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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 on-line 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 on-line assessment, as you will only have 2 hours to enter your answers. You have 3 attempts to submit the on-line homework portion of your homework. Your last score will be recorded in the grade book. On-line portion of the assignment is due by 5pm on Thursday, October 20th. Beginning of the on-line 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 68-95-99.7 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 68-95-99.7 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