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 42 48 41 51 40 44 37 48 44 52 Click here for the Excel Data File (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 multiple choice 1 a b (a-2) At α = .05, what is the decision rule? Assume unequal variances. Use the quick rule for degrees of freedom. a. Reject the null hypothesis if tcalc < −1.86 (8 df.) b. Reject the null hypothesis if tcalc > −1.86 (8 df.) multiple choice 2 a b (a-3) Calculate the test statistic. (Round your answer to 4 decimal places. Input the answer as a positive value.) (a-4) At α = .05, is the mean sound level reduced? (b-1) At α = .05, has the variance changed? Choose the correct hypothesis. a. H0: σ12 / σ22 ≠ 1 vs. H1: σ12 / σ22 = 1 b. H0: σ12 / σ22 = 1 vs. H1: σ12 / σ22 ≠ 1 multiple choice 3 a b (b-2) At α = .05, what is the decision rule? a. Reject H0 if Fcalc < 9.6 or Fcalc > .1042. b. Reject H0 if Fcalc > 9.6 or Fcalc < .1042 multiple choice 4 a b (b-3) What is the test statistic? (Round your answer to 2 decimal places.) (b-4) At α = .05, is the variance changed?
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 |
|---|---|
| 42 | 48 |
| 41 | 51 |
| 40 | 44 |
| 37 | 48 |
| 44 | 52 |
Click here for the Excel Data File
(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
multiple choice 1
-
a
-
b
(a-2) At α = .05, what is the decision rule? Assume unequal variances. Use the quick rule for degrees of freedom.
a. Reject the null hypothesis if tcalc < −1.86 (8 df.)
b. Reject the null hypothesis if tcalc > −1.86 (8 df.)
multiple choice 2
-
a
-
b
(a-3) Calculate the test statistic. (Round your answer to 4 decimal places. Input the answer as a positive value.)
(a-4) At α = .05, is the mean sound level reduced?
(b-1) At α = .05, has the variance changed? Choose the correct hypothesis.
a. H0: σ12 / σ22 ≠ 1 vs. H1: σ12 / σ22 = 1
b. H0: σ12 / σ22 = 1 vs. H1: σ12 / σ22 ≠ 1
multiple choice 3
-
a
-
b
(b-2) At α = .05, what is the decision rule?
a. Reject H0 if Fcalc < 9.6 or Fcalc > .1042.
b. Reject H0 if Fcalc > 9.6 or Fcalc < .1042
multiple choice 4
-
a
-
b
(b-3) What is the test statistic? (Round your answer to 2 decimal places.)
(b-4) At α = .05, is the variance changed?
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