Problem 3

When the background music tempo was slow, the mean amount of bar purchases for a sample of 20 restaurant patrons was $30.41 with a standard deviation of $15.90. When the background music tempo was fast, the mean amount of bar purchases for a sample of 15 patrons in the same restaurant was $21.32 with a standard deviation of $9.90. Assuming equal variances, at a = 0.01, is the true mean higher when the music is slow? Let sample 1 represent the slow tempo and sample 2 represent the fast tempo. (a-1) Choose the appropriate hypotheses. a. Ho: #1 - 12 5 0 vs. H1: M1 -uz > 0. Reject Ho if tsaks > 2.445 b. Ho: #1 - 12 5 0 vs. H1: u1 - 12 > 0. Reject Ho if taxis -2.445 a b (a-2) Calculate the teats (Round your answer to 3 decimal places.) (a-3) Based on the t-value determined, choose the correct decision. Fail to reject the null hypothesis Reject the null hypothesis (a-4) Is the true mean higher when the music is slow? Yes O No (b) Calculate the p-value using Excel. (Round your answer to 4 decimal places.) p-value