Question

Identify the null and alternative hypothesis(in symbolic and sentence form), test statistic, P-value(or critical values), conclusion about the null hypothesis, and final conclusion that addresses the original claim(Don’t just say Reject the null hypothesis or fail to reject the null hypothesis). If you used the calculator, identify everything mentioned above in addition to which calculator functions and inputs for each field were used. Test the claim that the mean age of the prison population in one city is less than 26 years. Sample data are summarized as n=25,x ̅=24.4,and s=9.2. Use a significance level of α=0.05.

Answer 1

The claim is that the mean age of the prison population in one city is less than 26 years.

Thus based on the claim the hypotheses are:

Null Hypothesis

The population mean is equal to 26

Alternate hypothesis

The Population mean is less than 26 years, this is the claim

Based on the hypothesis it will be a left-tailed test.

Given the Sample data are summarized as sample size n=25, sample mean x ̅=24.4,and sample standard deviation s=9.2. Use a significance level of α=0.05.

Since population standard deviation is unknown and the sample size is less than 30 hence t-distribution is applicable, thus the degree of freedom is used which is calculated as df = n-1= 25-1 = 24.

Rejection region:

Based on the type of hypothesis and given significance level the critical score for rejection region is calculated using the excel formula for t-distribution which is =T.INV(0.05, 24), thus the tc is computed as -1.71.

Thus reject Ho if t < tc, or reject Ho if P-value is less than 0.05.

Test statistic:

P-value:

The P-value is calculated using the excel formula for t-distribution which is =T.DIST(-0.87, 24, TRUE), thus the P-value is computed as 0.1966.

Conclusion:

Since the P-value is greater than 0.05 and the test statistic is greater than tc hence we fail to reject the null hypotheiss and conclude that there is insufficient evidence to support the claim that the mean age of the prison population in one city is less than 26 years.

NOTE: Feel free to ask if query remains.