The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club.She would now like to determine whether or not the mean age of her customers is greater than 30.If so,she plans to alter the entertainment to appeal to an older crowd.If not,no entertainment changes will be made.Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years.
-If she wants to have a level of significance at 0.01,what decision should she make?

Question

Quizplus · Accepted Answer

We need to conduct a one-sample t-test with the following hypotheses: H0: μ ≤ 30 (The population mean age is less than or equal to 30) Ha: μ > 30 (The population mean age is greater than 30) Using a t-test with a level of significance at 0.01 and 249 degrees of freedom (df = n-1), we find the t-critical value to be 2.492. The t-statistic for our sample is (30.45-30)/(5/sqrt(250)) = 1.767. Since our t-statistic is not greater than the t-critical value, we fail to reject the null hypothesis. We do not have enough evidence to suggest that the mean age of the club's customers is greater than 30. Therefore, the owner should not alter the entertainment to appeal to an older crowd. The best choice is B, fail to reject H₀.

The Owner of a Local Nightclub Has Recently Surveyed a Random