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.If she wants to have a level of significance at 0.01, what rejection region should she use?

Question

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.If she wants to have a level of significance at 0.01, what rejection region should she use? A) Reject $H _ { 0 } \text { if } t < - 2.3263 \text {. }$ B) Reject $H _ { 0 } \text { if } t < - 2.5758$ C) Reject $H _ { 0 } \text { if } t > 2.3263 \text {. }$ D) Reject $H _ { 0 } \text { if } t > 2.5758$

Quizplus · Accepted Answer

The owner is testing if the mean age is greater than 30, which is a one-tailed test. For a significance level of 0.01 and a one-tailed test, the critical value from the t-distribution table (or z-table for large sample sizes like n=250) is approximately 2.3263. Therefore, the rejection region is for t-values greater than this critical value, indicating that the mean age is significantly greater than 30.

The Owner of a Local Nightclub Has Recently Surveyed a Random