Question

According to the Current Population Survey by the Bureau of the Census, men with a bachelor’s degree earn an average of $46,700. A random sample of 42 women with a bachelor’s degree shows average earnings of $38,700 with a standard deviation of $12,500. Is there sufficient evidence to suggest that the average earnings of women with a bachelor’s degree are less than the average earnings of men with a bachelor’s degree?

Answer 1

To Test :-

H0 :- µ = 46700
H1 :- µ < 46700

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 38700 - 46700 ) / ( 12500 / √(42) )
t = -4.1477

Test Criteria :-
Reject null hypothesis if t < -t(α, n-1)
Critical value t(α, n-1) = t(0.05 , 42-1) = 1.683
t < - t(α, n-1) = -4.1477 < - 1.683
Result :- Reject null hypothesis

There is sufficient evidence to support the claim that the average earnings of women with a bachelor’s degree are less than the average earnings of men with a bachelor’s degree.