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# ass1sol - Stat 231 Winter 2005 Assignment 1 Please paste R...

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1 Stat 231 Winter 2005 Assignment 1 Please paste R output, as appropriate, into your assignment solution and make sure that the output is labeled so that we can easily find it. We do not require the solution to be typed. Do NOT include a lot of superfluous R output. Note that R code is given in red italics. You should be able to paste this code directly into R 1. The crankshaft is an integral part of an internal combustion engine that transfers power from the pistons to the transmission. During use, the crankshaft spins about its axis at thousands of revolutions per minute. To avoid excess wear and noise, the crankshaft must be balanced about its axis of revolution. In the production of crankshafts, one of the final steps is to measure the location of the center of gravity ( , ) x y relative to the axis of revolution (0,0) . If the center of gravity is too far from the axis of revolution, the crankshaft is re-balanced by drilling out material at the locations shown on the picture. The rebalancing adds a substantial cost to the process. Management assigned a Six Sigma process improvement team to reduce cost by reducing the number of crankshafts that needed rebalancing. As a first step, the team decided to assess the current performance of the process by measuring and recording the location of the center of gravity for all crankshafts produced in a single shift (about 500 parts). They planned to use the results of this investigation as a baseline against which to assess the effects of deliberate changes in the process. The team decided to record the center of gravity for each part in time order of production but measured no other variates. They had confidence in the measurement system based on earlier investigations. PROBLEM a) [2 marks] What is a target unit and the target population for this investigation? A target unit is a crankshaft and the target population is all crankshafts to be built in the future under current operating conditions. b) [2 marks] What are the response variates? The response variates are the coordinates (x,y) that give the center of gravity for each crankshaft. c) [2 marks] What is the aspect of the Problem? Explain. The problem is descriptive because we want to estimate attributes of the target population that describe its current performance. There are no explanatory variates involved in the questions of interest. The team decided to look at a number of attributes including histograms and a scatterplot.

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2 PLAN d) [2 marks] What is a study unit and the study population? A study unit is a crankshaft and the study population is all crankshafts produced in the selected shift. Alternately, we might consider the study population to be some unspecified longer period (the above description provides no information ) so that the sample is all crankshafts from a single shift. With this answer, it is difficult to think about study or sample error since the study population is not completely specified.
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ass1sol - Stat 231 Winter 2005 Assignment 1 Please paste R...

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