Question

Suppose that 88% of college men and 84% of college women were employed last summer. A sample survey interviewed SRSs of 400 college men and 400 college women. The two samples were independent.

a) What is the approximate distribution of the proportion pF of women who worked last summer? What is the approximate distribution of the proportion pM of men who worked?

b) The survey wants to compare men and women. What is the approximate distribution of the difference in the proportions who worked, pM - pF?

c) What is the probability that in the sample a higher proportion of women than men worked last summer?

Answer 1

approximate distribution of walked last proportion pf of Women summer is who Pf – proportion of women = 84% =0.84 10.84*(1-0.84) N ( 0.84, JP (1-1) ) =(-4, fosta lors) O 400 N/0084, 0.0183) PM - proportion of men Ilm+ (1-Pm) | = 88% = 0.88 1088*(1-0.88) 0.88 400 M N/0.68, 0.0162)

(b) PM-PE =) difference in proportions IP * (1-P) I IP * (1-P) Vn 8.88*(1-0.88) 1 2 10.84* (1-0.84) 400 400 N (0.88-0-84), ( N(0.04 0.0245)

probability that in Sample higher proportion of last sunpr. coomen that men worked as P (PM-P<o) - p/ PM - PE - (Pm - 1 рн, 0 -0.04 0.0245 -0.04 0.0245 P(za - 1063) -0.0511