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	1	1	2	2	3	3
Employee	1	2	3	4	5	6
Salary	24.7	28.6	25.2	28.6	20.8	24.7

(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. (Enter your answers for p(x) as fractions.)

x	22.75		24.70	24.95	26.65		28.60
p(x)		1 15				2 15

(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. (Enter your answers as fractions.)

x	22.75	26.65	26.90
p(x)

(c) How does E(X) from parts (a) and (b) compare to the population mean salary μ?

E(X) from part (a) is  _______ μ, and E(X) from part (b) is _______ μ.

Answer 1

sampling distribution is as follows:

x1	x2	xbar	P(x1,x2)
24.7	28.6	26.65	1/30
24.7	25.2	24.95	1/30
24.7	28.6	26.65	1/30
24.7	20.8	22.75	1/30
24.7	24.7	24.7	1/30
28.6	25.2	26.9	1/30
28.6	28.6	28.6	1/30
28.6	20.8	24.7	1/30
28.6	24.7	26.65	1/30
28.6	24.7	26.65	1/30
25.2	28.6	26.9	1/30
25.2	20.8	23	1/30
25.2	24.7	24.95	1/30
25.2	24.7	24.95	1/30
25.2	28.6	26.9	1/30
28.6	20.8	24.7	1/30
28.6	24.7	26.65	1/30
28.6	24.7	26.65	1/30
28.6	28.6	28.6	1/30
28.6	25.2	26.9	1/30
20.8	24.7	22.75	1/30
20.8	24.7	22.75	1/30
20.8	28.6	24.7	1/30
20.8	25.2	23	1/30
20.8	28.6	24.7	1/30
24.7	24.7	24.7	1/30
24.7	28.6	26.65	1/30
24.7	25.2	24.95	1/30
24.7	28.6	26.65	1/30
24.7	20.8	22.75	1/30

a)

xbar	22.75	23	24.7	24.95	26.65	26.9	28.6
p(xbar)	2/15	1/15	1/5	2/15	4/15	2/15	1/15

b)

x	22.75	26.65	26.90
p(x)	1/3	1/.3	1/3

c)

E(X) from part (a) is equal to μ, and E(X) from part (b) is equal to μ