# Confidence Interval & Sample Size

Q.8.1

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 to try to reduce the turn-around time for stress tests. Turn around time is defined as the time from when the test is ordered and when the radiologist signs off on the test result. Initially, the mean turn around time for a stress test is 68 hours. After incorporating changes into the stress test process, the quality improvement team collected a sample of 50 turn around times. In this turn around time, the mean turn around time was 32 hours, with a standard deviation of 9 hours.

a). Construct a 95% confidence interval for the population mean turn around time.

b). Interpret the interval constructed in (a).

c). Do you think the quality improvement project was a success? Explain.

Q.8.2

In a survey conducted for American Express, 27% of small business owners indicated that they never check in with the office when they are on vacation (Snapshots, USA Today.â? The article did not disclose the sample size used in the study.

A). Suppose that the survey was based on 500 small business owners, construct a 95% confidence interval estimate for the population proportion of small business owners of small business owners who never check in with their offices when they are on vacation.

b). Support that the survey was based on 1000 small business owners, construct a 95% confidence interval estimate for the population proportion of small business owners who never check in with their offices when on vacation.

c). Discuss the effect of sample size on confidence interval estimate.

Q8.4

A consumer group wants to estimate the mean of electric bill for the month of July for single family homes in a large city. Based on studies conducted in other cities, the standard deviation is assumed to be $25. The group wants to estimate the mean bill for July to within ± $5 with 99% confidence.

a). What sample size is needed?

b). If 95% confidence is desired, what sample size is necessary?

Q8.5

The personnel of a large corporation employing 3,000 workers wants to estimate the family dental expenses of its employees to determine the feasibility of providing a dental insurance plan. A random sample of 10 employees reveals the following family dental expenses (in dollars). For the preceding year, 110 362 246 85 510 208 173 425 316 179.

Construct a 90% confidence interval estimate of the total family dental expenses for all employees in the preceding year.

#### Solution Summary

The solution provides step by step method for the calculation of confidence interval and sample size for population mean and proportion. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.