The head of the department of management at Local University has noticed that the four secretaries in the departmental office seem to spend a lot of time answering questions from students that could better be answered by the university advising office, by faculty advisors, or simply from the available literature (i.e., course schedules, catalogues, the student handbook, and so on). As a result, the department head is considering remodeling the office with cubicles so students do not have easy access to the secretaries. However, before investing in this project, the head has decided to conduct a work sampling study to determine the proportion of time the secretaries spend assisting students. The head arranged for a graduate assistant to make observations for the work sample, but the graduate student’s schedule enabled her to make only 300 random observations in the time allotted for the study. The results of the work sampling study showed that the secretaries assisted students 12% of the time, somewhat less than the head anticipated.
a. Given the number of observations that were included in the work sampling study, how confident can the department head be that the sample result is within 3% of the actual proportion?
b. How many fewer or additional observations would be required for the department head to be 95% confident in the work sampling results?