Question

The Committee of Income in Africa conducted a contest for promotion. Of the 23 unsuccessful applicants, the mean age was 39.2 years with a standard deviation of 5.9. Of the 22 successful applicants, the mean age was 34 years with a standard deviation of 9.3. Test the claim that the unsuccessful applicants are from a population with a different than the mean age of successful applicants at the 0.05 significance level.

Claim:

Opposite:

The test is:

The test statistic is: t=

the P-Value:

Based on this we?

Conclusion?

Answer 1

To Test :-

H0 :- µ1 = µ2
H1 :- µ1 ≠ µ2

It is two tailed test

Test Statistic :-

t = (X1 - X2)/(${/n1)+(S3/12)

t = 2.23

P value = 2 * P ( t > 2.23 ) = 0.0324

Reject null hypothesis if P value < α = 0.05 level of significance
P - value = 0.0324 < 0.05, hence we reject null hypothesis
Conclusion :- Reject null hypothesis

There is sufficient evidence to support the claim that the unsuccessful applicants are from a population with a different than the mean age of successful applicants.