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=77​, x=35.8 ​years, and s=11.5 years. Use a 0.01 significance level to test the claim that the mean age of actresses when they win an acting award is 33 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. Fail to reject H0. There is insufficient evidence to warrant rejection of the claim that the mean age of actresses when they win an acting award is 33 years.

B. Fail to reject H0. There is sufficient evidence to warrant rejection of the claim that the mean age of actresses when they win an acting award is 33 years.

C. tReject H0. There is sufficient evidence to warrant rejection of the claim that the mean age of actresses when they win an acting award is 33 years.

D. Reject H0. There is insufficient evidence to warrant rejection of the claim that the mean age of actresses when they win an acting award is 33 years.

Answer 1

As we are testing here whether the mean age of actresses when they win an acting award is 33 years, therefore the null and the alternative hypothesis here are given as:

The test statistic here is computed as:

Therefore 2.137 is the test statistic value here.

As this is a two tailed test, for n - 1 = 76 degrees of freedom, we get the p-value from the t distribution tables here as:

p = 2P( t76 > 2.137) = 2*0.0179 = 0.0358

therefore 0.0358 is the required p-value here.

As the p-value here is 0.0358 > 0.01 which is the level of significance, therefore the test is not significant and we cannot reject the null hypothesis here. There is insufficient evidence to warrant rejection of the claim that the mean age of actresses when they win an acting award is 33 years.