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Chapter 10 Two-Sample Hypothesis Tests

Chapter 10 Two-Sample Hypothesis Tests - Two-Sample...

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Click to edit Master subtitle style © Professor Thomas R. Sexton 11 Two-Sample Hypothesis Tests Professor Thomas R. Sexton College of Business Stony Brook University
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© Professor Thomas R. Sexton 22 Referral to Cardiac Rehabilitation Patients who have had a heart attack or cardiac surgery should be referred to a cardiac rehabilitation program. Does placing a physician reminder in the patient’s medical chart increase the likelihood of referral? No reminder: nB = 300, XB = 120, 40% referred Reminder: nA = 200, XA = 90, 45% referred
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© Professor Thomas R. Sexton 33 Our Test Statistic Our test should look like this: Question: What should we use for the SE of the difference in sample proportions?
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© Professor Thomas R. Sexton 44 The Pooled Proportion We have πA = πB under the null hypothesis. Therefore, we compute the pooled sample proportion:
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© Professor Thomas R. Sexton 55 The Test Statistic + - - = B A P P B A calc n n p p p p Z 1 1 ) 1 ( is statistic test The
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© Professor Thomas R. Sexton 66 Testing the Hypotheses
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© Professor Thomas R. Sexton 77 SX Dialog Box
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© Professor Thomas R. Sexton 88 SX Output Two-Sample Proportion Test Sample 1 Sample 2 Sample Size 200 300 Successes 90 120 Proportion 0.45000 0.40000 Null Hypothesis: P1 = P2 Alternative Hyp: P1 > P2 Difference 0.05000 SE (diff) 0.04506 Z (uncorrected) 1.11 P 0.1336 Z (corrected) 1.02 P 0.1545 Fisher's Exact 0.1545 95% Confidence Interval of Difference Lower Limit -0.03831 Upper Limit 0.13831
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© Professor Thomas R. Sexton 99 Production Rework A company manufactures a sensitive motion detector and wants to reduce the rework rate. Before: 60 out of 400 units require rework. Company changes its production process. After: 50 out of 500 units require rework. Have the changes to the production process reduced the rework rate?
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© Professor Thomas R. Sexton 10 10 Testing the Hypotheses
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© Professor Thomas R. Sexton 11 11 SX Dialog Box
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© Professor Thomas R. Sexton 12 12 SX Output Two-Sample Proportion Test Sample 1 Sample 2 Sample Size 500 400 Successes 50 60 Proportion 0.10000 0.15000 Null Hypothesis: P1 = P2 Alternative Hyp: P1 < P2 Difference -0.05000 SE (diff) 0.02197 Z (uncorrected) -2.28 P 0.0114 Z (corrected) -2.17 P 0.0149 95% Confidence Interval of Difference Lower Limit -0.09377 Upper Limit -0.00623
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© Professor Thomas R. Sexton 13 13 Marital Status and Automobile Crashes An insurance company wants to know if there is a difference in automobile crash rates for single drivers relative to married drivers. 120 of 400 single drivers had at least one accident in the past three years. 150 of 600 married drivers had at least one accident in the past three years.
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© Professor Thomas R. Sexton 14 14 Testing the Hypotheses
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© Professor Thomas R. Sexton 15 15 SX Dialog Box
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© Professor Thomas R. Sexton 16 16 SX Output Two-Sample Proportion Test Sample 1 Sample 2 Sample Size 400 600 Successes 120 150 Proportion 0.30000 0.25000 Null Hypothesis: P1 = P2 Alternative Hyp: P1 <> P2 Difference 0.05000 SE (diff) 0.02866 Z (uncorrected) 1.74 P 0.0810 Z (corrected) 1.67 P 0.0945 95% Confidence Interval of Difference Lower Limit -0.00617 Upper Limit 0.10617
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© Professor Thomas R.
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