A company maintains three offices in a certain region, each staffed by two emplo

Question

A company maintains three offices in a certain region, each staffed by two employees. Information concerning yearly salaries (1000s of dollars) is as follows. Office Employee 1 Salary 29.4 33.3 307 33.3 25.1 29.4 (a) Suppose two of these employees are randomly selected from among the six (without replacement). Determine the sampling distribution of the sample mean salary X. (Give answers accurate to 3 decimal places.) 27.25 27.9 29.2 29.4 30.05 31.35 32 33.3 P(x) (b) Suppose one of the three offices is randomly selected. Let X1 and X2 denote the salaries of the two employees. Determine the sampling distribution of X. (Give answers accurate to 3 decimal places.) 27.25 31.35 32 P(x) (C) How does E(X) from parts (a) and (b) compare to the population mean salary ? E(X) from part (a) is-select- and E(X) from part (b) is Select- .

Explanation / Answer

from above as P(Xbar) =P(x1)*P(x2)

therefore

a)

b) as both employee are from same company theefore each probability =1/3

hence  

c)

E(Xbar) from part a is equal to mu and E(Xbar) from part b is equal to mu

xbar 27.25 27.9 29.2 29.4 30.05 31.35 32 33.3 P(xbar) 0.133 0.067 0.133 0.067 0.133 0.267 0.133 0.067

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