The employee benefits manager of a large public university would like to estimate the proportion of full-time employees who prefer adopting the first (plan A) of three available health care plans in the next annual enrollment period. A random sample of the university’s employees and their tentative health care preferences are given in the file P08_17.xlsx.
a. Find a 90% confidence interval for the proportion of all the university’s employees who favor plan A.
b. The file also includes the classification of each employee (administrative staff, support staff, or faculty). Find a separate 90% confidence interval for each of these groups for the proportion who favor plan A. How do these confidence intervals compare to one another? How do their lengths compare to the confidence interval in part a? Is this what you would expect? Explain.