A company maintalns three offices In a certaln reginn, each staffed by two emplo

Question

A company maintalns three offices In a certaln reginn, each staffed by two employees. Information concerning yearly salarles 00s of dollars) s as follows office Employee 1 Salary 22.7 26.6 23.2 25.6 18. 22.7 a) Suppose two of these employees are randomly selected from among the six without replacement Determine the sampling distribution of the sample mean 5alary X Enter your answers for x as fractions. 20.75 22.70 22.95 24.65 26.60 p(x) 15 15 (b) Suppose one of the three offices is randormly selected. Let X1 and X2 denote the salaries of the two employees. Determine the sampling distribution of X. (Enter your answers as fractions.) 20.75 21.65 21.90 p(x) oes E(X) frum parts (a) and (b) compat e L, the population mean salary ? F(X) (c) How from part (a) is-select , , and E(X) from part (b) is -Select .

Explanation / Answer

here as P(Xbar) =P(X1)*P(X2) where P(X1) and P(X2) is probabilty of selecting x1 and x2 salry.

frm above given data distribution of average is as follows:

b)as each office has equal probability of being selected :

hence

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

xbar 20.75 21 22.7 22.95 24.65 24.9 26.6 P(xbar)    1/6    1/15    1/6    2/15    4/15    2/15    1/15

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