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Chapter 9 Review 2008 Solution

Chapter 9 Review 2008 Solution - CHAPTER 9 INFERENCES...

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CHAPTER 9 INFERENCES CONCERNING PROPORTIONS SPRING 2008 STA 3032 Large Sample (1- α) 100% Confidence Interval for a population proportion (p) n q p Z p Z p p ˆ ˆ ˆ ˆ 2 / ˆ 2 / α α σ ± ± where p ˆ is the sample proportion of observations with the characteristic of interest and p q ˆ 1 ˆ - = ; 15 ˆ p n and 15 ˆ q n Example: In a sample of 295 steel alloy failures that occurred in oil refineries and petrochemicals plants in Japan over the last 10 years, 118 were caused by stress corrosion cracking and corrosion fatigue. Construct a 95% CI for the true proportion of alloy failures caused by stress corrosion cracking. 1
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Determination of the sample size If p is known, the sample is: 2 2 / = E Z pq n α where E is the maximum error of estimate or the half-width of the confidence interval.. If the p is unknown, p is equal to 0.5 and sample size is: 2 2 / 4 1 = E Z n α 2
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Large Sample (1- α) 100% Confidence Interval for two population proportions (p 1 -p 2 ) 2 2 2 1 1 1 2 / 2 1 ) ˆ ˆ ( 2 / 2 1 ˆ ˆ ˆ ˆ ) ˆ ˆ ( ) ˆ ˆ ( 2 1 n q p n q p Z p p Z p p p p + ± - ± - - α α σ where p ˆ
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