ESTIMATION OF MEDICAL CLAIMS

An insurance company takes a sample of 400 Medical claims in order to estimate the characteristics of the claims that have been submitted for reimbursement. In particular the insurance company wishes to estimate the mean size of the claims and the percentage of claims that exceed $1,000. The number of claims processed by the insurance company next year will be 200,000.

The following information was obtained:

A. Sample Mean = $600

B. Sample Standard Deviation = $500

C. Frequency Distribution of Medical Claims

FREQUENCY DISTRIBUTION
CLAIM SIZE RANGE (dollars)	FREQUENCY (NUMBER OF CLAIMS)
Xi 500	250
500 < Xi 1000	70
1000 < Xi 1500	50
1500 < Xi 2000	20
2000	10

1. Find a 95% confidence interval for the mean of all claims processed by the insurance company next year.

2. Estimate the percentage of claims processed by the insurance company next year that exceed $1,000 and find a 95% confidence interval for this percentage.

2

3. Estimate the number of claims processed by the insurance company next year that exceed $1,000 and find a 95% confidence interval for this number.

4. The Insurance Company wishes to increase the precision of its estimates by taking an additional sample of medical claims. There are two precision requirements:

I. 95% probability that the sampling error in estimating the mean claim size is less than $25.

II. 95% probability that the sampling error in estimating the percentage of claims exceeding $1,000 is less than 2.5%.

a. How many additional claims must be sampled to satisfy requirement I?

b. How many additional claims must be sampled to satisfy requirement II?

c. How many additional claims must be sampled to satisfy both requirements?