Researchers at the Mayo Clinic have studied the effect of sound levels on patient healing and have found a significant association (louder hospital ambient sound level is associated with slower postsurgical healing). Based on the Mayo Clinic's experience, Ardmore Hospital installed a new vinyl flooring that is supposed to reduce the mean sound level (decibels) in the hospital corridors. The sound level is measured at five randomly selected times in the main corridor.

New Flooring	Old Flooring
37	53
38	45
45	48
39	50
44	49

(a-1) Does the evidence convince you that the mean sound level has been reduced? Select the appropriate hypotheses.

a. H₀: _{1 2} 0 vs. H₁: _{1 2} < 0

b. H₀: _{1 2} = 0 vs. H₁: _{1 2} 0

c. H₀: _{1 2} 0 vs. H₁: _{1 2} > 0 (a-2) At = .05, what is the decision rule? Assume equal variances.

a. Reject the null hypothesis if t_calc > 1.86 (8 d.f.)

b. Reject the null hypothesis if t_calc < 1.86 (8 d.f.) (a-3) Calculate the test statistic. test statistic= (a-4) At = .05, is the mean sound level reduced?

yes / no (b-1) At = .05, has the variance changed? Choose the correct hypothesis.

a. H₀: ₁² / ₂² = 1vs. H₁: ₁² / ₂² 1.

b. H₀: ₁² / ₂² 1vs. H₁: ₁² / ₂² = 1. (b-2) At = .05, what is the decision rule?

a. Reject H₀ if F_calc < 9.60 or F_calc > .1042. (d.f.₁ = 4, d.f.₂ = 4.)

b. Reject H₀ if F_calc > 9.60 or F_calc < .1042. (d.f.₁ = 4, d.f.₂ = 4.) (b-3) What is the test statistic? test statistic= (b-4) At = .05, has the variance changed? yes/no