Question

You will perform a significance test of H_o : μ=25 based on an SRS of n=36. Assume σ=5.

A.) If x̅=27, what is the test statistic of z?

B.) What is the P-value if H_a : μ>25?

C.) What if the P-value if H_a : μ≠25?

D.) Combining part A and B, is there enough evidence to reject the null hypothesis? Make sure your answer is stated using the correct language.

Answer 1

Part a)

Test Statistic :-


Z = 2.4

Part b)

P ( Z > 2.4 ) = 1 - P ( Z < 2.4 ) = 0.0082

Part c)

P ( Z > 2.4 ) = 2 * ( 1 - P ( Z < 2.4 ) ) = 2 * 0.0082 = 0.0164

Part d)

Decision based on P value
P - value = P ( Z > 2.4 ) = 0.0082
Reject null hypothesis if P value < level of significance
P - value = 0.0082 < 0.05 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

There is sufficient evidence to reject the null hypothesis.