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Chapter 2 Exercises Solutions

Chapter 2 Exercises Solutions - Stat 332 R.J MacKay...

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Stat 332 R.J. MacKay, University of Waterloo, 2005 Chapter 2 Solutions-1 Chapter 2 Solutions to the Exercises 1. Look at the description of the investigation to compare two versions of the same Web page (http://www.dack.com/web/flashVhtml/). Use the notion of study error to criticize the conclusion that the Flash version is inferior to the HTML version. The target population is all web users who may wish to purchase items from the store. The study population appears to be employees from the author’s workplace many of whom are CS experts. There is a strong possibility of study error since the study population is likely to be much more proficient using either version than the target population 2. In a marketing investigation, a large supermarket chain wants to look at the effect of shelf placement for three brands of coffee. There are three shelf positions top, middle and bottom. a) Explain why there are 6 different treatments. The treatments are vertical arrangements of three letters A, B, C corresponding to the three brands. There are 3!=6 such arrangements. For a given treatment, the response variate is the total sales ($) over a one week period. There are 24 stores available. b) Describe an experimental plan that does not involve blocking – be sure to discuss randomization and replication. Divide the 24 stores into 6 groups of 4 at random. Then assign a different treatment to each group. Note that there are 4 units (replication) within each group. c) Repeat b) but include blocking in your plan. Divide the stores into 4 blocks of 6 based on some explanatory variate such as previous weekly average sales. Within each block this explanatory variate should be as constant as possible but it can vary between the blocks. Then, within each of the 4 blocks, assign the 6 treatments at random to the six stores. Note that each treatment is applied to 4 stores, one per block (replication). d) Compare the two plans. Blocking is useful to avoid confounding and to increase the precision of the treatment comparisons. It may cost a small amount to gather the information needed to form the blocks but it is almost always worthwhile. 3. To compare a distance education option versus a traditional lecture version of a course, a common examination is administered and the grades of the students are compared. The data are summarized below. style number of students average st dev lecture 47 71.3 10.2 distance ed 36 68.7 11.3
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Stat 332 R.J. MacKay, University of Waterloo, 2005 Chapter 2 Solutions-2 a) Is there any evidence of a difference in student performance with the two styles? Be sure write down the model you use. To model the data, we have Y R R G i j n ij i ij ij i = + = = μ σ , ~ ( , ), , ; ,..., 0 1 2 1 where n n 1 2 47 36 = = , . The estimates of the model parameters are $ . , $ . , $ . . . μ μ σ 1 2 2 2 713 68 7 46 10 2 35 113 46 35 10 7 = = = × + × + = See Question 6(a) for the formula for $ σ . To answer the question, we use a test of the hypothesis that θ μ μ = - = 2 1 0. The steps are Suppose that the hypothesis is true i.e.
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