Suppose we are planning to study gestational ages of children born in Atlanta, Georgia. If the mean gestational age in Atlanta is \"Atlanta, then we want to test the null hypothesis H0: [.1 Atlanta = 280 against the two-sided alternative H1: \"Atlanta at 280 at the 0.05 level, and to have 90% power to detect a difference of 7 days. Assume that the standard deviation of the gestational ages is 15.2 and the ages are normally distributed. What sample size is required? [Note that if Z is standard normal, then Pr(Z>l .28)=0. 10, Pr(Z>1.645)=0.05, and Pr(Z>l .96)=0.025.]