Notes - Chapter 09 - MGMT 2340 Section W01 Business Statistics I Instructor E Mark Leany contact via Blackboard online.uen.org alternately

# Notes - Chapter 09 - MGMT 2340 Section W01 Business...

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MGMT 2340 Section W01 Business Statistics I Instructor: E. Mark Leany contact via Blackboard online.uen.org alternately: [email protected] Estimation and Confidence Intervals Chapter 9 289 GOALS 1.Define a Point Estimate2.DefineLevel 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 ı 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 –ıKnown1.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 samplenXVV!= sample meanz= z -value for a particular confidence levelı= the population standard deviationn= the number of observations in the sampleX294Example: Confidence Interval for a Mean ıKnownThe 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:1.What is the population mean? 2.What is a reasonable range of values for the population mean? 3.What do these results mean?  • • • 