Question

a certain region, each staffed by two employees. Information concerning yearly salaries (1000s of dollars) is as follows. A company maintains three offices Office 1 1 2 3 Employee 1 2 3 4 5 6 Salary 29,4 33.1 30.6 33.1 25.0 29.4 (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. (Give answers accurate to 3 decimal places.) x 27.2 27.8 29.05 29,4 3о 31.25 31.85 33.1 p(x) f the three offices is randomly selected. Let X1 and X2 denote the salaries of the two employees. Determine the sampling distribution of X. (Give answers (b) Suppose one accurate to 3 decimal places.) 27.2 31.25 31.85 x р) (c) How does E(X) from parts (a) and (b) compare to the population mean salary ? E(X) from part (a) is -Select and EX) from part (b) isSelect- .

Answer 1

Solution: Selection of two random employees may have the following possibilities: Employee 1 Employee 2 13 Salary 2 33.1 30.6 33.1 25 Mean Salary 31.25 30 31.25 27.2 29.4 31.85 33.1 2 Salary 1 29.4 29.4 29.4 29.4 29.4 33.1 33.1 33.1 33.1 30.6 30.6 30.6 33.1 33.1 3 29.4 30.6 33.1 25 2 2 3 3 5 6 4 5 29.4 33.1 25 29.4 25 29.4 29.4 29.05 31.25 31.85 27.8 30 29.05 31.25 27.2 4 25 Part-A: Taking the unique values of Mean Salary from the above table:

Mean Salary 27.2 27.8 29.05 29.4 30 31.25 31.85 33.1 Probability P(X) 2/15 = 0.133 1/15 = 0.067 2/15 = 0.133 1/15 = 0.067 2/15 = 0.133 4/15 = 0.267 2/15 = 0.133 1/15 = 0.067 E(X) = LXP) = 27.2 x 0.133 + 27.8 x 0.067 +29.05 x 0.133 +29.4 x 0.067 + 30 x 0.133 + 31.25 x 0.267 + 31.85 x 0.133 + 33.1 x 0.067 = E(X) = 30.1 Part-B: Selection of two random offices may have the following possibilities: Employee 1 Employee 2 Mean Salary 29.4 33.1 31.25 30.6 33.1 31.85 25 29.4 27.2 Mean Salary 31.25 31.85 27.2 Probability P(X) 1/3 = 0.333 1/3 = 0.333 1/3 = 0.333

E(X) = EXP(X) = 31.25 x 0.333 + 31.85 x 0.333 + 27.2 x 0.333 = E(X) = 30.1 Part-C: , _ 294 + 331 + 30.5 + 33.+ 250 +294 – 30.1 29.4 + 33.1 + 30.6 + 33.1 + 25.0 + 29.4 -= 30.1 u =- Hence, E(X) from part-a is equal to y, and E(X) from part-b is equal to u