Exercises. 1. A manufacturer of wall papers is considering three alternative colors: red, green and blue

1. A manufacturer of wall papers is considering three alternative colors: red, green and blue. To check whether such consideration has an effect on sales, 21 stores are chosen. Red color papers are sent 7 of them, green color papers are sent 9 of them, and blue color papers are sent to the remaining 5. After a few days, a check is made on the number of sales in each store. The results are shown below

Red	Green	Blue

At the 5% significance level perform a Kruskal-Wallis test of the null hypothesis that the population mean sales levels are identical for three wall paper colors. Also find the p -value.

2. A study was conducted in which samples were selected independently from four populations. The sample size from each population was 21. The data were converted to ranks. The sum of the ranks for the data from each sample is

	Sample A	Sample B	Sample C	Sample D
Sum of ranks

a) State the appropriate null and alternative hypothesis if you wish to determine whether the populations have equal means.

b) At the 2.5% significance level perform a Kruskal-Wallis test.

3. The following summary data have been collected from three samples selected from three populations

Based on these data, what can be concluded about the means for three populations? Apply Kruskal-Wallis test at an .

4. Given the following data:

Group 1	Group 2	Group 3	Group 4

Use the Kruskal-Wallis procedure to test the null hypothesis that the mean values for all four populations are the same. What conclusion should be reached using a significance level of 0.10? Also find the p-value.

5. Suppose as a part of your job you are responsible for installing emergency lighting in a series of buildings. Bids have been received from four manufacturers of battery-operated emergency lights. The costs are about equal, so the decision will be based on the length of time the lights last before failing. A sample of five lights from each manufacturer has been tested, and values (time in hours) recorded for each manufacturer

Type I	Type 2	Type 3	Type 4

Using , what conclusion should you reach about the mean length of time the lights last before failing for the four manufacturers? Explain.

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