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Unformatted text preview: STATISTICS 500 Fall 2009 Homework 7 - handed out 16 Oct 2009 DUE DATE: on campus Friday, 23 Oct 2009, in lecture (11 am) or by e-mailto Chuanlong, firstname.lastname@example.org, no later than noon. off campus Monday, 26 Oct 2009, by 4 pm to Nicole Rembert, email: email@example.com or FAX: 515-294-4040 (please include cover page with Stat 500 / Nicole Rembert). 1. Regression Design snow data, part 3 I havent lectured specifically on design (e.g. choice of sample size and choice of Xs) because it is just another application of principles weve seen before. We have talked about how the s.e. of the slope depends on the number of observations and spread of the Xs. Thats all you need to apply ideas from earlier to regression. This problem explores some of those issues, using the snow density and gain study from last week. For all parts here, use the regression of Y = log(gain) on X=density. (a) The investigators are concerned about the large s.e. for the slope, 1 . They plan to repeat the study using the same 9 densities. Based on the current data and previous studies, they believe 0.25 is a good estimate of , the s.d. of observations among blocks of the same density. It may help to know that i ( X i- X ) 2 = 0 . 4557 when that sum is calculated for 1 block of each of the 9 densities. The investigators want to reduce the s.e. of the slope to 0.075. They will use n blocks at each density, i.e. the same number of blocks at each density. What is the appropriate n ? (b) It is expensive to buy these blocks, especially in all the different densities. And, it is hard to get some of the densities. It is easy and cheap to get blocks with densities of 0.001 and 0.686. If the investigators only used these two densities and used n of each, what is the appropriate n so that the s.e. of the slope is 0.075?...
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- Fall '08