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Chapter 13

OMIS 2010 Chapter Notes - Chapter 13: Test Statistic

Operations Management and Information System
Course Code
OMIS 2010
Alan Marshall

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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
-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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