Suppose that the (unknown) probability that a woman is left-handed isp1and the (unknown) probability that a man is left-handed isp2.We sample 400 women and find that 80 are left-handed. We also sample 200 men and find that 32 are left-handed.

1. (a)Construct a 95% confidence interval forp1p2. (5 points)
2. (b)ConsiderH0:p1p2= 0 v.s.H1:p1p2= 0. Please apply the result in (a) to conduct the
3. hypothesis testing. (5 points)
4. (c)ConsiderH0:p1p2= 0 v.s.H1:p1p2= 0 and set the level of significance at 0.05.Conduct the
5. hypothesis testing with thep-value approach. Does your conclusion agree with (b)?(5 points)