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	26.7	30.6	27.2	30.6	22.8	26.7

(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	24.75		26.70	26.95	28.65		30.60
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	24.75	28.65	28.90
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  ---Select--- greater than less than equal to μ, and

E(X)

from part (b) is  ---Select--- greater than less than equal to μ.

Answer 1

Answer: A company maintains three offices in a certain region, each staffed by two employees. Information concerning yearly salaries (1000s of dollars) is given.

(a) Suppose two of these employees are randomly selected from among the six (without replacement).

the sampling distribution of the sample mean salary:

Employee 1	Employee 2	Salary 1	Salary 2	Sample mean
1	2	26.7	30.6	28.65
1	3	26.7	27.2	26.95
1	4	26.7	30.6	28.65
1	5	26.7	22.8	24.75
1	6	26.7	26.7	26.7
2	3	30.6	27.2	28.9
2	4	30.6	30.6	30.6
2	5	30.6	22.8	26.7
2	6	30.6	26.7	28.65
3	4	27.2	30.6	28.90
3	5	27.2	22.8	25.00
3	6	27.2	26.7	26.95
4	5	30.6	22.8	26.7
4	6	30.6	26.7	28.65
5	6	22.8	26.7	24.75
Average				27.43

x 24.75 25.00 26.70 26.95 28.65 28.9 30.60

p(x) 2/15 1/15 3/15 2/15 4/15 2/15 1/15

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.)

There are three offices each having two employee

x 24.75 28.65 28.90

p(x) .1/3 1/3 1/3

(c) How does

E(X)

from parts (a) and (b) compare to the population mean salary μ?

E(X)

from part (a) is ---Select--- greater

E(X) = 27.43

From part b)

E(X) = 27.43

From comparing part a) and part b) the population mean salary is equal.