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Chapter 13

School

York UniversityDepartment

Operations Management and Information SystemCourse Code

OMIS 2010Professor

Alan MarshallChapter

13This

**preview**shows half of the first page. to view the full**3 pages of the document.**Chapter 13: Inference about Comparing Two Populations

Inference about Difference between Two Means: Independent Samples

-To test and estimate difference between two population means, draw random samples from each of two

populations

-Independent samples: samples completely unrelated to one another

oDraw sample of size n1 from pop. 1 and n2 from pop. 2

oBest estimator of difference between two means is difference between two sample means

Sampling Distribution of “x bar 1 – x bar 2”

-This is normally distributed if pop. Are normal

-Approx. normal if pop. Are non-normal and sample sizes are large

-E(x-bar 1 – x-bar 2) = Mean 1 – Mean 2

-Estimate std. error of sampling distribution

-When unknown variances are equal, follow the “s2p” formula

o“s2p” is pooled variance estimator

oWeighted average of two sample variances with # of degrees of freedom in each sample

used as weights

oProduces better estimates by combining both samples

oPop. Must be normal or approx. normal

-Estimate pop. Variance with sample variance when pop. Variances not equal

-Conduct F-test to determine whether there is evidence to infer that population variances differ

oTest statistic is ratio of sample variances; F-distributed

oBoth pop. Must be normally distributed

Violation of Required Condition

-When not normally distributed, use nonparametric technique

Data Formats

-Un-stacked: observations from sample 1 stored in one column and observations from sample 2 stored

in second column

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