Question

A survey question of men and women workers asked if they expected to receive a raise or promotion during the upcoming year. Two hundred men and 200 women were sampled. Of the men, 110 said yes but only 90 of the women said yes. Develop the hypotheses and test at 95% confidence to see if the percentage of women expecting to receive a raise or promotion is less than that of the men. What is your conclusion?

Answer 1

P1 :- Proportion of men expecting raise or promotion

P2 :-  Proportion of women expecting raise or promotion

To Test :-

H0 - P1 <= P2

H1 :- P1 > P2

Test Statistic :-

is the pooled estimate of the proportion P
= ( x1 + x2) / ( n1 + n2)
= ( 110 + 90 ) / ( 200 + 200 )
= 0.5

Z = 2

Test Criteria :-
Reject null hypothesis if

= 2 > 1.64, hence we reject the null hypothesis
Conclusion :- We Reject H0

Decision based on P value
P value = P ( Z > 2 )
P value = 0.0228
Reject null hypothesis if P value <
Since P value = 0.0228 < 0.05, hence we reject the null hypothesis
Conclusion :- We Reject H0

There is sufficient evidence to support the claim that the percentage of women expecting to receive a raise or promotion is less than that of the men.