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=78, x=35.4 years, and s=11.5 years. Use a 0.05 significance level to test the claim that the mean age of actresses when they win an acting award is 32 years.

Identify the test statistic.

t=____ ?(Round to three decimal places as? needed.)

Identify the? P-value.

The? P-value is _____ (Round to four decimal places as? needed.)

State the final conclusion that addresses the original claim. Choose the correct answer below.

A. Reject Ho. There is insufficient evidence to warrant rejection of the claim that the mean age of actresses when they win an acting award is 32 years.

B. Reject Ho. There is sufficient evidence to warrant rejection of the claim that the mean age of actresses when they win an acting award is 32 years.

C. Fail to reject Ho. There is sufficient evidence to warrant rejection of the claim that the mean age of actresses when they win an acting award is 32 years.

D. Fail to reject Ho. There is insufficient evidence to warrant rejection of the claim that the mean age of actresses when they win an acting award is 32 years.

Answer 1

The statistical software output for this problem is:

One sample T summary hypothesis test:
? : Mean of population
H₀ : ? = 32
H_A : ? ? 32

Hypothesis test results:

Mean	Sample Mean	Std. Err.	DF	T-Stat	P-value
?	35.4	1.3021186	77	2.6111293	0.0108

Hence,

t = 2.611

P - value = 0.0108

Final conclusion: Reject Ho. There is sufficient evidence to warrant rejection of the claim that the mean age of actresses when they win an acting award is 32 years.

Option B is correct.