The head of the department of management at State University has noticed that the four secretaries in the departmentaloffice seem to spend a lot of time answering questions fromstudents that could better be answered by the college advising office, by faculty advisors, or simply from the availableliterature; that is, course schedules, catalogues, the studenthandbook, and so on. As a result, the department head isconsidering remodeling the office with cubicles so studentsdo not have easy access to the secretaries. However, beforeinvesting in this project the head has decided to conduct awork sampling study to determine the proportion of timethe secretaries spend assisting students. The head arrangedfor a graduate assistant to make observations for the worksample, but the graduate student’s schedule enabled her tomake only 300 random observations in the time allotted forthe study. The results of the work sampling study showedthat the secretaries assisted students 12% of the time, somewhat less than the head anticipated.a. Given the number of observations that were included inthe work sampling study, how confident can the department head be that the sample result is within 3% of theactual proportion?b. How many fewer or additional observations would berequired for the department head to be 95% confidentin the work sampling results?
The head of the department of management at State 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 college advising office, by faculty advisors, or simply from the available
literature; that is, 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?
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