Hospitals commonly conduct stress tests to study the heart m

Hospitals commonly conduct stress tests to study the heart muscle after a person has had a heart attahce. Members of a diagnostic imaging departments conduct quaility improvements projects 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 turnarouns tome for a stress test was 61 hours. After incorporating changes into the stress test process, a quaility improvement team collected a sample of 50 turnaround times. In this sample, the mean trunaround time was 37 hours, with a standard deviation of 7 hours.

1. Construct a 90% confidence interval estimate for the population mean turnaround time.

_____<u<_____

2. Interpret the interval constructed in (1). Choose the correct answer below.

a. the quality improvement team can be 90% confident that the new population mean turnaround time is the midpoint of the confidence interval.

b. the quality improvement team can be completly sure that the new population mean trunaround time is the midpoint of the confidence interval.

c. the quality improvement team can be 90% confident that the new population mean turnaround time is contained within the confidence interval.

d. the quality improvement team can be completly sure that they new population mean turnaround time is contained within the confidence interval.

2. Do you think the quality improvement project was a sucess?

a. With a 90% confidence it appears that the project was a sucess; the initial turnaround time of 61 hours falls within the interval found in par (1)

b. one can be completly sure that the project was a sucess; the initial turnaround time of 61 hours does not fall within the interval found in par (1)

c. one can be sure that the project was a success; the initial turnaround time o 61 hours falls withing the interval found in part (1)

d. With a 90% confidence it appears that the project was a sucess the initial turnaround time of 61 hours does not fall within the interval found in part (1)

Solution

(1) Given a=1-0.9=0.1, Z(0.05) = 1.645 (from standard normal table)

So the lower bound is

xbar - Z*s/vn =37 -1.645*7/sqrt(50) =35.37153

So the upper bound is

xbar + Z*s/vn =37 +1.645*7/sqrt(50) =38.62847

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(2)c. the quality improvement team can be 90% confident that the new population mean turnaround time is contained within the confidence interval.

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(2)d. With a 90% confidence it appears that the project was a sucess the initial turnaround time of 61 hours does not fall within the interval found in part (1)