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

Kruskal-Wallis Test: Holding Time Versus Group

Telephone holding times by type of recorded message Recorded Message Muzak Advertisement Classical Holding Time Observations Ranks 0,1,3,4. 61,2.5, 5,6,8 1,2, 5,8,1 2.5, 4, 7, 10.5, 13 7.8.9, 13, 15 Mean Rank 4.5 7.4 12.1 9.10.5, 12, 14. 15 Group Muzak advert classical 5 H-7.38 DF# 2 P-0.025 (adjusted for ties) Median 3.000 5.000 9.000 Ave Rank 4.5 7.4 12.1 5