# 11_09_11ans - STAT 409 1 Fall 2011 Examples for The...

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STAT 409 Examples for 11/09/2011 Fall 2011 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
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## This note was uploaded on 11/15/2011 for the course STAT 409 taught by Professor Stephanov during the Fall '11 term at University of Illinois at Urbana–Champaign.

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11_09_11ans - STAT 409 1 Fall 2011 Examples for The...

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