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 nequals75?, xequals35.6 ?years, and sequals11.6 years. Use a 0.05 significance level to test the claim that the mean age of actresses when they win an acting award is 34 years. What are the? hypotheses? A. Upper H 0?: muequals34 years Upper H 1?: muless than34 years B. Upper H 0?: muequals34 years Upper H 1?: munot equals34 years C. Upper H 0?: muequals34 years Upper H 1?: mugreater than or equals34 years D. Upper H 0?: munot equals34 years Upper H 1?: muequals34 years identify the test statistic? identify the p value? state the final conclusion? what do the results suggest?

Answer 1

Let denotes the mean age of actresses when they win an acting award.

To test against

Given

sample mean

sample standard deviation

and sample size

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 5% level of significance if P-value < 0.05

Now,

The value of the test statistic

P-value

Since P-value = 0.23609 > 0.05, so we fail to reject H₀ at 5% level of significance and we can conclude that the mean age of actresses when they win an acting award is not signficantly different from 34 years