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S479 F 10 Final

S479 F 10 Final - STAT 479 Final 1 A health insurance...

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STAT 479 Final December 13, 2010 1. A health insurance company has the following sample of five claims: 500, 500, 700, 800, 1500 The company wants to model their claims using a Gamma distribution. Calculate the parameters for the Gamma distribution using the Method of Moments.

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2. The variance of a distribution will be estimated using: 2 2 ( ) ˆ X X n The following sample is selected from the distribution: 5, 5, 8 Using the bootstrap method, estimate the mean square error in the above estimator.
3. During the last calendar year, Purdue incurred 100 worker’s compensation claims which are summarized in the following table: Amount of Claim Number of Claims 0 5000 14 5000-15,000 16 15,000-45,000 40 More than 45,000 30 Sally wants to test the following hypothesis using the Chi Square Test at a 10% significance level: H 0 : Workers Compensation claims are uniformly distributed with θ = 60,000. H 1 : Workers Compensation claims are not uniformly distributed with θ = 60,000. Calculate the Chi Square test statistic. Determine the critical value for this test. State your conclusion with regard to the hypothesis.

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4. Using simulation, Farhana estimates the claim payments that will be made under a dental insurance policy. The policy has a \$50 deductible for each claim. The maximum that will be paid under the dental policy for all claims in a year is \$500.
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