QA 233 (Basic Business Statistics)
Case Assignments
Case 3
“Grand Health HMO”
Llewellyn Industries is considering a change from its current health insurance provider (Good Neighbor Insurance) to the Grand Health HMO. Julia Saffron, Manager of Llewellyn's Human Resources Department, has carefully compared the two policies and determined that Grand Health can provide coverage very similar to the policy Llewellyn has with Good Neighbor Insurance at a substantially lower cost. However, Ms. Saffron remembers a situation that occurred at Llewellyn seven years ago (soon after she began working at Llewellyn as a college intern) - the organization switched its insurance provider to Good Neighbor Insurance without first asking for input from the employees, and this unilateral decision caused hard feelings between management and labor.
In order to avoid a recurrence of this unfortunate scenario, Ms. Saffron has decided to distribute information about the new policy to the ninety day shift and sixty-six night shift employees and ask each to indicate whether s/he finds the new health insurance program (provided by Grand Health Insurance) to be acceptable. Because Ms. Saffron recalls that female employees were particularly upset by the decision to change providers seven years ago, she has also collected information by gender. The data collected by Ms. Saffron are provided in the table below:
|
Shift |
Gender |
Grand
Health HMO Acceptable? |
|
2 |
Male |
Yes |
|
1 |
Male |
No |
|
1 |
Male |
Yes |
|
2 |
Female |
Yes |
|
1 |
Male |
Yes |
|
1 |
Female |
Yes |
|
1 |
Male |
Yes |
|
1 |
Female |
Yes |
|
2 |
Male |
No |
|
1 |
Female |
Yes |
|
1 |
Female |
Yes |
|
1 |
Female |
No |
|
2 |
Male |
Yes |
|
2 |
Male |
No |
|
1 |
Male |
No |
|
1 |
Female |
Yes |
|
1 |
Male |
Yes |
|
1 |
Female |
Yes |
|
1 |
Male |
Yes |
|
2 |
Male |
Yes |
|
2 |
Male |
Yes |
|
2 |
Male |
Yes |
|
2 |
Male |
No |
|
2 |
Male |
Yes |
|
2 |
Male |
Yes |
|
2 |
Male |
Yes |
|
2 |
Male |
No |
|
1 |
Male |
Yes |
|
2 |
Male |
No |
|
1 |
Female |
Yes |
|
1 |
Male |
No |
|
1 |
Female |
Yes |
|
1 |
Female |
No |
|
1 |
Female |
No |
|
2 |
Male |
Yes |
|
1 |
Male |
No |
|
1 |
Male |
Yes |
|
1 |
Male |
No |
|
2 |
Male |
Yes |
|
2 |
Male |
Yes |
|
1 |
Male |
Yes |
|
1 |
Female |
Yes |
|
1 |
Male |
Yes |
|
1 |
Male |
Yes |
|
2 |
Male |
Yes |
|
2 |
Male |
No |
|
2 |
Male |
Yes |
|
1 |
Male |
No |
|
2 |
Male |
Yes |
|
1 |
Female |
Yes |
|
2 |
Male |
No |
|
1 |
Male |
Yes |
|
1 |
Female |
Yes |
|
1 |
Female |
Yes |
|
1 |
Female |
Yes |
|
1 |
Male |
Yes |
|
2 |
Male |
Yes |
|
1 |
Male |
No |
|
1 |
Male |
Yes |
|
1 |
Male |
Yes |
|
2 |
Male |
Yes |
|
1 |
Male |
No |
|
2 |
Male |
Yes |
|
2 |
Male |
Yes |
|
1 |
Male |
Yes |
|
1 |
Female |
Yes |
|
1 |
Male |
Yes |
|
1 |
Male |
Yes |
|
1 |
Female |
Yes |
|
2 |
Male |
Yes |
|
2 |
Male |
No |
|
1 |
Female |
No |
|
1 |
Female |
No |
|
1 |
Female |
No |
|
1 |
Male |
Yes |
|
2 |
Male |
Yes |
|
2 |
Male |
Yes |
|
2 |
Male |
Yes |
|
2 |
Male |
Yes |
|
2 |
Male |
Yes |
|
2 |
Male |
No |
|
1 |
Male |
Yes |
|
2 |
Male |
No |
|
2 |
Male |
No |
|
1 |
Female |
Yes |
|
1 |
Male |
Yes |
|
1 |
Male |
Yes |
|
2 |
Female |
Yes |
|
1 |
Female |
No |
|
2 |
Male |
No |
|
1 |
Male |
Yes |
|
1 |
Female |
No |
|
1 |
Male |
No |
|
1 |
Female |
Yes |
|
2 |
Male |
Yes |
|
2 |
Male |
Yes |
|
2 |
Male |
Yes |
|
1 |
Male |
Yes |
|
2 |
Male |
Yes |
|
1 |
Male |
No |
|
1 |
Male |
Yes |
|
1 |
Male |
Yes |
|
1 |
Female |
Yes |
|
2 |
Male |
Yes |
|
1 |
Male |
Yes |
|
1 |
Female |
Yes |
|
1 |
Male |
Yes |
|
2 |
Male |
Yes |
|
2 |
Male |
Yes |
|
1 |
Female |
No |
|
1 |
Male |
Yes |
|
1 |
Male |
Yes |
|
2 |
Male |
No |
|
1 |
Male |
No |
|
1 |
Female |
Yes |
|
1 |
Male |
Yes |
|
1 |
Female |
Yes |
|
2 |
Male |
Yes |
|
2 |
Male |
No |
|
2 |
Male |
Yes |
|
2 |
Male |
Yes |
|
1 |
Female |
Yes |
|
1 |
Male |
No |
|
2 |
Male |
No |
|
2 |
Male |
No |
|
1 |
Male |
Yes |
|
1 |
Female |
Yes |
|
2 |
Male |
Yes |
|
2 |
Male |
Yes |
|
1 |
Female |
Yes |
|
2 |
Male |
Yes |
|
1 |
Female |
No |
|
2 |
Male |
No |
|
1 |
Male |
Yes |
|
1 |
Female |
Yes |
|
2 |
Male |
No |
|
2 |
Male |
Yes |
|
1 |
Male |
Yes |
|
2 |
Male |
Yes |
|
2 |
Female |
No |
|
1 |
Female |
Yes |
|
1 |
Female |
Yes |
|
2 |
Male |
Yes |
|
1 |
Male |
Yes |
|
1 |
Male |
Yes |
|
1 |
Female |
Yes |
|
1 |
Female |
Yes |
|
2 |
Male |
Yes |
|
1 |
Male |
Yes |
|
2 |
Male |
Yes |
|
2 |
Male |
No |
|
2 |
Male |
Yes |
|
1 |
Male |
Yes |
|
1 |
Male |
Yes |
|
1 |
Female |
Yes |
|
2 |
Male |
Yes |
Ms. Saffron will feel comfortable if i) the proportion of employees who indicate that the Grand Health HMO plan is acceptable exceeds 0.70 and ii) the proportion of female employees who favor the plan is no less than the proportion of male employees who favor the plan. She also wants to know whether a difference in acceptance rates of the Grand Health HMO plan exists between shifts. She has asked you, as a business student with some background in probability, to help her address these issues.
Click here to download an Excel® file containing the raw data used in this case.