MSci609_Quiz_5

MSci609_Quiz_5 - Department of Management Sciences Faculty...

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Unformatted text preview: Department of Management Sciences Faculty of Engineering University of Waterloo MSci 609 Quantitative data Analysis for Management Sciences QUIZ 5 NAME: ID: Problem A random sample of 300 circuit boards generated 13 defectives. 1. Use the data to test the hypotheses H0 : p = 0.05 versus H1 : p 0.05 , where p is proportion of defected circuit board. Use = 0.05 . Find the P‐value for the test. 2. Use confidence interval test to answer the question in part (1). 3. Do the two tests provide the same conclusions? Solution: a) 1) The parameter of interest is the true fraction defective integrated circuits 2) H0 : p = 0.05 3) H1 : p 0.05 4) = 0.05 5) z 0 conclusion 6) Reject H0 if z0 < z/2 where z/2 = z0.025 = 1.96 or z0 > z/2 where z/2 = z0.025 = 1.96 7) x = 13 n = 300 p x np0 np0 1 p 0 z0 ˆ p p0 or z 0 p 0 1 p 0 n ; Either approach will yield the same 13 0.043 300 x np0 np0 1 p 0 13 300(0.05) 300(0.05)(0.95) 0.53 8) Since 0.53 > 1.65, do not reject null hypothesis and conclude the true fraction of defective integrated circuits is not significantly less than 0.05, at = 0.05. The P‐value: 2(1‐(0.53))=2(1‐0.70194)=0.59612 b) The 95% confidence interval is: ˆ p z / 2 ˆ ˆ p(1 p) ˆ p p z / 2 n ˆ ˆ p(1 p) n 0.043(0.957) 0.043(0.957) p 043 1.96 300 300 0.02004 p 0.065 Since 0.02004 p 0.05 0.065 , then we fail to reject the null hypothesis. .043 1.96 ...
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