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 conclusion can she make?
A) There is sufficient evidence that the mean age of her customers is not over 30.
B) There is not sufficient evidence that the mean age of her customers is not over 30.
C) There is not sufficient evidence that the mean age of her customers is over 30.
D) There is sufficient evidence that the mean age of her customers is over 30.

Question

Quizplus · Accepted Answer

We need to perform a one-sample t-test using the given information. The null hypothesis is that the mean age of customers is 30 or less, and the alternative hypothesis is that the mean age is greater than 30. The level of significance is 0.01, which means we will reject the null hypothesis if the p-value is less than 0.01.

The test statistic is calculated as:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(n))
t = (30.45 - 30) / (5 / sqrt(250))
t = 1.87

Using a t-distribution table with 249 degrees of freedom (df = n-1), we find that the p-value for a two-tailed test (since the alternative hypothesis is not directional) is approximately 0.062. Since this p-value is greater than the level of significance of 0.01, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the mean age of customers is over 30. The correct answer is C.

The Owner of a Local Nightclub Has Recently Surveyed a Random