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 20.7 246 212 24.6 16.8 20.7 (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.) 13.75 20.70 (b) Suppose one of the three offices is randomly selected. Let X, and X, denote the salaries of the two employees. Determine the sampling distribution of X. (Enter your answers as fractions.) 18.75 22.65 22.90 P(X) (c) How does E(X) from parts (a) and (b) compare to the population mean salary? EX) from part (ə) is --Select- p, and ElXfrom part (b) is --Select-

Answer 1

a) There are 6 employees and choosing 2. Total number of combinations are 6C2=15 ways S.No 1 Employ1 1 Employ2 2 salaryl 20.7 20.7 20.7 20.7 20.7 24.6 24.6 24.6 salary2 | 24.6 21.2 24.6 16.8 20.7 21.2 24.6 16.8 20.7 24.6 16.8 20.7 16.8 20.7 20.7 average Mean 22.65 20.95 22.65 18.75 20.7 22.9 24.6 20.7 22.65 22.9 19 20.95 20.7 22.65 18.75 21.43333 24.6 21.2 21.2 21.2 24.6 24.6 16.8

Probability of sampling distribution of i 18.75 2/15 19.00 1/15 20.70 3/15 20.95 /15 22.65 4/15 22.9024.60 2/15 1/15 P(7) 2 b) One of the three officers randomly selected Office 1 2 3 salary1 20.7 21.2 16.8 salary2 24.6 24.6 20.7 Average Mean 22.65 22.9 18.75 21.43333 Probability sampling distribution is l 22.9 18.75 1/3 22.65 1/3 PX) /

From the parta and b Population mean salary part(a) is (u)=21.43333 Population mean salary part(b) is(u)=21.43333 Both means are same