Question

Assume that a simple random sample has been selected and test the given claim. Use the​ P-value method for testing hypotheses. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

The ages of actresses when they won an acting award is summarized by the statistics n= 85​, x= 35.8 years, and s= 11.8 years. Use a 0.01 significance level to test the claim that the mean age of actresses when they win an acting award is 32 years.

Answer 1

x̅ = 35.8, s = 11.8, n = 85

Null and Alternative hypothesis:

Ho : µ = 32 ; H1 : µ ≠ 32

Test statistic:

t = (x̅ - µ)/(s/√n) = (35.8 - 32)/(11.8/√85) = 2.9690

df = n-1 = 84

p-value = T.DIST.2T(ABS(2.969), 84) = 0.0039

Decision:

p-value < α, Reject the null hypothesis.

Conclusion:

There is enough evidence to reject the claim that the mean age of actresses when they win an acting award is 32 years.