Question

A large software company gives job applicants a test of programming ability and the mean for the test has been 160 in the past. Twenty-five job applicants are selected from one large university and they produce a mean score and standard deviation of 183 and 12, respectively. Use a 0.05 level of significance to test the claim that this sample comes from a population with a mean score greater than 160.

Answer 1

H0: = 160

Ha: > 160

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 183 - 160 ) / ( 12 / √(25) )
t = 9.58

Test Criteria :-
Reject null hypothesis if t > t(α, n-1)
Critical value t(α, n-1) = t(0.05 , 25-1) = 1.711
t > t(α, n-1) = 9.5833 > 1.711
Result :- Reject null hypothesis

Conclusion -

We have sufficient evidence to support the claim that population mean score is greater than 160.