Question

assume a normal distribution and use a hypothesis test to test the given claim.
according to city reports, it was found that the mean age of the prison population in the city was 26 years. marc wants to test the claim that
the mean age of the prison population in his city is less than 26 years. he obtains a random sample of 25 prisoners and finds a mean age of
24.4 years and a standard deviation of 9.2 years. at a significance level of 0.05, what should his conclusion be?
note: the p - value = 0.1966.
do not reject the null hypothesis. there is not sufficient evidence that the mean age is less than 26 years.
reject the null hypothesis. the evidence suggests that the mean age is less than 26 years.
there is not enough information to perform the test.
do not reject the null hypothesis. there is not sufficient evidence that the mean age is less than 24.4 years.
reject the null hypothesis. there is sufficient evidence that the mean age is less than 24.4 years.

Explanation:

Step1: Compare p - value and significance level

In hypothesis testing, if the p - value ($p = 0.1966$) is greater than the significance level ($\alpha=0.05$), we do not reject the null hypothesis.

Answer:

Do not reject the null hypothesis. There is not sufficient evidence that the mean age is less than 26 years.