Exam 19: Nonparametric Methods

Exhibit 19-6 Forty-one individuals from a sample of 60 indicated they oppose legalized abortion.We are interested in determining whether or not there is a significant difference between the proportions of opponents and proponents of legalized abortion. -Refer to Exhibit 19-6.The conclusion is that there

Statistical methods that require assumptions about the population are known as

In a sample of 400 people,250 indicated that they prefer domestic wines,while 140 said they prefer European wines,and 10 indicated no preference.We want to use the sign test to determine if there is evidence of a significant difference in the preferences for the two types of wine. a.Provide the hypotheses to be tested. b.Compute the mean. c.Compute the standard deviation. d..At 95% confidence,test to determine if there is evidence of a significant difference in the preferences for the two types of wine.

Exhibit 19-3 It is believed that the median yearly income in a suburb of Atlanta is $70,000.A sample of 67 residents was taken.Thirty-eight had yearly incomes above $70,000,26 had yearly incomes below $70,000,and 3 had yearly incomes equal to $70,000.The null hypothesis to be tested is H₀: median = $70,000. -Refer to Exhibit 19-3.The test statistic has a value of

Ten drivers were asked to drive two models of a car.Each car was given one gallon of gasoline.The distance that each automobile traveled on a gallon of gasoline is shown below. At $\alpha$ = 0.05,what can be concluded about the performance of the two models?

When ranking combined data in a Wilcoxon signed rank test,the data that receives a rank of 1 is the

Test scores of ten individuals before and after a training program are shown below. At $\alpha$ = 0.05,what can be concluded about the effectiveness of the training program?

Two faculty members (X and Y)ranked five candidates for scholarships.The rankings are shown below. Compute the Spearman rank-correlation and test it for significance.Let $\alpha$ = 0.05.

Three universities in your state have decided to administer the same comprehensive examination to the recipients of MBA degrees.From each institution,a random sample of MBA recipients has been selected and given the test.The following table shows the scores of the students from each university. Use the Kruskal-Wallis test to determine if there is a significant difference in the average scores of the students from the three universities.Let $\alpha$ = 0.01.

The monthly sales records of two branches of a department store (Branch A and Branch B)over the last year (12 months)were gathered.It was decided to use the Mann-Whitney-Wilcoxon test to determine if there has been a significant difference between the sales of the two branches. a.Provide the hypotheses for this test. b.Compute the mean $\mu$ _T. c.Compute the standard deviation $\sigma$ _T. d.The sum of the ranks for branch A was determined to be 184.5.Compute the test statistic Z. e.Use $\alpha$ = 0.05 and test to determine if there is a significant difference in the populations of the sales of the two branches.

In a sample of 300 shoppers,160 indicated they prefer fluoride toothpaste,120 favored nonfluoride,and 20 were indifferent.At a 0.05 level of significance,test for a difference in the preference for the two kinds of toothpaste.

The Spearman rank-correlation coefficient is

The sales records of two branches of a department store over the last 12 months are shown below.(Sales figures are in thousands of dollars. )We want to use the Mann-Whitney-Wilcoxon test to determine if there is a significant difference in the sales of the two branches. a.Compute the sum of the ranks (T)for branch A. b.Compute the mean $\mu$ _T. c.Compute $\sigma$ _T. d..Use $\alpha$ = 0.05 and test to determine if there is a significant difference in the populations of the sales of the two branches.

Exhibit 19-2 Students in statistics classes were asked whether they preferred a 10-minute break or to get out of class 10 minutes early.In a sample of 150 students,40 preferred a 10-minute break,80 preferred to get out 10 minutes early,and 30 had no preference.We want to determine if there is a difference in students' preferences. -Refer to Exhibit 19-2.The null hypothesis that is being tested is

Exhibit 19-4 A company advertises that food preparation time can be significantly reduced with the Handy Dandy Slicer.A sample of 12 individuals prepared the ingredients for a meal with and without the slicer.You are given the preparation times below. -Refer to Exhibit 19-4.To test the null hypothesis,the appropriate probability distribution to use is

Exhibit 19-6 Forty-one individuals from a sample of 60 indicated they oppose legalized abortion.We are interested in determining whether or not there is a significant difference between the proportions of opponents and proponents of legalized abortion. -Refer to Exhibit 19-6.The null hypothesis should be

On a teacher evaluation form students are asked to rate their professor's performance as excellent,very good,good,and poor.This is an example of the

Exhibit 19-1 Fifteen people were given two types of cereal,Brand X and Brand Y.Two people preferred Brand X and thirteen people preferred Brand Y.We want to determine whether or not customers prefer one brand over the other. -Refer to Exhibit 19-1.To test the null hypothesis,the appropriate probability distribution to use is

The following data show the test scores of six individuals on a standardized test before and after attending a preparation seminar for the test. Use the Wilcoxon Signed-Rank test in order to determine whether or nor the seminar has been effective.Hint: This is a one tailed test.Let $\alpha$ = 0.05.

Independent random samples of the scores of 10 daily quizzes from day students and 15 quizzes from evening students were gathered.It was decided to use the Mann-Whitney-Wilcoxon test to determine if there is a significant difference between the scores of the two groups of students. a.Provide the hypotheses for this test. b.Compute the mean $\mu$ _T. c.Compute the standard deviation $\sigma$ _T. d.The sum of the ranks for the day students was determined to be 184.5.Compute the test statistic Z. e.Use $\alpha$ = 0.05 and test to determine if there is a significant difference in the populations of the scores of the two groups.