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Unformatted text preview: Stat 332 R.J. MacKay, University of Waterloo, 2005 Chapter 4 Solutions -1 Chapter 4 Exercise Solutions 1. Suppose you were asked to help plan an investigation to compare 5 types of road paint with respect to their durability. The response variate is the time from application of a test stripe on a highway until the paint has lost 90% of its brightness. The rest of the planning team has no formal training in statistical planning. a) Explain the notion of blocking in this context. To form a block, we find a set of 5 units (pieces of pavement where we can apply a test stripe) that are similar with respect to explanatory variates other than paint type that may affect durability. For example, we want all the units in a block to experience the same traffic load. b) Why would you recommend blocking? Blocking will prevent confounding by the explanatory variates that are held fixed. For example, by ensuring that the units within a block all experience the same traffic load, we know that we differences in durability among the paint types within the block cannot be attributed to traffic load. Blocking also increases the precision of the treatment comparisons because the residual standard deviation is reduced by holding, for example, the traffic load fixed. c) How might blocking be implemented? We can implement blocking by selecting sections of road that experience different traffic loads, have different pavement types and ages etc. Within each section, we specify 5 units, strips of pavement where we can apply the 5 paint types. A section is a block. 2. A seed company has produced three new varieties of corn using genetic modification. They plan to field test these varieties in south-western Ontario using their current best seller as a control. The trial is for one growing season only. The response variate is the yield, measured in kilograms per hectare. The company has available 60 two hectare test plots scattered throughout the region....
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This note was uploaded on 06/27/2009 for the course STAT 332 taught by Professor Xu(sunny)wang during the Spring '09 term at Waterloo.
- Spring '09