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# hw10 - ORIE 360/560 Fall 2007 Assignment 10 Due Tuesday Nov...

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ORIE 360/560 Fall 2007 Assignment 10 Due Tuesday, Nov. 27 at 2:00 pm Problem 1. Consider a normal ( μ, σ 2 ) population distribution with the value of σ 2 known. (a) What is the confidence level for the interval ¯ x ± 2 . 81 σ/ n ? (b) What is the confidence level for the interval ¯ x ± 1 . 44 σ/ n ? (c) What value of z α/ 2 gives a 99.7% confidence level in the confidence interval formula? (d) How large a sample size (i.e., what value of n ) is necessary for a 95% confidence level confidence interval of width 1? Of width 1/2? Of width 2? (e) What value of n is necessary for a confidence interval of width 1 at the 90% confidence level? At the 99% 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 have to report a whole lot of 95% confidence intervals. In fact, during the month of August, you reported 1,000 such confidence intervals. Let Y be the number of confidence intervals you reported in August which actually contained the true mean for the particular problem you were working one.
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