Exam 17: Introduction to Nonparametric Statistics

In conducting the Wilcoxon Matched-Pairs Signed Rank test,the difference between each pair of values must be found prior to conducting any ranking.

A recent study was conducted to determine if any of three suppliers of electronic components has a different median delivery time on special orders.To test this,five orders were given to each supplier and the delivery days were recorded.These data are shown as follows: If a Kruskal-Wallis test is to be performed,the number of degrees of freedom for determining the critical value is 2.

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 managers are unwilling to assume that the populations are normally distributed,the appropriate test in this case would be the Mann-Whitney U test.

Assume that 4 populations are to be compared using a Kruskal-Wallis one-way analysis of variance.What is the critical value using a 0.05 level of significance?

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.

Assume that a Kruskal-Wallis test is being conducted to determine whether or not the medians of three populations are equal.The sum of rankings and the sample size for each group are below. What is the value of the test statistic?

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:

The following null and alternative hypotheses are appropriate when using a Wilcoxon signed rank test. H_o: Population Median equals 14.5. H_A: Population Median is not equal to 14.5.

In the Wilcoxon signed rank test using either small or large sample sizes,any value that equals the hypothesized median is discarded from the analysis.

The Wilcoxon signed rank test is used to test which of the following type of hypotheses?

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 critical value for the test about median service times,using a .05 level of significance,is:

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,what is the appropriate critical value if the test is to be conducted using an alpha = .05 level?

The procedure of the Wilcoxon signed rank test is the same for either small or large sample sizes.

A real estate broker claims that the median days that one of his listings stays on the market is 45 or less days.To test this,he has collected the following random sample of properties sold showing the days they were on the market prior to selling: The broker is unwilling to assume that the population data are normally distributed. a.What is the correct null and alternative hypothesis to be tested? b.What statistical test would you recommend be used to test this hypothesis? c.Conduct the test and indicate what conclusion should be reached if we test at an alpha = .05 level?

The Wilcoxon signed rank test should be used in place of the t-test whenever the sample size is less than 20.

A marketing firm is interested to know whether 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.The conclusion is that

In conducting the Wilcoxon signed rank test,after collecting the sample data the next step is to find the sample median and subtract this value from each data value to obtain the deviations.

If a decision maker wishes to test to determine whether the medians are equal for two populations the Mann-Whitney U test is appropriate for either independent or dependent sampling situations.

Recently,a legislative committee commissioned a study of incomes in a western state.At issue was whether the ratings of the legislature's performance differed between rural citizens and city residents.A random sample of 25 city residents and 35 rural residents was asked to rate the performance of the legislature on a scale of 1 to 100.The analysts believe that the population distribution of ratings would be highly skewed so they decided to use the Mann-Whiney U test to test whether there is a difference in median ratings by the two groups.Given this information,which of the following is the correct critical value if the test is to be conducted at the .10 level of significance?

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