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# sol1 - MAT 3378 3X Spring 2010 Assignment 1 solutions Total...

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MAT 3378 3X - Spring 2010 Assignment 1 - solutions Total = 20 points Question 1: [6 points] 1. An automotive engineer was interested in the effect of four alternative rubber compounds on the life of automobile tires. To carry out the study, five tires were manufactured from each of the four compounds and five automobiles were obtained for testing. With each automobile, the four tire types were assigned at random to the four wheels. Each automobile was driven for 40,000 miles and the amount of wear on each of the four tires was recorded. (a) What type of study is this, experimental, observational, or mixed? Why? (b) What is the basic unit of study? (c) What factors and factor levels are being studied here? (d) Suppose that six compounds were under study instead of four. What type of study design is suggested? solution: (a) The compound is randomly assigned to a wheel on the car. So com- pound is an experimental factor. The automobile might effect the wear of the tires, so it can be considered as a factor. This factor is observational. Hence it is a mixed study. (b) We are assigning a tire made with a particular compound to a wheel on the automobile. So the wheel on the automobile is the basic unit of study. (c) The compound is an experimental factor with 4 levels. The automo- bile is an observational factor. (d) If we consider the automobile as a block, within this block we are randomly assigning the four treatments to the units which are the wheels. So it is a randomized complete block design. It is also a repeated measures design. However with 6 treatments, then within a block we cannot assign all the treatments to the units, since there are only four units within a block. Hence it is an incomplete block design. 1

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2. A rehabilitation center was interested in examining the relationship be- tween physical fitness prior to surgery of persons undergoing corrective knee surgery and the time required in physical therapy until successful rehabilitation. Data on the number of days required for successful com- pletion of physical therapy and the prior physical fitness status (below average, average, above average) were collected.
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