When the background music tempo was slow, the mean amount of bar purchases for a sample of 19 restaurant patrons was $30.54 with a standard deviation of $15.10. When the background music tempo was fast, the mean amount of bar purchases for a sample of 12 patrons in the same restaurant was $20.98 with a standard deviation of $9.60.

Assuming equal variances, at α = 0.01, is the true mean higher when the music is slow?

(a-1) Choose the appropriate hypotheses.

1. H₀: μ₁ – μ₂ ≤ 0 vs. H₁: μ₁ – μ₂ > 0. Reject H₀ if t_calc > 2.462
2. H₀: μ₁ – μ₂ ≤ 0 vs. H₁: μ₁ – μ₂ > 0. Reject H₀ if t_calc < 2.462
3. H₀: μ₁ – μ₂ ≥ 0 vs. H₁: μ₁ – μ₂ < 0. Reject H₀ if t_calc < –2.462
4. H₀: μ₁ – μ₂ ≥ 0 vs. H₁: μ₁ – μ₂ < 0. Reject H₀ if t_calc > –2.462

• a

• b

• c

• d

(a-2) Calculate the t_calc. (Round your answer to 3 decimal places.)

t_calc =

(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

• No
  
  (b) Calculate the p-value using Excel. (Round your answer to 4 decimal places.)
  
  p-value =