Exam 17: Introduction to Nonparametric Statistics

When the Mann-Whitney U test is performed,which of the following is true?

Consider the situation in which a study was recently conducted to determine whether the median price of houses is the same in Seattle and Phoenix.The following data were collected. Given these data,if a Mann-Whitney U test is to be used,the U statistic for Phoenix is:

A restaurant has three separate dining areas: the patio,the alcove,and the main hall.At question is whether the median dollar amount per customer is the same or different between these three restaurant locations.To test this,the manager has randomly selected samples from each location.These data are shown as follows: a.If the manager is unwilling to make the assumption that the bill amounts are normally distributed at all three locations,what statistical technique would you suggest to test whether the median bill amounts are the same or different? b.State the appropriate null and alternative hypotheses. c.Using an alpha level equal to .05,test the null hypothesis and state your conclusion.

A survey was recently conducted in which random samples of car owners of Chrysler,GM,and Ford cars were surveyed to determine their satisfaction.Each owner was asked to rate overall satisfaction on a scale of 1 (poor)to 1000 (excellent).The following data were recorded: If the analysts are not willing to assume that the population ratings are normally distributed and will use the Kruskal-Wallis test to determine if the three companies have different median ratings,which company has the smallest sum of ranks?

If a decision maker believes that the population is normally distributed and the data are known to be ratio level,then the either the t-test or the Wilcoxon signed rank test can be used to test null hypotheses about a single population mean.

Recently,a study was done to determine whether the median speed on a section of highway is the same for cars versus trucks.A sample of 12 cars (n₁ = 12)and 15 trucks (n₂ = 15)was collected.If the Mann-Whitney U test is to be performed using an alpha = .05,the test critical U value is 49.

The Wilcoxon signed rank test is used for testing hypotheses about a population median if the data are at nominal level.

Consider the situation in which a human resources manager wishes to determine whether the median number of days of sick leave per year is the same for female employees as for male employees.The following data represent random samples of males and females: If the manager is unwilling to assume that the populations are normally distributed,which of the following would be the appropriate null hypothesis to be tested?

In a Kruskal-Wallis test when ties occur,each observation is given the ________ for which it is tied.

The General Electric service department believes that the median time for a service call should be 30 or fewer minutes.To test this,the following random sample of service times was collected: Given that the managers do not wish to make the assumption that the population is normally distributed,the test statistic for the Wilcoxon signed rank sum test is:

In a Mann-Whitney U test,if the sample sizes are large then the test statistic can be approximated by the student's t-distribution.

The makers of furnace filters recently conducted a test to determine whether the median number of particulates that would pass through their four leading filters was the same.A random sample of 6 of each type of filter was used with the following data being recorded: If the Kruskal-Wallis test is used,the critical value for an alpha = .05 is 7.814

The Wilcoxon matched-pairs signed rank test assumes that the two samples are:

The distribution of T-values in the Wilcoxon Matched-Pairs Signed Rank test is approximately normal if the sample size (number of matched pairs)exceeds 25.

Assume that you are conducting a small sample Mann-Whitney U test where n₁ = 14 and n₂ = 16 and that U₁ = 98.Assuming that U₁ has been found correctly,what is the value of U₂?

In order to determine whether the median distance for the X-Special golf ball exceeds the median distance for the best-selling golf ball,six golfers were selected and asked to hit each ball with their driver.The distance was recorded.The following data were observed. The appropriate null and alternative hypotheses are: H₀ : ₁ ≤ ₂ H₀ : ₁ > ₂

Managers for a company that produces a weight loss product claim that the median weight lost over six weeks for people who use this product will be at least 20 pounds.The following data were collected from a sample of nine people who used the product. Based on these data,the test statistic is W = 12.

The Wilcoxon Matched-Pairs Signed rank test is an alternative to the paired sample t-test when we are unwilling to assume that the populations are normally distributed.

The makers of furnace filters recently conducted a test to determine whether the median number of particulates that would pass through their four leading filters was the same.A random sample of 6 of each type of filter was used with the following data being recorded: If the Kruskal-Wallis test is used,the test statistic is approximately H = 7.814

Consider the situation in which a study was recently conducted to determine whether the median price of houses is the same in Seattle and Phoenix.The following data were collected. Given these data,if a Mann-Whitney U test is to be used,the sum of the ranks for Seattle is: