Refer to the International Journal of Obesity (Jan. 2007) study of the physiological changes that accompany laughter, presented in Exercise. Recall that pairs of subjects watched film clips designed to evoke laughter. In addition to heart rate, the researchers measured the duration of laughter (seconds per minute) and the energy expenditure (kilojoules per minute) of each pair during the laughing period. The subject pairs were then divided into four groups (quartiles)-0-5, 6 10, 10-20, and more than 20 seconds per minute-on the basis of duration of laughter. The energy expenditure values for the 45 subject pairs in the study are shown in the next table and saved in the LAUGHTER file. (The data are simulated on the basis of reported summary statistics.) The researchers compared the energy expenditure distributions across the four laughter duration groups by means of the Kruskal Wallis test.

a. State H0 and Ha for the desired test of hypothesis.
b. Find the rejection region for the test, using a = .10.
c. Compute the value of the test statistic.
d. On the basis of the results from parts b and c , what is the appropriate conclusion?
e. Compare the 0-5 and 7 20 quartile groups, using the Wilcoxon rank sum test. What do you infer about the relationship between energy expenditure and duration of laughter?
f. Demonstrate why the researchers employed a nonpara metric test on the data.

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