# 420Hw03ans - STAT 420 Fall 2009 Homework #3 (10 points)...

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STAT 420 Fall 2009 Homework #3 (10 points) (due Friday, September 18, by 3:00 p.m.) 1. The friendly folks at the Internal Revenue Service (IRS) are always looking for ways to improve the wording and format of its tax return forms. Three new forms have been developed recently. To determine which, if any, are superior to current form, 120 individuals were asked to participate in an experiment. Each of the three new forms and the currently used form were filled out by 30 different people. The amount of time (in minutes) taken by each person to complete the task was recorded and stored in columns 1 through 4 (forms Form1 through Form4, respectively) in file Hw02_1.csv. c) Use a 95% confidence level and Scheffé’s multiple comparison procedure to compare the average time required to fill forms Form1, Form2, and Form3 with the average time required to fill the current form (Form4). j y 90.16666667 95.76666667 106.8333333 111.1666667 c 1 = 3 1 - c 2 = 3 1 - c 3 = 3 1 - c 4 = 1 MSW = 961.0333333 = = ± 4 1 2 4 1 30 3 0333333 . 961 6828 . 2 j j j j j c y c 13.578 ± 18.541 ( 4.963 , 32.119 )

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2. 4.7 c The makers of “Tasty Tacos” have divided their U.S. market into five regions – Northeast, Mideast, South, Midwest, and West – which have approximately equal populations. They wish to compare their sales performance in the five areas. Data on sales are available for the past 10 months for each region. The data are assumed to be independent samples from normal populations with the same variance but possibly different means. The sales figures are in thousands of tacos. (c) Compare average sales in the West and Midwest with the average sales for the remaining three regions using Scheffé’s multiple comparison procedure. Use a 95-percent confidence level. ( Hint: Consider the contrast: ( 29 ( 29 3 2 1 3 1 5 4 2 1 μ μ μ μ μ + + - + , where μ 1 , μ 2 , … , μ 5 are the mean sales for the regions in the order in which they are listed above. ) j y 25.2 29.5 27.9 34.6 42.7 c j 3 1 - 3 1 - 3 1 - 2 1 2 1 MSW = 45 50 . 459 = 10.21111 = = ± 5 1 2 5 1 10 4 21111 . 10 57874 . 2 j j j j j c y c 11.117 ± 2.963 ( 8.154 , 14.080 )
3. Use Packages > Install Package(s)… to download and install package (library) faraway . Use the infmort data set where Y is income and the grouping variable is region (Asia, Europe, Americas and Africa). > library(faraway)

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## This note was uploaded on 12/17/2010 for the course STAT 420 taught by Professor Stepanov during the Spring '08 term at University of Illinois, Urbana Champaign.

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420Hw03ans - STAT 420 Fall 2009 Homework #3 (10 points)...

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