Must use my work showing Excel 948 Southside Hospital in Bay

Must use my work showing Excel.

9.48 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. (Data
extracted from E. Godin, D. Raven, C. Sweetapple, and
F. R. Del Guidice, “Faster Test Results,” Quality Progress,
January 2004, 37(1), pp. 33–39.)
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.

Solution

Ho=mean is 68 hours

Ha=mean is not 68 hours

alpha=0.01

test statistic is t df=50-1=49

Critical value at 001 is given as -2.33

calculation t= (value-68)/s/sqrt (n)

t= (32-68)*sqrt(50)/9

t= -28.3

Since the test statistics value is smaller than the lower critical value so we will reject the null hypothesis

so we can conclude that the population mean turnaround time for a stress test was less than 68 hours.

There is evidence that the new process has reduced turnaround time because the Z statistics value is

negative

b)

P-value is given as 0.133663

Since 0.133663 is > 0.01, there is significant evidence that the mean is different from 68