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 $15.50. When the background music tempo was fast, the mean amount of bar purchases for a sample of 13 patrons in the same restaurant was $20.65 with a standard deviation of $9.90.
Assuming equal variances, at α = 0.10, is the true mean higher when the music is slow?
(a-1) Choose the appropriate hypotheses.
H0: μ1 − μ2 ≤ 0 vs. H1: μ1 − μ2 > 0. Reject H0 if tcalc > 1.309H0: μ1 − μ2 ≤ 0 vs. H1: μ1 − μ2 > 0. Reject H0 if tcalc < 1.309H0: μ1 − μ2 ≥ 0 vs. H1: μ1 − μ2 < 0. Reject H0 if tcalc < −1.309H0: μ1 − μ2 ≥ 0 vs. H1: μ1 − μ2 < 0. Reject H0 if tcalc > −1.309
multiple choice 1
a
b
c
d
(a-2) Calculate the tcalc.
Note: Round your answer to 3 decimal places.
(a-3) Based on the t-value determined, choose the correct decision.
multiple choice 2
Reject the null hypothesis
Fail to reject the null hypothesis
(a-4) Is the true mean higher when the music is slow?
multiple choice 3
No
Yes
(b) Calculate the p-value using Excel.
Note: Round your answer to 4 decimal places.