320_hw10_ans - Economic Statistics Homework 10 Tests of...

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Economic Statistics: Homework 10 Tests of Population Proportion, Tests of Mean Differences, Tests of Population Variance. 1. A hospital is comparing its performance against an industry benchmark that no more than 50 percent of normal births should result in a hospital stay exceeding 2 days. In their sample of 50 normal births, 31 had stays longer than 2 days. At a 0.025 significance level, is the hospital exceeding the benchmark? Hypotheses: 50 . 0 : 0 = Π H 5 . 0 : 1 Π H Test Statistic: n p / ) 1 ( ˆ Π - Π Π - is distributed as Z Rejection Region: This is a one-tailed test and we have an area of .025 under the right tail; so the cutoff value of Z is 1.96. Conclusion: The p = x/n = 31/50 = 0.62. The value of the test statistic is Z = 697 . 1 071 . 0 12 . 0 50 ) 5 . 0 1 ( 5 . 0 5 . 0 62 . 0 = = - - . This means that the Z statistic does not fall in the rejection region, so we cannot reject Ho. We cannot claim the hospital is exceeding the benchmark. 2. An insurance company’s procedure in settling a claim under $10000 is to require two estimates before allowing the insured to proceed with the work. The insurance company compares estimates from two contractors (A and B) for the 10 most recent estimates and finds that the mean difference ( d ) is $-240 with a standard deviation of $327. At the 0.05 level of significance is there a difference between the two contractors?
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