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Unformatted text preview: 1 Two Sample Comparison  I 1 Two Sample Comparisons Part 1 Chapter 10 Two Sample Comparison  I 2 Comparison Problems h Take a sample from two separate populations. h Compare the statistics (???) of interest. h Are the statistics different enough for us to say there is a difference in the populations? 2 Two Sample Comparison  I 3 Some Examples 1.Does a soft drink sell better on the end of an aisle than in the middle? 2.Are workaholics more often men or women? 3.How much do people save using an online auto insurance company? Two Sample Comparison  I 4 What we could do: 1.Compare _______ to ________. Goal? 2.Compare _______ to ________. Goal? 3.Compare _______ to ________. Goal? 3 Two Sample Comparison  I 5 Organization of this topic 1. Comparing means, independent populations 2. Comparing means, related populations 3. Comparing proportions 4. Comparing variances 5. Comparing medians (Chapter 12) Two Sample Comparison  I 6 Notation is a little complicated We now have two means, two standard deviations, two sample sizes. We will use subscripts to keep it all straight. Population 1: 1 and 1 Sample 1: n 1 Xbar 1 and S 1 For population 2, use n 2 etc. 4 Two Sample Comparison  I 7 Comparing population means h We might want to estimate the difference ( 1 2 ) using the sample data. h Or, it could be a test H : 1 = 2 h The test can be restated H : 1 2 = 0 so it is almost the same problem Two Sample Comparison  I 8 Estimating the difference h Because we want to estimate ( 1  2 ) we need to know something about the distribution of ( Xbar 1 Xbar 2 ) h We will first look at the (unlikely?) case when we know 1 and 2 . 5 Two Sample Comparison  I 9 Theory 2 2 2 1 2 1 1 ) ( 2 n n x x Var + = From theory about functions of random variables, we would just combine the two standard errors Two Sample Comparison  I 10 Confidence interval h A confidence interval is generated by: h Where the ME is given by: ME x x  ) ( 2 1 2 2 2 1 2 1 2 / n n Z ME + = 6 Two Sample Comparison  I 11 Hypothesis test If we just want to test to determine if there is a difference, we would look at: H : 1 2 = D H 1 : 1 2 D where D = 0 (no difference). Two Sample Comparison  I 12 The test statistic Compute: Decision rule: At = .05, Reject H if Z CALC &gt; 1.96 or if Z CALC &lt; 1.96 2 2 2 1 2 1 2 1 ) ( n n D x x Z + = 7 Two Sample Comparison  I 13 Waiting times at OMarios At OMarios IrishItalian restaurant, the standard deviation in waiting time is 6 minutes. On Thursday night, a sample of 26 customer groups waited an average of 38.5 minutes before being seated. On Saturday night, a sample of 32 groups waited an average of 43.2 minutes....
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 Spring '08
 Thompson
 Standard Deviation, Variance, Statistical hypothesis testing, sample comparison, Med Low High Med High Med Med High Med Local

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