# OSU BUSMGT 2320 - s_4_Comparisons [mu] Autumn 2014 (37 pages)

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## s_4_Comparisons [mu] Autumn 2014

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- Pages:
- 37
- School:
- Ohio State University
- Course:
- Busmgt 2320 - Decision Sciences: Statistical Techniques

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Lecture 4 Comparing Two Groups If you don t know where you re going any road will take you there C S Lewis 1898 1963 1 Learning Objectives 1 Be able to identify the various approaches for comparing two populations with respect to the mean Paired matched Samples Independent Samples Population variances known Population variances unknown Assumed equal Assumed unequal Learning Objectives 2 Know the parameter and the corresponding sample statistic for each of the approaches for comparing two populations with respect to the mean 3 Understand the sampling distribution for each of the sample statistics used to compare two populations with respect to the mean 4 Understand and be able to calculate a pooled variance estimate of 2 3 Learning Objectives 5 Be able to construct the appropriate 1 confidence interval estimate of both D and 1 2 6 Be able to conduct appropriate hypothesis tests for both D and 1 2 4 Terminology Matched paired Samples D sD nD X D Independent Samples 1 2 and X 1 X 2 Pooled Variance Estimate sp2 Satterthwaite Approximation 5 INTRODUCTION 6 Selecting the Case All Classical applications require SRS and Normal distribution for the sample statistic Type of data Quantitative use means and standard deviations Nominal use proportions Number of populations groups How was the data collected For example Paired or Independent Samples What assumptions can be made For example equal or unequal population variances 7 Selecting the Case Means quantitative data One Group See lectures 1 3 Population Variances Unknown Independent Samples Parameter 1 2 Statistic X 1 X 2 Two Groups Paired Samples Use Di X1i X2i Parameter D XD Statistic Population Variances known Use Z X1 X 2 Assumed Use Satterthwaite t Approximation S X1 X 2 s12 s22 n1 n2 Assume Use t n1 n2 2 SX 1 X2 s 2p n1 s 2p n2 12 22 n1 n2 8 Matched Samples v Independent Samples Nike wants to see if there is a difference in the durability of 2 sole materials 1 One type of material is placed on one shoe the other type on

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