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Unformatted text preview: MGMT 2340 Section W01 Business Statistics I Instructor: E. Mark Leany contact via Blackboard online.uen.org alternately: professorleany@gmail.com Estimation and Confidence Intervals Chapter 9 289 GOALS 1. Define a Point Estimate . 2. Define Level of Confidence . 3. Construct a confidence interval for the population mean when the population standard deviation is known. 4. Construct a confidence interval for a population mean when the population standard deviation is unknown. 5. Construct a confidence interval for a population proportion. 6. Determine the sample size for attribute and variable sampling. 289 Why Sample the Population? 1. To contact the whole population would be time consuming . 2. The cost of studying all the items in a population may be prohibitive . CENSUS 3. The physical impossibility of checking all items in the population. 4. The destructive nature of some tests. 5. The sample results are adequate . 258 Point and Interval Estimates z A point estimate is a single value (point) derived from a sample and used to estimate a population value. is a point estimate of the population mean p is a point estimate of the population proportion z A confidence interval estimate is a range of values constructed from sample data so that the population parameter is likely to occur within that range at a specified probability. The specified probability is called the level of confidence. 290 X ) ( P ) ( S Factors Affecting Confidence Interval Estimates The factors that determine the width of a confidence interval are: 1.The sample size , n. 2.The variability in the population , usually estimated by s. 3.The desired level of confidence . 293 Interval Estimates  Interpretation For a 95% confidence interval about 95% of the similarly constructed intervals will contain the parameter being estimated. Also 95% of the sample means for a specified sample size will lie within 1.96 standard deviations of the hypothesized population 295 How to Obtain z value for a Given Confidence Level The 95 percent confidence refers to the middle 95 percent of the observations. Therefore, the remaining 5 percent are equally divided between the two tails. Following is a portion of Appendix B.1. 292 Point Estimates and Confidence Intervals for a Mean Known 1. The width of the interval is determined by the level of confidence and the size of the standard error of the mean. 2. The standard error is affected by two values: Standard deviation Number of observations in the sample n X V V ! = sample mean z = z value for a particular confidence level = the population standard deviation n = the number of observations in the sample X 294 Example: Confidence Interval for a Mean Known The American Management Association wishes to have information on the mean income of middle managers in the retail industry. A random sample of 256 managers reveals a sample mean of $45,420. The standard deviation of this population is $2,050. The association would like answers to the following questions:...
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 Winter '11
 Leany

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