Question

A professor gives his class a final examination that he knows from years of experience yields a population mean of 84. His present class of 24 obtains a mean of 88 and a standard deviation of 8. Is he correct in assuming that the performance of the most recent class differs significantly from that of other classes? Use a one-tailed test here since the professor assumes that the class will score higher.

1. Null hypothesis:
2. Alternative hypothesis:
3. Statistical test:
4. Significance level (I'll pick it for you; alpha = .05)
5. Critical region for rejecting null hypothesis:
6. Calculate the statistic (please show your work):
7. Decision:

Answer 1

To Test :-

H0 :-  $\mu = 84$

H1 :-  $\mu > 84$

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 88 - 84 ) / ( 8 / √(24) )
t = 2.4495

Test Criteria :-
Reject null hypothesis if t > t(α, n-1)

Critical Region t(α, n-1) = t(0.05 , 24-1) = 1.714

t > t(α, n-1) = 2.4495 > 1.714
Result :- Reject null hypothesis

Decision based on P value
P - value = P ( t > 2.4495 ) = 0.0112
Reject null hypothesis if P value < α = 0.05 level of significance
P - value = 0.0112 < 0.05 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

There is sufficient evidence to support the claim that the professor assumes that the class will score higher.