department at a college asked professors and students in the drama department to rank 8 actors according to their performance. The data are listed below. A 10 is the highest ranking and a 1 the lowest ranking. Test the claim of no correlation between the rankings. Use α = .05. Actor 1 2 3 4 5 6 7 8 Professors 2 3 6 10 8 1 5 4 Students 4 3 1 4 5 7 9 6