Question

A company, studying the relation between job satisfaction and length of service of employees, classified employees into three length-of-service groups (less than 5 years, 5-10 years, more than 10 years). Suppose µ1 = 65, µ2 = 80, µ3 = 95, and σ= 3, and that ANOVA model Yij=μi+ϵij is applicable.
a. Draw a representation of this model
b. Find E(MSTR) and E(MSE) if 25 employees from each group are selected at random for intensive interviewing about job satisfaction.
c. Is E(MSTR) substantially large than E(MSE) here?

Answer 1

Answer:

Below see details

Explanation:

A) It is attached. Please see the picture

B) First to calculate the overall mean,  

μ=65∗25/75+80∗25/75+95∗25/75  

μ=65∗25/75+80∗25/75+95∗25/75 = 80

Next to calculate E(MSTR) = σ2+(1/r−1) ∑ni(μi−μ)^2 = 5634

And E(MSE) = σ^2= 9

C) Yes, it is substantially large than E(MSE) in this case.

D) If we sampled 25 employees from each group, we are likely to get a F statistics to indicate differences of job satisfactions among three types of length of service of employees.