TwoSampleComparison

TwoSampleComparison - Two Sample Comparisons Part 1 Chapter...

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1 Two Sample Comparison - I 1 Two Sample Comparisons Part 1 Chapter 10 Two Sample Comparison - I 2 Comparison Problems Take a sample from two separate populations. Compare the statistics (???) of interest. Are the statistics different enough for us to say there is a difference in the populations?

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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: μ 1 and σ 1 Sample 1: n 1 X-bar 1 and S 1 For population 2, use n 2 etc.

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4 Two Sample Comparison - I 7 Comparing population means We might want to estimate the difference ( μ 1 - 2 )us ing the samp le data. Or, it could be a test H 0 : 1 = 2 The test can be restated H 0 : 1 - 2 = 0 so it is almost the same problem Two Sample Comparison - I 8 Estimating the difference Because we want to estimate 1 2 ) we need to know something about the distribution of ( X-bar 1 -X-bar 2 ) We will first look at the (unlikely?) case when we know σ 1 and 2 .
5 Two Sample Comparison - I 9 Theory 2 2 2 1 2 1 1 ) ( 2 n n x x Var σ + = - From theory about functions of random variables, we would just combine the two standard errors Two Sample Comparison - I 10 Confidence interval A confidence interval is generated by: Where the ME is given by: ME x x ± - ) ( 2 1 2 2 2 1 2 1 2/ n n Z ME α + =

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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 0 : μ 1 - 2 = D 0 H 1 : 1 - 2 D 0 where D 0 = 0 (no difference). Two Sample Comparison - I 12 The test statistic Compute: Decision rule: At α = .05, Reject H 0 if Z CALC > 1.96 or if Z CALC < -1.96 2 2 2 1 2 1 0 2 1 ) ( n n D x x Z σ + - - =
7 Two Sample Comparison - I 13 Waiting times at O’Marios At O’Marios 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. 1. Test to determine if there was a difference 2. Estimate the average difference. Two Sample Comparison - I 14 Hypothesis Test Hypotheses: Decision Rule: Results:

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8 Two Sample Comparison - I 15 Interval estimation Interval: Interpretation: Two Sample Comparison - I 16 Population Variances Unknown If you don’t know the means, how would you know σ 1 and 2 ?
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This note was uploaded on 02/12/2011 for the course QMB 3250 taught by Professor Thompson during the Spring '08 term at University of Florida.

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TwoSampleComparison - Two Sample Comparisons Part 1 Chapter...

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