Lec23 - IOE/Stat IOE/Stat 265, Fall 2009 Lecture #23:...

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IOE/Stat 265, Fall 2009 Lecture #23: ectu e 3 Hypothesis Testing for Two Variances nd Two Proportions ad o o p o os Case 5: Tests for 2 Proportions (Section 9-4) Case 6: Tests for 2 Variances 1 (Section 9-5) ase 5: Tests of Two Proportions Case 5: Tests of Two Proportions xamples: ± Examples: ± Test if defect rate from 1st Shift is the same as the efect rate on 2nd Shift. defect rate on 2nd Shift. ± Test if one model has a higher repair rate than another model. ± Key Assumptions ± Require large # samples from each group to use the normal approximation. 2 roportion Test Proportion Test ± Null Hypothesis: H 0 : p 1 - 2 = 0 or 1 = 2 ± Test Statistic: 12 ˆˆ )(1/ 1/ ) o pp z = + (1 n ˆ xx + = ± Alt Hypothesis Reject Region nn + 11 2 1 2 : 0 Hp H zz α −> −< 3 2 / 2 / 2 or oo −≠ xample 1: Molding Machines Example 1: Molding Machines ± Two different injection molding machines are compared. (assume α = 0.05) ± Machine 1: 15 out of 300 are defective (p 1 = 0.050) ± Machine 2: 7 out of 290 are defective (p 2 = 0.024) ± Note: ± Compute Z 0 ± Z α /2 (Z 0 > Z 0.025 = 1.96 or Z 0 < - Z 0.025 = -1.96 ) ± Is it reasonable to conclude that both machines produce the same fraction defective? 4
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tep y tep Approach Step-by-Step Approach ) entify the parameter of interest 1) Identify the parameter of interest. 2) State the Null Hypothesis H 0 . 3) Specify Alt. Hypothesis H 1 . 4) Choose a significance level α . ) g 5) State Test Statistic. 6) State the Rejection Region. 7) Substitute sample statistics and compute. 7 8) State statistical conclusion in problem context. roportion Test Using Minitab Proportion Test Using Minitab TAT asic Statistics Proportions ± STAT » Basic Statistics » 2 Proportions ± Note: Minitab provides p-value ± If p-value α→ Reject H 0 , ± If p-value > Fail to Reject H 0 Test and CI for Two Proportions Sample X N Sample p 1 15 300 0.050000 Are the proportions different?
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This note was uploaded on 03/17/2010 for the course IOE 265 taught by Professor Garyherrin during the Fall '09 term at University of Michigan-Dearborn.

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Lec23 - IOE/Stat IOE/Stat 265, Fall 2009 Lecture #23:...

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