Question: A large medical insurance company wants to find out if the proportion of its policyholders who require hospitalization each year (around 10% for this company) will decrease if they expand their coverage for certain types of alternative medicine. This coverage would be less expensive than hospitalization for the insurance company.

The company plans to conduct a study where this extra coverage is offered to a simple random sample of n=500 policy holders for a year. The proportion of those 500 policy holders in need of hospitalization will be computed so the following hypothesis test can be conducted at a 5% significance level:

H 0 : proportion requiring hospitalization per year remains the same

H a : proportion requiring a hospitalization per year decreases

Use this information to answer both a. and b. below.

1. i. Explain what a Type II error is in this context.

ii. What would the consequences of a Type II Error be to the insurance company?

b.

1. Explain what Power is in this context.
2. Suppose the insurance company wants to increase the Power of the hypothesis test. Explain how each of the following strategies would increase Power in this situation.

• Take a sample 1000 policy ‐ holders rather than 500 policy ‐ holders

• Change the significance level to 10% from 5%

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