Question

III. Proof of assertion regarding a mean: σ unknown

1. In a promotions contest in Ireland, the ages of unsuccessful applicants and those who succeeded in obtaining the promotion were studied. For unsuccessful applicants, a sample of 23 was used, which reflected an average age of 47 and a standard deviation of 7.2. The sample of them succeeded, showed an average of 43.9, with a standard deviation of 5.9, in 30 cases analyzed. It uses a .05 level of significance to test the assertion that unsuccessful applicants come from a larger average population than that of successful applicants.

Answer 1

µ1 :- Average population of unsuccessful applicants

µ2 :- Average population of successful applicants

To Test :-
H0 :- µ1 = µ2
H1 :- µ1 > µ2

Test Statistic :-


t = 1.6777

Test Criteria :-
Reject null hypothesis if t > t(α, DF)


DF = 42
t(α, DF) = t( 0.05 , 42 ) = 1.682
t > t(α, DF) = 1.6777 < 1.682
Result :- Fail to Reject Null Hypothesis

Decision based on P value
P - value = P ( t > 1.6777 ) = 0.0504
Reject null hypothesis if P value < α level of significance
P - value = 0.0504 > 0.05 ,hence we fail to reject null hypothesis
Conclusion :- Fail to Reject Null Hypothesis

There is insufficient evidence to support the claim that unsuccessful applicants come from a larger average population than that of successful applicants.