Exam 18: Nonparametric Methods

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

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 Suburbia Health Department inspects restaurants for compliance to laws regulating the storage, preparation, and serving of food to the public. Two of the department's inspectors ranked ten restaurants in terms of cleanliness as shown below (with a 1 indicating cleanest and 10 indicating least clean). Use rank correlation, with $\alpha$ = .05, to comment on the agreement of the two inspectors' rankings.

Excel's ____ function can be used to conduct the Wilcoxon signed-rank test.

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?

A market researcher is asked to compare the responses to two questions on a customer satisfaction survey that was completed by 20 consumers. The first question asks the respondents to rate the product's quality and the second question asks the respondents to rate the product's ease of use. The results follow. Use Excel to calculate the Spearman correlation coefficient and then interpret its value.

The print capacity of ink cartridges in computer printers is a concern to many buyers due to the cost of cartridges. The observed print capacities (in number of pages) of black ink cartridges in a sample of 12 Epsmark printers and a sample of 12 Lexson printers are shown below. Do the data indicate, using $\alpha$ = .10, that a difference exists in the print capacities associated with the two brands of printers?

Exhibit 18-4 It has been hypothesized that there is no difference in the mathematical accuracy of men and women. A sample of men and women were given math tests. The scores on the tests are given below. -Refer to Exhibit 18-4. Calculate a Spearman rank-correlation coefficient for 20 pairs of data when $\Sigma$ d_i² = 50.

Exhibit 18-3 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 18-3. The hypothesis is to be tested at the 5% level of significance. The decision rule is not to reject the null hypothesis if

For the Wilcoxon signed-rank test, differences of 0 are

Exhibit 18-1 Ten people were given two types of cereal, Brand X and Brand Y. Three people preferred Brand X, 5 people preferred Brand Y, and 2 people were undecided. We want to determine whether or not the two products are equal. -Refer to Exhibit 18-1. The hypothesis is to be tested at the 5% level. The decision rule is not to reject the null hypothesis if

The Spearman rank-correlation coefficient for 20 pairs of data when $\Sigma$ d_i² = 50 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 Wilcoxon Signed-Rank test in order to determine whether or not the seminar has been effective. Hint: This is a one tailed test. Let $\alpha$ = 0.05.

The labeling of parts as "defective" or "non-defective" is an example of

Exhibit 18-5 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 18-5. $\mu$ in this situation is

A market research firm is conducting a study to determine which of two package designs for a liquid soap product potential customers prefer, the current design (A) or a new design (B). A sample of 40 potential customers is taken. The results follow. Use Excel to conduct the appropriate hypothesis test at $\alpha$ = .05 to determine if the data indicate that there is a difference in preference between the two designs.

The following data show the preference of 20 people for a candidate to a public office. A "+" indicates a preference for the Democratic candidate, and a "-" indicates a preference for the Republican candidate. With $\alpha$ = 0.05, test for a significant difference in the preference for the candidates.

Nonparametric methods which can be used to make inferences about a population without requiring an assumption about the distribution of the population are called

A real estate agency conducts a study to determine if the median selling price of homes in a particular neighborhood has changed since last year. Last year the median selling price was $188,500. The agency randomly selects 20 recently sold homes in that particular neighborhood and finds that 14 of the homes sold for more than $188,500 and that 6 of the homes sold for less than $188,500. Use Excel to conduct the appropriate hypothesis test at $\alpha$ = .10.

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.