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252HW2Soln

# 252HW2Soln - Statistics 252 Homework#2 Solutions Summer...

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Statistics 252 – Homework #2 Solutions – Summer 2011 STAT 252 Homework 2 Solutions (30 marks) – Due Monday, July 18 at 10 pm 1. (3 marks) A psychology student, interested in the migratory eating habits of human organisms during the lunch hour upon the university campus, sections “Quad” into six sections. Over the course of two full weeks, the student measured the organism concentration for each day in each section. Set up the null and alternative hypotheses to test for any difference between the average concentrations of humans among the sections. What is the distribution of the test statistic under the null hypothesis? Define : μ i = average concentration of humans from i th section, i = 1, …, 6 Given : I = 6, N = 6 × 14 = 84. H 0 : All sections have the same average concentration. Æ All means are equal (One-Mean model: μ 1 = μ 2 = μ 3 = μ 4 = μ 5 = μ 6 Æ μ ) H A : Not all sections have the same average concentration. Æ Not all means are equal (Six-Mean model: μ 1 , μ 2 , μ 3 , μ 4 , μ 5 , μ 6 ) 1 ) ( ) ( ) ( 0 ~ = I I N f df r df f df F F F (since the test is a One-Factor ANOVA F -test) Thus, the distribution of the test statistic under H 0 is 5 78 F . 2. (3 marks) Consider a situation where there are nine sections of Statistics 252. There are three instructors and each instructor teaches three sections. Each section has 50 students enrolled. Define the null and alternative hypotheses for the test to determine if any instructor has different marks between their own sections. What is the distribution of the test statistic under the null hypothesis? Define : μ i = average mark from i th section, i = 1, …, 9 Also, let the instructors be instructor A, B, and C. Let μ 1 , μ 2 , and μ 3 be the means for the three sections for instructor A.

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252HW2Soln - Statistics 252 Homework#2 Solutions Summer...

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