A survey of footwear preferences of a random sample of 100 undergraduate students (50 females and 50 males) from a large university resulted in the following data.

(a) Let pi, i = 1, 2, 3, 4, 5, represent the respective true proportions of students with a particular footwear preference, and let
H0: p1 = 0:20; p2 = 0:20; p3 = 0:30; p4 = 0:20; p5 = 0:10
versus
Ha: At least one of the probabilities is different from the hypothesized value: Test this hypothesis using a = 0.05.
(b) Test the hypothesis that the choice of footwear by undergraduate students in this university is independent of their gender, using a = 0.05.

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Boots Leather shoes Sneakers Sandals Other Female 12 Male 12 17 10 10 12 4