Question 986137: Southside Hospital in Bay Shore, New York, commonly conducts stress tests to study the heart muscle after a person has a heart attack. Members of the diagnostic imaging department conducted a quality improvement project with the objective of reducing the turnaround time for stress tests. Turnaround time is defined as the time from when a test is ordered to when the radiologist signs off on the test results. Initially, the mean turnaround time for a stress test was 68 hours. After incorporating changes into the stress-test process, the quality improvement team collected a sample of 50 turnaround times. In this sample, the mean turnaround time was 32 hours, with a standard deviation of 9 hours.
a) if you test the null hypothesis at the 0.01 level of significance, is there evidence that the new process has reduced turnaround time?
b)interpret the meaning of the p-value in this problem
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Ho=mean is 68 hours
Ha=mean is not 68 hours
alpha=0.01
test statistic is t df=49
critical value |t|>2.68
calculation t= (value-68)/s/sqrt (n)
t= (32-68)*sqrt(50)/9
t=-28.3
This is highly significant, which makes intuitive sense, given that that the sample +4 sds would be needed to reach the first mean. There is very strong evidence to say that the change could not have occurred by chance.
The likelihood of this result's occurring by chance is well less than one in a million.
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