ORIE 360/560 Fall 2007Assignment 10Due Tuesday, Nov. 27 at 2:00 pmProblem 1.Consider a normal (μ, σ2) population distribution with the value ofσ2known.(a) What is the confidence level for the interval ¯x±2.81σ/√n?(b) What is the confidence level for the interval ¯x±1.44σ/√n?(c) What value ofzα/2gives a 99.7% confidence level in the confidence interval formula?(d) How large a sample size (i.e., what value ofn) is necessary for a 95% confidence level confidence intervalof width 1? Of width 1/2? Of width 2?(e) What value ofnis necessary for a confidence interval of width 1 at the 90% confidence level? At the99% confidence level? At the 99.9% confidence level?Problem 2.Suppose you are a statistical consulatant for a large consulting firm. In your job, you haveto report a whole lot of 95% confidence intervals. In fact, during the month of August, you reported 1,000such confidence intervals.LetYbe the number of confidence intervals you reported in August which actually contained the true meanfor the particular problem you were working one.
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