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A company maintains three offices in a certain region, each staffed by two employees. Information concerning...

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Basic Math

A company maintains three offices in a certain region, eachstaffed by two employees. Information concerning yearly salaries(1000s of dollars) is as follows:

Office112233
Employee123456
Salary  24.7    28.6    25.2    28.6    20.8    24.7  

(a) Suppose two of these employees are randomly selected fromamong the six (without replacement). Determine the samplingdistribution of the sample mean salary X. (Enter youranswers for p(x) as fractions.)

x    22.7524.7024.9526.6528.60
p(x)            
1
15
  		                    
2
15
  		      


(b) Suppose one of the three offices is randomly selected. LetX1 and X2 denote thesalaries of the two employees. Determine the sampling distributionof X. (Enter your answers as fractions.)

x22.7526.6526.90
p(x)                      


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

E(X) from part (a)is  _______ ?, andE(X) from part (b) is _______?.

Answer & Explanation Solved by verified expert
3.6 Ratings (365 Votes)

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