A company maintains three offices in a certain region, each staffed by two emplo
ID: 3218935 • Letter: A
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:
(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.) 24.75 26.70 26.95 28.65 30.60 p(x) 15 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 24.75 28.65 28.90 p(x) (c) How does E(X) from parts (a) and (b) compare to the population mean salary u? E(X) from part (a) is Select v A, and E(X) from part (b) is Select u.Explanation / Answer
(a) Suppose two of these employees are randomly selected from the six (without replacement). Determine the sampling distribution of the sample mean salary .
S={(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,4),(3,5),(3,6), (4,1),(4,2),(4,3),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5)}. There are 30 outcomes.
24.75 with 4 outcomes=4/30=2/15
28.9 with 4 outcomes=4/30=2/15
26.70 with 6 outcomes=6/30=3/15
26.95 with 4 outcomes=4/30=2/15
28.65 with 8 outcomes=8/30=4/15
25 with 2 outcomes=2/30=1/15
30.60 with 2 outcomes=2/30=1/15
(b) Suppose one of the three offices is randomly selected. Determine the sampling distribution of the sample mean salary .
S={(1,2),(2,1),(3,4),(4,3),(5,6),(6,5)}. There are 6 outcomes
24.75 with probability 1/3
28.65 with probability 1/3
28.90 with probability 1/3
c)
X
p(x)
x*p(x)
28.65
0.266667
7.64
26.95
0.266667
7.186667
24.75
0.266667
6.6
28.9
0.266667
7.706667
30.6
0.266667
8.16
26.7
0.266667
7.12
25
0.266667
6.666667
Total
51.08
x
p(x)
x*p(x)
24.75
0.333333
8.25
28.65
0.333333
9.55
28.9
0.333333
9.633333
Total
27.43333
51.08, 27.43
X
p(x)
x*p(x)
28.65
0.266667
7.64
26.95
0.266667
7.186667
24.75
0.266667
6.6
28.9
0.266667
7.706667
30.6
0.266667
8.16
26.7
0.266667
7.12
25
0.266667
6.666667
Total
51.08
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