A 7,000-seat theater is interested in determining whether there is a difference in attendance between shows on Tuesday evening and those on Wednesday evening. Two independent samples of 25 weeks are collected for Tuesday and Wednesday. The mean attendance on Tuesday evening is calculated as 5,500, while the mean attendance on Wednesday evening is calculated as 5,850. The known population standard deviation for attendance on Tuesday evening is 550 and the known population standard deviation for attendance on Wednesday evening is 445. Which of the following is the value of the appropriate test statistic? A) z = -2.4736 B) z = 2.4736 C) t_df= -2.4736 D) t_df= 2.4736

Question

Quizplus · Accepted Answer

The correct test statistic is a z-test because the population standard deviations are known. The formula for the z-test statistic in comparing two means is $z = \frac{(\bar{x}_1 - \bar{x}_2)}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}}$. Plugging in the given values, the negative result indicates that the mean attendance on Tuesday is less than on Wednesday, which corresponds to option A.

A 7,000-Seat Theater Is Interested in Determining Whether There Is