An economic researcher wants to know whether he can reject the null hypothesis, at the 10% significance level, that no more than 20% of the households in Pennsylvania make more than $70,000 per year.
a. If 200 Pennsylvania households are chosen at random, how many of them would have to be earning more than $70,000 per year to allow the researcher to reject the null hypothesis?
b. Assuming that the true proportion of all Pennsylvania households with annual incomes of at least $70,000 is 0.217, find the probability of not rejecting a false null hypothesis when the sample size is 200.