In 2005 Congress passed the Bankruptcy Abuse Prevention and

In 2005, Congress passed the Bankruptcy Abuse Prevention and Consumer Protection Act. This Act made significant changes to the administration of bankruptcy relief. The Government Accountability Office (GAO) was commissioned to study the effects of the bankruptcy reform law on consumers. Attorney fees in consumer bankruptcy cases were studied by the GAO and reported in their 2008 Bankruptcy Reform report. In the period February to March 2007 there were 71,106 Chapter 7 consumer bankruptcy cases. To estimate the legal fees for Chapter 7 consumer bankruptcy cases, the GAO conducted a nationwide random sample of Chapter 7 consumer bankruptcy filings. Business bankruptcy cases not involving attorneys were excluded. In the end, the GAO had the sample size, n=292 consumer cases with attorney involvement. The mean attorney fee in the sample is x = $1078 and the standard deviation is s=$592. For 95% confidence interval, the z-score (from Standard Normal Probabilities table) is 1.96 Note: For this large sample, we assume x = and we use Standard Norm al Distribution. For smaller sample sizes (n30 ) we use t-distribution. The margin of error m= z^* /n=1.96 592/292=67.9 So, 95% confidence interval for the mean of the whole population () is: x ±67.9=1078±67.9=(1010.10,1145.90) The margin of error for 95% confidence interval (as calculated above): = z^* /n=1.96 592/292=67.9 If we wish to answer the question: “What should be the sample size if we want the margin of error to be $100 (instead of $67.90)”, then the desired sample size can be calculated as follows: n=((z^* )/m)^2=((1.96*592)/100)^2=134.6 So a sample size of 135 should be chosen. Calculate the sample size for a margin of error of $100 for various confidence intervals and complete the following table: Confidence Interval Sample Size 99.96%_____ 99%_____ 95%_135_ 90%______ 80%_____

Solution

at 99.96% confidence Z= 3.352 hence n = ((3.352*592)/100)^2 = 393

99% Z= 2.58 hence n = 233

90% Z = 1.645 hence n = 95

80% Z= ,8416 hence n = 25