The Spike network commissioned a telephone poll of randomly sampled U.S. men. Of the 712 respondents who had children, 22% said yes to the question Are you a stay-at-home dad? (Time, August 23, 2004)
a) To help market commercial time, Spike wants an accurate estimate of the true percentage of stay-at-home dads. Construct a 95% confidence interval.
b) An advertiser of baby-carrying slings for dads will buy commercial time if at least 25% of men are stayat-home dads. Use your confidence interval to test an appropriate hypothesis, and make a recommendation to the advertiser.
c) Could Spike claim to the advertiser that it is possible that 25% of men with young children are stay-at-home dads? What is wrong with the reasoning?