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^H0 ^if^t^{^2.5758.

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^H0 ^if^t^{< -}^2.3263. B)^Reject^H0 ^if^t^{< -}^2.5758. C)^Reject^H0 ^if^t^>^2.3263. D)^Reject^H0 ^if^t^>^2.5758.

Quizplus · Accepted Answer

The null hypothesis is that the mean age of the customers is equal to 30, whereas the alternative hypothesis is that it is greater than 30. Since we want a level of significance at 0.01, we need to use a critical t-value with 249 degrees of freedom (250-1) and a one-tailed test. Using a t-table or calculator, we can find that the critical t-value is 2.3263 (or approximately 2.33) at a 0.01 level of significance.

Since we are testing whether the mean age is greater than 30, the rejection region should be in the upper tail of the t-distribution. Therefore, we reject the null hypothesis if the calculated t-statistic is greater than the critical t-value of 2.3263. The answer is choice C, which specifies the rejection region as t > 2.3263.

The Owner of a Local Nightclub Has Recently Surveyed a Random