Question: 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 health care preferences are given in the file P08_25.xlsx.

1. Use Excel to choose a simple random sample of size 45 from the given frame
2. Using the sample found in part a, 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.
3. Interpret the \(99 \%\) confidence interval constructed in part b.

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