# QMS202 Lecture 6 Related Means & F Test - Business...

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Business Statistics II QMS202 Lecture 6 Paired Differences; F-TEST. Instructor: Irwin Pressman [email protected] 1 CQMS 202
Why Study Differences between Means of Two Populations To compare and contrast the differences between two populations: compare and contrast these similarities and dissimilarities. TO MAKE DECISIONS IN A SCIENTIFIC, UNBIASED MANNER . § For example: By how much do they differ in size, or mass, or age? By how much do two products differ in C Q M S 2 0 2
CQMS 202 Two-Sample Tests Population Means, Independent Samples Population Means, Related Samples Population Variances Group 1 vs. Group 2 Same group before vs. after treatment Variance 1 vs. Variance 2 Examples: Population Proportions Proportion 1 vs. Proportion 2 \$\$\$ You must be able to recognize which test is needed from the facts available. This represents a major part of what you will be tested on!
Mini Review: Hypothesis Tests for Two Population Means H0: µ1=µ2 H1: µ1≠µ2 1. standard deviation known: Use Z test 2. standard deviation NOT known use t- test a) (POOLED ON) CASE : we can assume that σ1=σ2 , i.e., std. dev. equal, so use pooled variance b) (POOLED OFF) CASE : we don’t assume that σ1=σ2 , i.e., std. devs are not not equal, so use the Welch technique of computing the variance SPECIAL CASE: Related Populations: The CQMS 202
RELATED POPULATIONS This is a brand new different test! IMPORTANT! It makes the assumption that we can “pair” each reading; e.g., weigh a person before running a marathon and after running it. Repeat for 30 people. We have EXTRA information here! H0: µ1=µ2 mean weight before= mean weight after H1: µ1≠µ2 This has greater POWER than the previous CQMS 202
C Q M S 2 0 2 Related Populations: The Paired Difference Test . Let X 1i  be the score of the ith individual on the 1st test;  let X2i be the score of the ith individual on the 2nd test.    The i th paired difference is D i , where Related samples: e.g., math scores of a group of students before and after drinking a can of RED BULL. D i = X1i -  X2i The point estimate for the paired difference population mean μD is D : n is the number of pairs in the paired sample The sample standard deviation is SD D = D i i = 1 n å n S D = (D i - D ) 2 i = 1 n å n - 1
Examples  take 60 pairs of people  in Halifax & Regina  matched by sex, age and income and measure  how many hours a week they spend watching TV shop for a litre of gasoline and get prices at 33  stations in 2 cities– eg London and Kitchener–  matched by dealer name,  e.g.,ESSO, PetroCan find weights of 45 new members at a Weight  Watchers clinic before and after 3 months of  visits. CQMS 202
C Q M S 2 0 2 The test statistic for μD Paired samples where tSTAT has df=n–1 The Paired Difference Test: Finding tSTAT THIS IS EASY: All we have to do is a simple t-test as before!
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