An opinion poll asks a sample of 500 adults (a SRS) whether they favor giving parents of school-age children vouchers that can be exchanged for education at any public or private school of their choice. Each school would be paid by the government on the basis of how many vouchers it collected. Suppose that in fact 45% of the population favor this idea.
a.) What is the mean of the sampling distribution of p-hat, the proportion of adults in samples of 500 who favor giving parents of school-age children these vouchers?
b.) What is the standard deviation of p-hat?
c.) Explain why you can use the formula for the standard deviation of p-hat in this setting.
d.) Check that you can use the normal approximation for the distribution of p-hat.
e.) What is the probability that more than half of the samples are in favor?