A specialist in the Human Resources department of a national hotel chain is looking for ways to

Question:

A specialist in the Human Resources department of a national hotel chain is looking for ways to improve retention among hotel staff. The problem is particularly acute among those who maintain rooms, work in the hotel restaurant, and greet guests. Within this chain, among those who greet and register guests at the front desk, the annual percentage who quit is 36% (see the accompanying bar chart for more information).17 Among the employees who work the front desk, more than half are expected to quit during the next year. The specialist in HR has estimated that the turnover rate costs $20,000 per quitter, with the cost attributed to factors such as
– The time a supervisor spends to orient and train a new employee
– The effort to recruit and interview replacement workers
– The loss of efficiencies with a new employee rather than one who is more experienced and takes less time to complete tasks
– Administrative time both to add the new employee to the payroll and to remove the prior employee
To increase retention by lowering the quit rate, the specialist has formulated a benefits program targeted at employees who staff the front desk. The cost of offering these benefits averages $2,000 per employee. The chain operates 225 hotels, each with 16 front-desk employees. As a test, the specialist has proposed extending improved benefits to 320 employees who work the front desk in 20 hotels.
Motivation
(a) Why would it be important to test the effect of the employee benefits program before offering it to all front-desk employees at the hotel chain?
(b) If the benefits program is to be tested, how would you recommend choosing the hotels? How long will the test take to run? (There is no best answer to this question; do your best to articulate the relevant issues.)
Method
(c) An analyst proposed testing the null hypothesis H0 : p ‰¤ 0.36, where p is the annual quit rate for employees who work the main desk if the new program is implemented. Explain why this is not the right null hypothesis.
(d) Another analyst proposed the null hypothesis H0: p ‰¥ 0.36. While better than the choice in part
(c), what key issue does this choice of H0 ignore? What is needed in order to improve this null hypothesis?
Mechanics
(e) If the chosen null hypothesis is H0: p ‰¥ 0.30, what percentage of these 320 must stay on (not quit) in order to reject H0 if Î± = 0.05?

(f) Assume the chosen null hypothesis is H0: p ‰¥ 0.30. Suppose that the actual quit rate among employees who receive these new benefits is 25%. What is the chance that the test of H0 will correctly reject H0?
Message
(g) Do you think that the owners of this hotel chain should run the test of the proposed benefits plan? Explain your conclusion without using technical language.