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 origina The ages of actresses when they won an acting award is summarized by the statistics n = 80, x = 35.9 years, and s = 11.6 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. O A. Ho: 734 years H: = 34 years OB. Ho u = 34 years Hu<34 years OC. Ho u = 34 years H:#34 years OD. Ho u = 34 years Hu2 34 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.)

Answer 1

The null and alternative hypothesis is ,

$H_0:\mu=34$ years

$H_a:\mu\neq 34$ years

The test is two-tailed test.

The test statistic is ,

$t_{stat}=\frac{\bar{X}-\mu_0}{s/\sqrt{n}}=\frac{35.9-34}{11.6/\sqrt{80}}=1.465$

Now , df=degrees of freedom=n-1=80-1=79

The p-value is ,

p-value=$P(t_{df}>|t_{stat}|)=P(t_{79}>1.465)=0.1469$ ; The Excel function is , =TDIST(1.465,79,2)

Decision : Here , p-value>0.05

Therefore , fail to reject the null hypothesis.

Conclusion :

A. 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 34 years.