A Company Maintains Three Offices in a Certain Region, Each

Essay

A company maintains three offices in a certain region, each staffed by two employees. Information concerning yearly salaries (1000's of dollars) is as follows: $$\begin{array} { l c c c c c c } \hline & 1 & 1 & 2 & 2 & 3 & 3 \\\text { Office }\\\hline \text { Employee } & 1 & 2 & 3 & 4 & 5 & 6 \\\text { Salary } & 19.7 & 23.6 & 20.2 & 23.6 & 15.8 & 19.7 \\\hline\end{array}$$
a. Suppose two of these employees are randomly selected from among the six (without replacement). Determine the sampling distribution of the sample mean salary $\bar { X }$
b. Suppose one of the three offices is randomly selected. Let $X _ { 1 } \text { and } X _ { 2 }$
denote the salaries of the two employees. Determine the sampling distribution of $\bar { X }$
c. How does $E ( \bar { X } )$
from parts (a) and (b) compare to the population mean salary $\mu ?$