MGMT 2340 Section W01Business Statistics IInstructor: E. Mark Leanycontact viaBlackboardonline.uen.orgalternately:[email protected]Estimation and Confidence IntervalsChapter 9289
GOALS1.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..289Why Sample the Population?1.To contact the whole population would be time consuming.2.Thecostof studying all the items in a populationmay be prohibitive.CENSUS3.Thephysical impossibilityof checking all items in the population.4.Thedestructive natureof some tests.5.Thesample resultsareadequate.258
Point and Interval EstimateszApoint estimateis a single value (point) derived from a sample and used to estimate a population value.–is a point estimateof the population mean–p is a point estimateof the population proportionzAconfidence interval estimateis 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.290X)(P)(SFactors Affecting Confidence Interval EstimatesThe factors that determine the width of a confidence interval are:1.Thesample size,n.2.Thevariability in the population, usually ıestimated by s.3.The desired level of confidence.293
Interval Estimates - InterpretationFor 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 population295How to Obtain z value for a Given Confidence LevelThe95 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?