In a study of preening behavior in the fruitfly Drosophila melanogaster, a single experimental fly was observed for 3 minutes while in a chamber with 10 other flies of the same sex. The observer recorded the timing of each episode ("bout") of preening by the experimental fly. This experiment was replicated 15 times with male flies and 15 times with female flies (different flies each time). One question of interest was whether there is a sex difference in preening behavior. The observed preening times (average time per bout, in seconds) were as follows:

(a) For these data, the value of the Wilcoxon-Mann-Whitney statistic is Us = 189.5. Use a Wilcoxon-Mann-Whitney test to investigate the sex difference in preening behavior. Let HA be nondirectional and let α = 0.01.
(b) For these data, the standard error of (1 - 2) is SE = 0.7933 sec. Use a t test to investigate the sex difference in preening behavior. Let HA be non-directional and let α = 0.01.
(c) What condition is required for the validity of the t test but not for the Wilcoxon-Mann-Whitney test? What feature or features of the data suggest that this condition may not hold in this case?
(d) Verify the value of Us given in part (a).

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Male: 1.2, 1.2, 1.3, 1.9, 1.9, 2.0, 2.1, 2.2, 2.2, 2.3, 2.3, 2.4, 2.7, 2.9, 3.3 У 2.127 s 0.5936 Female: 2.0, 2.2, 2.4, 2.4, 2.4, 2.8, 2.8, 2.8, 2.9, 3.2, 3.7, 4.0, 5.4, 10.7, 11.7 у 4.093 s:: 3.014