Given the following data:

Group 1 Group 2 Group 3 Group 4 20 28 17 21 27 26 15 23 26 21 18 19 22 29 20 17 25 30 14 20 30 25 23

a. State the appropriate null and alternative hypotheses for determining whether a difference exists in the median value for the four populations.

b. Based on the sample data, use the Kruskal–Wallis one-way ANOVA procedure to test the null hypothesis. What conclusion should be reached using a significance level of 0.10? Discuss.

c. Determine the H-value adjusted for ties.

d. Given the results in part

b, is it necessary to use the H-value adjusted for ties? If it is, conduct the hypothesis test using this adjusted value of H.
If not, explain why not.