Question

600 men and 750 women are polled as to whether power in a member of the opposite sex is attractive to them with 196 of the men and 448 of the women replying in the affirmative. To a 1% level of significance, can it be asserted that, in general, a smaller percentage of men than women find power in a member of the opposite sex attractive?

Answer 1

Sample 1:

n1 = 600, x1 = 196

p̂1 = x1/n1 = 0.3267

Sample 2:

n2 = 750, x2 = 448

p̂2 = x2/n2 = 0.5973

α = 0.01

Null and Alternative hypothesis:

Ho : p1 = p2

H1 : p1 < p2

Pooled proportion:

p̄ = (x1+x2)/(n1+n2) = (196+448)/(600+750) = 0.477037

Test statistic:

z = (p̂1 - p̂2)/√ [p̄*(1-p̄)*(1/n1+1/n2)] = (0.3267 - 0.5973)/√[0.477*0.523*(1/600+1/750)] = -9.8938

p-value = NORM.S.DIST(-9.8938, 1) = 0.0000

Decision:

p-value < α, Reject the null hypothesis

Conclusion:

There is enough evidence to conclude that smaller percentage of men than women find power in a member of the opposite sex attractive at 0.01 significance level.