A Large Software Development Firm Recently Relocated Its Facilities A Based on the Sample Results, Find the 95% Confidence

Essay

A large software development firm recently relocated its facilities. Top management
is interested in fostering good relations with their new local community and has
encouraged their professional employees to engage in local service activities. They wish
to determine the average number of hours the firm's professionals volunteer per month.
A random sample of 24 professionals reported the following number of hours: $$\begin{array} { | l | l | l | l | l | l | l | l | l | l | l | l | } \hline 12 & 13 & 14 & 14 & 15 & 15 & 15 & 16 & 16 & 16 & 16 & 16 \\\hline 17 & 17 & 17 & 18 & 18 & 18 & 18 & 19 & 19 & 19 & 20 & 21 \\\hline\end{array}$$
A. Based on the sample results, find the 95% confidence interval and interpret.
b. For a more accurate determination, top management wants to estimate the average
number of hours volunteered per month by their professional staff to within one hour with
99% confidence. How many randomly selected professional employees would they need
to sample?
c. Suppose 40 professional employees are randomly selected. This sample yields a mean
of 15.2 hours and a standard deviation of 1.8 hours. Find a 95% confidence interval and
interpret.