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
39	47
44	50
40	51
40	53
45	48

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

a.	H0: μ1 – μ2 ≥ 0 vs. H1: μ1 – μ2 < 0
b.	H0: μ1 – μ2 = 0 vs. H1: μ1 – μ2 ≠ 0
c.	H0: μ1 – μ2 ≤ 0 vs. H1: μ1 – μ2 > 0
	a b c

(a-2)	At α = 0.05, what is the decision rule? Assume equal variances.

a.	Reject the null hypothesis if tcalc > –1.86 (8 d.f.)
b.	Reject the null hypothesis if tcalc < –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

(a-4)

At α = .05, is the mean sound level reduced?

(Click to select)  Reject / Do not reject  H0, the mean  (Click to select)  has been / has not been  reduced.?

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

a.	H0: σ12 / σ22 = 1vs. H1: σ12 / σ22 ≠ 1.
b.	H0: σ12 / σ22 ≠ 1vs. H1: σ12 / σ22 = 1.
	a b

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

a.	Reject H0 if Fcalc < 9.60 or Fcalc > .1042. (d.f.1 = 4, d.f.2 = 4.)
b.	Reject H0 if Fcalc > 9.60 or Fcalc < .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)  Reject / Do not reject  H0, the variance  (Click to select)  has / has not  been changed.?

Answer 1