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 2 2 3 4 6 29.5 33.3 30.6 33.3 25.0 29.5 (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 27.8 29.15 29.5 30.05 31.4 31.95 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 31.4 31.95 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 there are total 6*5=30 sample possible each sample has probability =1/30

from above

b)

as each office has equal probability of election =1/3 =0.333

c)

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

x 27.25 27.8 29.15 29.5 30.05 31.4 31.95 33.3 P(x) 0.133 0.067 0.133 0.067 0.133 0.267 0.133 0.067

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