Question:

1. An advertising agency that serves a major radio station wants to estimate the mean amount of time that the station’ audience spends listening to the radio daily. From past studies, the standard deviation is estimated a 45 minutes. What sample size is needed if the agency wants to be 90% confident of being correct to within ± 5 minutes?
2. North Shore Hospitalin Sydney, 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 to try to reduce the turnaround time for stress tests. Turnaround time is defined as the time from when the 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.

1. Construct a 95% confidence interval for the population mean turnaround time.
2. Interpret the interval constructed in (i).
3. Do you think the quality improvement project was a success? Explain.

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