Exam 18: Nonparametric Methods

Temperature is an example of a variable that uses

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

A nonparametric version of the Parametric analysis of variance test is the

In a sample of 200 racquetball players, 120 indicated they prefer Penn racquetballs, 75 favored Ektelon, and 5 were indifferent. 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 racquetballs. 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 racquetballs.

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

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. To test the null hypothesis, the appropriate probability distribution to use is

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

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.

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

A nonparametric test for the equivalence of two populations would be used instead of a parametric test for the equivalence of the population parameters if

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

The collection of statistical methods that require assumptions about the population is known as

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 test statistics is

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 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. The mean ( $\mu$ _T) is

A clothing manufacturer purchased some newly designed sewing machines in the hopes that production would be increased. The production records of a random sample of workers are shown below. Use the Wilcoxon signed-rank test to determine whether the new machines have significantly increased production. Use a .05 level of significance.

The manager of a company believes that differences in sales performance depends upon the salesperson's age. Independent samples of salespeople were taken and their weekly sales record is reported below. a.State the null and alternative hypotheses. b.At 95% confidence, test the hypotheses.

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. $\sigma$ in this problem is

The speed of an automobile is an example of a variable that uses the

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