A company maintains three offices in a certain region, each staffed by two emplo

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.)

(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.)

Office 1 1 2 2 3 3 Employee 1 2 3 4 5 6 Salary   32.7     36.6     33.2     36.6     28.8     32.7  

Explanation / Answer

(a)

Number of ways of selecting two employees out of 6 is C(6,2) = 15

Folloiwng table shows all the possibe samples and corresponding salaries:

Following table shows the probability distribution of sample mean:

(b)

Following is the probability distribution:

X1 X2 Salaries Mean P(mean) 1 2 32.7 36.6 34.65 1/15 1 3 32.7 33.2 32.95 1/15 1 4 32.7 36.6 34.65 1/15 1 5 32.7 28.8 30.75 1/15 1 6 32.7 32.7 32.7 1/15 2 3 36.6 33.2 34.9 1/15 2 4 36.6 36.6 36.6 1/15 2 5 36.6 28.8 32.7 1/15 2 6 36.6 32.7 34.65 1/15 3 4 33.2 36.6 34.9 1/15 3 5 33.2 28.8 31 1/15 3 6 33.2 32.7 32.95 1/15 4 5 36.6 28.8 32.7 1/15 4 6 36.6 32.7 34.65 1/15 5 6 28.8 32.7 30.75 1/15

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