In an experiment involving 800 subjects, each subject received either treatment I or treatment II, and each subject was classified into one of the following four categories: older males, younger males, older females, and younger females. At the end of the experiment, it was determined for each subject whether the treatment that the subject had received was helpful or not. The results for each of the four categories of subjects are given in Table 10.31.
a. Show that treatment II is more helpful than treatment I within each of the four categories of subjects.
b. Show that if these four categories are aggregated into only the two categories, older subjects and younger subjects, then treatment I is more helpful than treatment II within each of these categories.
c. Show that if the two categories in part (b) are aggregated into a single category containing all 800 subjects, then treatment II again appears to be more helpful than treatment I.
Table 10.31 Data for Exercise 7

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Helpfu Not 120 10 Older males Treatment I Treatment II Younger males Treatment I Treatment II 120 20 60 40 10 Older females Treatment I Treatment II Younger females Treatment I Treatment II 10 50 20 50 10 10 160 90