13. A large software development firm recently relocated itsfacilities. Top management is interested in fostering goodrelations with its new local community and has encouraged itsprofessional employees to engage in local service activities. Thecompany believes that its professionals volunteer an average ofmore than 15 hours per month. If this is not the case, it willinstitute an incentive program to increase communityinvolvement.
(a) A random sample of 24 professionals reported the sample meanand standard deviation are 16.6 hours and 2.22 hours respectively.For a more accurate determination, top management wants to estimatethe average number of hours volunteered per month by theirprofessional staff to within half an hour with 99% confidence. Howmany randomly selected professional employees would they need tosample?
(b) Now, suppose 40 professional employees are randomlyselected. This sample yields a mean of 15.2 hours and a standarddeviation of 1.8 hours. Construct the 95% confidence interval.(Hint: 1.8 is the sample standard deviation, not the populationstandard deviation)
