ISYE3039+spring+2013+hw1+sol

# Saltwater quench oil quench 145 152 150 150 153 147

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Saltwater Quench Oil Quench 145 152 150 150 153 147 148 155 141 140 152 146 146 158 154 152 139 151 148 143 (a) Test the hypothesis that the mean hardness for the saltwater quenching process equals the mean hardness for the oil quenching process. Please use α=0.05 and assume equal variances. (b) Assuming that the variances and are equal, construct a 95% confidence interval on the difference in mean hardness. (c) Construct a 95% confidence interval on the ratio. Does the assumption made earlier of equal variances seem reasonable? Solution: Saltwater quench:

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Oil quench: (a) Assume Do not reject H 0 , and conclude that there is no difference between the quenching processes. (b) (c) Since the interval of the ratio does include 1, the equal variance assumption is reasonable. Problem 5 Solution: (a) (b)
(c) Problem 6:

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Solution: This is a hypergeometric distribution with N = 25 and n = 5, without replacement. (a) Given D = 2 and x = 0: (b) For the binomial approximation to the hypergeometric, and n = 5. This approximation, though close to the exact x = 0, violates the rule-of-thumb that be less than the suggested 0.1. The binomial approximation is not satisfactory in this case. (c) For, so the binomial approximation would be a satisfactory approximation the hypergeometric in this case.
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