Scenario #8: Retirement Topic: Two sample z-test for a difference in population proportions The Employee Benefit Research Institute reports that 27% of males anticipate having enough money to live comfortably in retirement, but only 18% of females express that confidence. If these results were based on random samples of 250 people of each gender, would you consider this strong evidence that men are more likely to anticipate having enough money for retirement than women? (Bock, Vellerman, Deveaux, p. 435) a) Test the hypotheses Ho : P, - P2 =0 versus H. : P, - P> > 0 where p, = the true proportion of males who anticipate having enough money for retirement and P, = the true proportion of females who anticipate having enough money for retirement. b) In the context of this situation, describe Type I and Type II errors and describe the consequences of each of these