## Related questions with answers

A company maintains three offices in a certain region, each staffed by two employees. Information concerning yearly salaries (1000s of dollars) is as follows:

$\begin{array}{lcccccc} \text {Office} & 1 & 1 & 2 & 2 & 3 & 3 \\ \text {Employee} & 1 & 2 & 3 & 4 & 5 & 6 \\ \text {Salary} & 29.7 & 33.6 & 30.2 & 33.6 & 25.8 & 29.7 \end{array}$

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 $X_{1}$ 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 $\mu$?

Solution

Verifieda. Determine the sample mean salary (sum of all values divided by the number of values) for each sample of 2 employees:

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