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two sample comparison noteshells

# two sample comparison noteshells - 1 Two Sample Comparison...

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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 on-line 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 X-bar 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 ( X-bar 1- X-bar 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 &amp;gt; 1.96 or if Z CALC &amp;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 Irish-Italian 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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two sample comparison noteshells - 1 Two Sample Comparison...

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