Question

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	45
37	48
45	46
45	46
42	47

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

1. H₀: μ₁ – μ₂ ≥ 0 vs. H₁: μ₁ – μ₂ < 0
2. H₀: μ₁ – μ₂ = 0 vs. H₁: μ₁ – μ₂ ≠ 0
3. H₀: μ₁ – μ₂ ≤ 0 vs. H₁: μ₁ – μ₂ > 0

• a

• b

• c

(a-2) At α = .05, what is the decision rule? Assume equal variances.

1. Reject the null hypothesis if t_calc > –1.86 (8 d.f.)
2. Reject the null hypothesis if t_calc < –1.86 (8 d.f.)

• a

• b

(a-3) Calculate the test statistic. (Round your answer to 4 decimal places. Input the answer as a positive value.)

Test statistic           

(b-1) At α = .05, has the variance changed? Choose the correct hypothesis.

1. H₀: σ₁² / σ₂² = 1vs. H₁: σ₁² / σ₂² ≠ 1.
2. H₀: σ₁² / σ₂² ≠ 1vs. H₁: σ₁² / σ₂² = 1.

• a

• b

(b-2) At α = .05, what is the decision rule?

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

• a

• b

  
(b-3) What is the test statistic? (Round the test statistic value to 4 decimal places.)

Test statistic           

(b-4) At α = .05, has the variance changed?
  
(Click to select)  Do not reject  Reject  H₀, the variance  (Click to select)  has not  has  been changed.

        

Answer 1