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11_16_09ans - STAT 409 1 Fall 2009 Examples for The...

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STAT 409 Examples for 11/16/2009 Fall 2009 1. The following is a random sample from a certain population: 24 19 17 12 20 11 22 15 22 26 18 We wish to test H 0 : m = 17 vs. H 1 : m > 17, where m is the population median. a) Use the sign test. What is the p-value of this test? x 24 19 17 12 20 11 22 15 22 26 18 x – 17 7 2 0 5 3 6 5 2 5 9 1 3 negative differences out of 10 (non-zero). p-value = P ( Y 3 ) , where Y has a Binomial distribution with n = 10, p = 0.50 = 0.1719 . p-value > α Do NOT Reject H 0 . b) Use the (Wilcoxon) signed-rank test. What is the p-value of this test? 0 1 2 2 3 5 5 5 6 7 9 1 2.5 2.5 4 6 6 6 8 9 10 W = 1 – 2.5 + 2.5 + 4 – 6 + 6 + 6 – 8 + 9 + 10 = 22 . Z = 6 21 11 10 0 22 - = 1.12 . p-value = P ( Z 1.12 ) = 0.1314 . p-value > α Do NOT Reject H 0 . With a unit correction for continuity: Z = 6 21 11 10 0 21 - = 1.07 . p-value = P ( Z 1.07 ) = 0.1423 .
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2. A and B are two fast food restaurants located across the street from one another. They are extremely competitive and closely monitor each other’s business in terms of number of customers served. The number of customers served at each
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