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# Random Sampling and Confidence Interval

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The employee benefits manager of a small private university would like to estimate the proportion of full-time employees who prefer adopting the first (i.e., plan A) of three available health care plans in the coming annual enrollment period. A reliable frame of the university's employees and their tentative preferences are in the file P08_25.xlsx.

a. Use Excel to choose a simple random sample of size 45 from the given frame.
b. Use the sample found in part a. to construct a 99% confidence interval for the proportion of university employees who prefer plan A. Assume that the population consists of the preferences of all employees in the given frame.
c. Interpret the 99% confidence interval constructed in Part b.

Continuing Problem, select simple random samples of 30 individuals from each of the given employee classifications (i.e., administrative staff, support staff, and faculty). Construct a 99% confidence interval for the proportion of employees who prefer adopting plan A for each of the classifications. Do you see evidence of significant differences among these three interval estimates. Summarize your findings.

https://brainmass.com/statistics/confidence-interval/random-sampling-and-confidence-interval-382279

#### Solution Summary

This solution is comprised of the detailed procedure of Random Sampling in EXCEL and step-by-step calculation of Confidence Interval. The solution provides students with a clear perspective of the underlying concepts.

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## Confidence Interval & Sample Size for a Random Sample

1 (b). A survey of a random sample of 250 car commuters indicates that 80 would switch to commuting by public transport if they had to pay at least \$10 per week for parking at their work places.

(i) Using a 95% confidence level, calculate the confidence interval for the proportion of the commuters who might be expected to change to using public transport for the journey-to-work.

(ii) Comment on the relationship between sample size and margin of error.

(c) Suppose we want to estimate, with 95% confidence, the percentage of commuters who would change to using public transport for the journey-to-work with a margin of error of +-3%. How large a sample of people will need to be taken:

(i) A preliminary estimate suggests that the true percentage is about 32%.

(ii) No preliminary estimate is available.

see attached file.

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