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Unformatted text preview: Stat 226 Homework 8 Fall 2011 Due Thu, October 20th in class Answer problems 1, 2 and 3 via the online submission in Blackboard. Written solutions to problems 1, 2, and 3 will NOT be accepted. Problems 4 and 5 should be handwritten and turned in at the beginning of class on Thursday, October 20th. All problems are given below and should be solved BEFORE opening the online assessment, as you will only have 2 hours to enter your answers. You have 3 attempts to submit the online homework portion of your homework. Your last score will be recorded in the grade book. Online portion of the assignment is due by 5pm on Thursday, October 20th. Beginning of the online portion 1. Backward Normal Calculations for ¯ X . A confidence interval for the population mean μ is essentially a backwards Normal calculation from the sampling distribution of ¯ X . Suppose that the distribution of monthly utility costs at your local Orangefly’s restaurant is Normal with mean μ = $2 , 300 and standard deviation σ = $150. A random sample of 9 monthly utility costs is collected. (a) What is the mean and standard error of the sampling distribution of ¯ X for samples of size 9? (b) What mean value of 9 random monthly costs corresponds to the 97.5 percentile? Do not use the 689599.7 rule to answer this problem. (c) The middle 95% of sample mean monthly utility costs ( n = 9) will be between what two values? Do not use the 689599.7 rule to answer this problem. 2. Critical Values. As we learned in class, the critical value z * in the formula for a level C confidence interval is the value that captures the central C % area under the standard Normal curve between z * and z * . Find the critical values for confidence intervals with the following confidence levels: (a) 39% (b) 77% (c) 92% (d) What happens to the size of the critical value z * as you increase the confidence level? i. It stays the same. ii. It varies unpredictably. iii. It decreases. iv. It increases. 1 3. Confidence Intervals. In reality, we do not know Orangefly’s true mean monthly cost of utilities. However, we can estimate reasonable mean monthly utility costs, μ , with a certain level of confidence, C . Assume n = 9 monthly utility costs were randomly drawn from the population, and a sample mean of $2,689 was calculated. Under the assumption that σ = $150, calculate confidence intervals for μ with the following confidence levels: (a) C = 39% (b) C = 77% (c) C = 92% (d) What happens to the width of the interval as you increase the confidence level?(d) What happens to the width of the interval as you increase the confidence level?...
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This note was uploaded on 10/20/2011 for the course STAT 226 taught by Professor Abbey during the Spring '08 term at Iowa State.
 Spring '08
 ABBEY
 Statistics

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