Question

Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic, P-value, critical value(s), and state the final conclusion.

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 bar= 24.4 years, and s = 9.2 years. Use a significance level of α = 0.01. Select the corresponding P-value and final conclusion

Answer 1

The test statistic value is equal to sample mean minus population mean divided by the standard deviation upon square root of sample size, so that will be equal to (24.4 - 26) / (9.2 / sqrt(25)) = -0.871. The corresponding P-value is 0.1942. The critical value(s) can be found using a t-distribution table with degrees of freedom n-1=24 and a significance level of α = 0.011. The critical value for a left-tailed test is -2.4921. Since the test statistic value (-0.87) is greater than the critical value (-2.492), we fail to reject the null hypothesis that the mean age of the prison population in one city is less than 26 years34. Therefore, there is not enough evidence to claim that the mean age of the prison population in one city is less than 26 years

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Explanation: