A sample of 200 executives is asked the question:

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< 11 - 56 - 10> 10   Total

Remain1030575  120

Leave25 15 1030    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< 11 - 56 - 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?