Question 261514: Im stuck on this question. can you please help?
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
a) What are the null and alternative hypotheses to test if the variance in sound levels
has changed?
b) Using α = 0.05, what is the critical value for the hypothesis test?
c) What is the test statistic for the hypothesis test? You may find it helpful to use
excel to calculate the two sample variances
d) Draw a conclusion for the hypothesis test. Make sure you state your conclusion
in the context of the problem.
e) What is the p-value for the hypothesis test
Thanks!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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
---
s^2(new) =6.6977
s^2(old) =9.800
numerator df = 4 = denominator df
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a) What are the null and alternative hypotheses to test if the variance in sound levels has changed?
------------------------------
Ho: s^2(new)-s^2(old) = 0
H1: s^2(new)-s^2(old is not zero
------------------------------
b) Using α = 0.05, what is the critical value for the hypothesis test?
1/9.6= 0.1042 is the left CV; 9.6 is the right CV
--------
c) What is the test statistic for the hypothesis test? You may find it helpful to use excel to calculate the two sample variances
I used a TI calculator to get:
test statistic: F = 0.68367
d) Draw a conclusion for the hypothesis test. Make sure you state your conclusion in the context of the problem.
Since the test statistic is not in the rejection interval fail to reject
Ho. The Variance for the new flooring sound level is not different than
the old flooring sound level
e) What is the p-value for the hypothesis test
p-value = 2*P(F > 9.6) = 2*Fcdf(9.6,1000,4,4) = 2*0.25 = 0.50
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Cheers,
Stan H.
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