Class Meeting 19

Class Meeting 19 - CHEN 3010 Applied Data Analysis Class...

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1 CHEN 3010 Applied Data Analysis Class Meeting #19 Tuesday, Nov. 2 nd Today's Topics Reading for Thursday: pages 109 - 235 Reminder: Mid term #2 on Tuesday, Nov. 9 th Two old Mid term tests posted on the web Inference on two population proportions Analysis of Variance
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2 Problem 5-50 Two different types of injection-molding machines are used to form plastic parts. A part is considered defective if it has excessive shrinkage or is discolored Two random samples, each of size 300, are selected, and 15 defective parts are found in the sample from machine 1 whereas 8 defective parts are found in sample from machine 2 Is it reasonable to conclude that both machines produce the same fraction of defective parts, using α = 0.05? Find the P-value. Problem 5-51 Consider the situation described in Problem 5-50. Suppose that p 1 = 0.05 and p 2 = 0.01. (a) With the sample sizes given here, what is the power of the test for this two-sided alternative? (b) Determine the sample size needed to detect this difference with a probability of at least 0.9. Use α = 0.05
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3 p p 1 2 = p p 1 2 z p p p p n n 0 1 2 1 2 1 1 1 = + ( ) p x x n n = + + 1 2 1 2 z 0 025 . z 0 025 . z 0 025 . z 0 025 . n 1 = n 2 = x 1 = x 2 = p 1 = p 2 = . p = + + = 15 8 300 300 00383 z 0 005 00267 00383 1 00383 1 300 1 300 149 = + = . . . ( . ) . 5-50. 1) the parameters of interest are the proportion of defective parts, p 1 and p 2 2) H 0 : 3) H 1 : 4) α = 0.05 5) Test statistic is where 6) Reject the null hypothesis if z 0 < where = 1.96 or z 0 > where = 1.96 300 300 15 8 0.05 0.0267 8) Since 1.96 < 1.49 < 1.96 do not reject the null hypothesis and conclude that yes the evidence indicates that there is not a significant difference in the fraction of defective parts produced by the two machines at the 0.05 level of significance.
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Class Meeting 19 - CHEN 3010 Applied Data Analysis Class...

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