MT2 and Solutions - 1 ISyE 2028 Spring 2007 Midterm 2...

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1 ISyE 2028 – Spring 2007 Midterm 2 - Friday 03/30/2007 Time: 09:05 - 09:55 Total: 80 points SOLUTIONS Calculators and 1 page, double sided formula sheet are allowed, required statistical tables will be provided. To get partial credit, show all your work. 1. (20 pts) Suppose a sample of 16 wires is selected and each is tested to determine tensile strength. The resulting sample mean and standard deviation are 2160 and 30, respectively. (a) (3 pts) What hypothesis should be tested to determine if the mean tensile strength exceeds 2150? H o : μ 2150 vs H 1 : μ < 2150 (b) (5 pts) Assuming that the tensile strength distribution is approximately normal, what test statistic would you use to test the hypothesis in part (a)? What is the value of this statistic? t = ¯ X - μ o s n = 2160 - 2150 30 16 = 1 . 33 (c) (7 pts) Place bounds on the p-value associated with the value of the test statistic computed in part (b). p-value= P ( X < t ) where X t n - 1 . p-value= P ( X < 1 . 33) = 1 - P ( X > 1 . 33).
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