Data were obtained on health care plans chosen by employees of small, medium and

Question

Data were obtained on health care plans chosen by employees of small, medium and large companies. These companies offer their employees HMO ( Health Maintenance Organizations) plans, PPO plans and fee-for-service plans. In a sample of 833,303 employees, .603% worked for small companies, 2.686% worked for medium companies, 40.94% chose fee-for-service plans, 30% chose PPO plans, 1,808 worked for small companies and chose fee-for-service plans while 1,757 worked for small companies and chose PPO plans, 6,491 worked for medium companies and chose PPO plans while 6,938 worked for medium companies and chose HMO plans. Suppose a single employee is to be randomly selected from among the 833,303.

a. What is the probability that the employee chooses an HMO plan?

b. What is the probability that the employee works for a large company?

c. What is the probability that the employee chooses an HMO plan given that he or she works for a large company?

d. Are company size and health care plan type statistically independent? Explain.

Explanation / Answer

P (small company) = 0.603% = 5025 employees

P(medium company) = 2.686% = 22383 employees

So, P(large company) = 96.711% = 805896 employees

P(FFS plan) = 40.94% = 341154 employees

P(PPO plan) = 30% = 249991 employees

So, P(HMO plan) = 29.06% = 242158 employees

a) P ( HMO plan) = 29.06%

b) P (Large company) = 96.711%

c) P (HMO | large company) = 234300 / 805896 = 29.07%

P (Large and HMO) = 0.2907

P (large) * P(HMO) = 0.9671 * 0.2906

= 0.2810

Hence the two events are not independent.

Hope this helps.

FFS PPO HMO Total Small 1808 1757 1460 5025 Medium 9494 6491 6398 22383 Large 329853 241743 234300 805896 Total 341154 249991 242158

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