Question

4- (14%) A random sample of 10 yields a mean and standard deviation, respectively, of 80 and 7.9. Does this sample confirm that the population mean is greater than 78 with 95% confidence level?

Answer 1

H0: $\mu$ = 78

Ha: $\mu$ > 78

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 80 - 78 ) / ( 7.9 / √(10) )
t = 0.80

Test Criteria :-
Reject null hypothesis if t > t(α, n-1)
Critical value t(α, n-1) = t(0.05 , 10-1) = 1.833
t > t(α, n-1) = 0.80 < 1.833
Result :- Fail to reject null hypothesis

We do not have sufficient evidence to support the claim that population mean is

greater than 78.