A sample of 200 executives is asked the question: "If you were given an offer by another company equal to or slightly better than your present position, would you remain with the company or take the other position?" The responses of the 200 executives in the survey were cross-classified with their length of service with the company, giving the results below:
Length of Service
Loyalty < 1 1 - 5 6 - 10 > 10 Total
Remain 10 30 5 75 120
Leave 25 15 10 30 80
Total 35 45 15 105 200
Suppose we want to carry out a formal test of whether Loyalty is related to Length of Service.
(a) State the hypotheses to be tested.
(b) Calculate the expected frequencies.
Length of Service
Loyalty < 1 1 - 5 6 - 10 > 10
Remain
Leave
(c) What is the p-value?
(d) State the conclusion in context, justifying your answer.
(e) Calculate the proportion who would leave for each age group. What does it suggest?