Chapter 12.docx

4 Pages

Operations Management and Information System
Course Code
OMIS 2010
Alan Marshall

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Chapter 12 Inference About PopulationsInference about a Population Mean When the Standard Deviation is UnknownConfidence interval estimator and test statistic derived from sampling distribution of the sample with mean and sigma knownIf population mean is unknown then so is population standard deviationoSubstitute sample standard deviation s in place of unknown population std devoResult called tstatistic called Student t distributionWhen pop std dev is unknown and pop is normal test statistic for testing hypotheses about the mean is tstatistic formulaoDefined as Student t distributed with vn1 degrees of freedomMath process that derived Student t distribution is robustoIf pop is nonnormal then results of tstatistic and confidence interval estimate still valid as long as pop is not extremely nonnormaloWith large sample size results of ttest and estimator of mean are valid when pop is extremely nonnormalEstimating Totals of Finite Populations For small populations must adjust test statistic and interval estimator using finite pop correction factorPopulations large relative to sample size ignore correction factor 20 times largerFinite populations allow for use of confidence interval estimator of the mean to produce confidence interval estimator of population totaloMultiply LCL and UCL of estimate of mean by population size Developing Understanding of Statistical Concepts 1Student t distribution based on using sample variance to estimate unknown pop varianceDeveloping Understanding of Statistical Concepts 2Tstatistic like zstatistic measures difference between sample mean and hypothesized value of mean in terms ofif standard errors Estimate standard error by ssqrt n when pop std dev Is unknownDeveloping Understanding of Statistical Concepts 2Tdistribution more widely spread out than standard normal
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