SUPP 3.4.About 22% of a population takes multivitamins. Our study has 10,000 participants from this population. In our study we compute phat== proportion in sample who take multivitamins.

a) Compute E(X)= and Var(X)=², and explain them in words.

b) How is phat distributed (shape, mean, standard deviation . . .)?

c) If you found that phat = 0.24, would you be surprised with how large this value is? (Compute the P(phat>0.24), and comment on whether the probability is "small," which means it is an unusual event.) This is foreshadowing of p-values.