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​, xequals35.9 ​years, and sequals11.3 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.

Answer 1

n = 75

S = 11.3

claim : mean age of actresses when they win an acting award is 34 years.

Null and alternative hypothesis is

H0 : u = 34

H1 : u ≠ 34

Level of significance = 0.05

Here population standard deviation is not known so we use t-test statistic.

Test statistic is

Degrees of freedom = n - 1 = 75-1=74

P-value = 0.1496 ( using t table)

P-value , Failed to Reject H0

conclusion : There is sufficient evidence to conclude that the mean age of actresses when they win an acting award is 34 years.