Exam 19: Nonparametric Methods

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.The p-value for this test is

Fifteen people were asked to indicate their preference for domestic versus imported cars.The following data showed their preferences. With $\alpha$ = 0.05,test for a significant difference in the preferences for cars.A "+" indicates a preference for imported cars.

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.The null hypothesis should

If a null hypothesis that states that two populations are identical is rejected using a nonparametric test,then it is safe to assume that

In a sample of 120 people,50 indicated that they prefer domestic automobiles,60 said they prefer foreign-made cars,and 10 indicated no difference in their preference.At a 0.05 level of significance,determine if there is evidence of a significant difference in the preferences for the two makes of automobiles.

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 mean and the standard deviation (respectively)for this test about the median are

It is believed that the median age of college students is 21 years.A sample of 80 college students is taken.Thirty of the students were under 21,45 of the students were over 21,and 10 were 21 years old. a.State the null and alternative hypotheses. b.Test the null hypothesis at the 1% level of significance.

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 null hypothesis should be

Exhibit 19-5 It has been hypothesized that there is no difference in the mathematical ability of men and women.To test this hypothesis,it was decided to use the Mann-Whitney-Wilcoxon test.A sample of men and women were given math tests.The scores on the tests are given below. -Refer to Exhibit 19-5.To test the null hypothesis,the appropriate probability distribution to use is

Two individuals were asked to rank the performances of eight different automobiles.The following show their rankings. Determine the Spearman rank-correlation coefficient;and at 95% confidence,test for its significance.

We want to see if the workers on the day and night shifts differ significantly in their productivity levels.A sample of workers from both shifts was taken. a.State the null and alternative hypotheses. b.Test the null hypothesis at the 5% level of significance.

A survey of male and female students showed the following ranking of 12 professors in the management department: Do the rankings given by the female students agree with the rankings given by the male students? Use $\alpha$ = 0.05.

The president of a company wants to see if the new anti-smoking campaign is having any influence on his employees.A sample of 100 employees who smoked prior to the campaign is taken.Thirty-six employees said they smoked less,15 employees said they smoked more,and 49 employees said there was no change. a.State the null and alternative hypotheses. b.Test the null hypothesis at the 1% level of significance.

Statistical methods that generally require very few,if any,assumptions about the population distribution are known as

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.The test statistic equals

Parametric methods are statistical methods that

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 p-value for testing the hypotheses 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 that is being tested is

Independent random samples of ten day students and ten evening students at a university showed the following age distributions.We want to use the Mann-Whitney-Wilcoxon test to determine if there is a significant difference in the age distribution of the two groups. a.Compute the sum of the ranks (T)for the day students. b.Compute the mean $\mu$ _T. c.Compute $\sigma$ _T. d..Use $\alpha$ = 0.05 and test for any significant differences in the age distribution of the two populations.

Exhibit 19-5 It has been hypothesized that there is no difference in the mathematical ability of men and women.To test this hypothesis,it was decided to use the Mann-Whitney-Wilcoxon test.A sample of men and women were given math tests.The scores on the tests are given below. -Refer to Exhibit 19-5.The mean ( $\mu$ _T)is