Chapter 15, Problem 19CP

Telephone holding times In Exercise 15.8, the telephone holding times for Muzak and classical music were

Muzak 0, 1, 4, 6, 3

Classical 13, 9, 8, 15, 7

1. a. For comparing these two groups with the Wilcoxon test, report the ranks and the mean rank for each group.
2. b. Two groups of size 5 each have 252 possible allocations of rankings. For a two-sided test of H₀: identical distributions with these data, explain why the P-value is 2/252 = 0.008. Interpret the P-value.

15.8 How long do you tolerate being put on hold?

Examples 1–4 and 7 in Chapter 14 referred to the following randomized experiment: An airline analyzed whether telephone callers to their reservations office would remain on hold longer, on average, if they heard (a) an advertisement about the airline, (b) Muzak, or (c) classical music. For 15 callers randomly assigned to these three conditions, the table shows the data. It also shows the ranks for the 15 observations as well as the mean rank for each group and some results from using MINITAB to conduct the Kruskal-Wallis test.

1. a. State the null and alternative hypotheses for the Kruskal-Wallis test.
2. b. Identify the value of the test statistic for the Kruskal-Wallis test and state its approximate sampling distribution, presuming H₀ is true.
3. c. Report and interpret the P-value shown for the Kruskal-Wallis test.
4. d. To find out which pairs of groups significantly differ, how could you follow up the Kruskal-Wallis test?

Telephone holding times by type of recorded message

Kruskal-Wallis Test: Holding Time Versus Group

H = 7.38 DF = 2 P = 0.025 (adjusted for ties)