Chapter 5 Exercises Solutions

Chapter 5 Exercises Solutions - Chapter 5 Exercise...

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Stat 332 R.J. MacKay, University of Waterloo, 2005 Chapter 5 Solutions -1 Chapter 5 Exercise Solutions 1. A large organization is planning a massive retraining of its employees in the use of Office programs. As part of the planning, the HR department considers two factors that might impact the success of the training Factor 1; use of internal versus external trainers Factor 2: use of interactive computer-aided materials versus non-interactive materials To investigate these two factors, a pilot experiment is organized in which 10 employees are randomly assigned to one of the four treatments. Two weeks after the training, each subject in the experiment is given a standard test. a) What does it mean to say that the two factors interact? The factors interact if the effect on test scores of changing from internal to external trainers depends on whether or not computer-aided materials are used b) The HR director pointed out that the cost of the pilot could be substantially reduced if only three treatments were used. Treatment 1: internal trainers, non-interactive materials Treatment 2: internal trainers, interactive materials Treatment 3: external trainers, non-interactive materials The effect of the use of interactive materials can be assessed by comparing treatment 2 to treatment 1. The effect of using external trainers can be assessed by comparing treatment 3 to treatment 1. Write a careful explanation to the Director explaining the drawbacks to this suggestion. If we use your plan, we will not see if there is interaction between the two factors and we may miss a large opportunity to improve the training program. The average test scores could look like Computer aided standard internal 35 32 external 36 We will not know the average score in the missing cell and it would be a mistake to assume that it is around 39 (i.e. that the effect of changing trainers is the same for both types of materials). We may make the wrong decision unless we use all four treatments in the experiment. 2. The manufacturer of a “frost-free” refrigerator found that in a high humidity, high temperature environment that frost did build up inside the fridge. To remedy the problem, a new design was developed and 4 prototypes were built. In an experimental investigation, the 4 prototypes and 4 standard fridges were tested in two environments, one normal and one with high temperature and humidity. Frost build- up was measured after one week’s operation. A lower score is better. The data are shown below.
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Stat 332 R.J. MacKay, University of Waterloo, 2005 Chapter 5 Solutions -2 design condition response design condition response new extreme 1.35 old extreme 2.56 new extreme 1.63 old extreme 2.51 new extreme 1.43 old extreme 2.22 new extreme 1.57 old extreme 2.35 new normal 1.27 old normal 1.45 new normal 1.44 old normal 1.67 new normal 1.53 old normal 1.34 new normal 1.40 old normal 1.47 Based on the standard model, the estimate of the residual standard deviation is $ . σ = 0133 .
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