The power of the two-sample mean comparison is maximized when we maximize ET , where
ET = = =
x - y
2 2 x /nx + y /ny x - y nx + ny 2 2 x /px + y /py x - y nx + ny 2 2 x /px + y /(1 - px )
2 Suppose t
Statistics 403 Problem Set 1 Due in lab on Friday, September 17th 1. Suppose we have the following probability distribution: x 1 2 3 4 5 6 7 8 9 10 P (X = x) 0.19 0.09 0.07 0.15 0.21 0.03 0.01 0.03 0.
Statistics 403 Problem Set 2 Due in lab on Friday, September 24th 1. We are given the following probability distribution, where p is an unspecified probability: x P (X = x) -1 0 0.3 p 1 0.7 - p
(a) Fi
Statistics 403 Problem Set 3 Due in lab on Friday, October 1st 1. Suppose we are interested in estimating a quantity , and we can obtain independent measurements Xi with EXi = . We intend to use X to
Statistics 403 Problem Set 4 Due in lab on Friday, October 8th 1. Suppose we are interested in comparing the support for a certain political candidate in Michigan to the support for the candidate in O
Statistics 403 Problem Set 5 Due in lab on Friday, October 15th 1. The following questions are about a population of people, some of whom are home owners, and some of whom are renters. (a) Suppose 65%
Statistics 403 Problem Set 6 Due in lab on Friday, October 29th 1. Three processes for collecting data X1 , . . . , X10 are described below. For each, deter mine the 15th , 50th , and 90th percentiles
Statistics 403 Problem Set 7 Due in lab on Friday, November 5th 1. Suppose we are planning to studying a treatment for depression. We will obtain baseline depression scores Xi , i = 1, . . . , 30 on a
Statistics 403 Problem Set 8 Due in lab on Friday, November 12th 1. Suppose X1 , . . . , Xn and Y1 , . . . , Yn are both iid samples, with EXi = EYi = 0, 2 2 var(Xi ) = X , var(Yi ) = Y , cor(Xi , Yi
Statistics 403 Problem Set 9 Due in lab on Friday, November 19th 1. Suppose we are planning to collect paired data Xi , Yi with the goal of estimating EX - EY . We want to have 80% power to detect a r
Statistics 403 Problem Set 10 Due in lab on Friday, December 3rd 1. Suppose we are using stratification to estimate a treatment effect (i.e. we want to estimate EY T - EY U while controlling for the e
Statistics 403 Problem Set 11 Due in lab on Friday, December 10th 1. Suppose we are conducting a study to assess whether heavy drinking is associated with the development of pancreatic cancer. We iden
Statistics 403 Practice Exam Questions for Exam 2 I have not included practice problems that are very similar to the homework problems, so you should study those too, along with the solutions to the f
Practice exercises for exam 1 If you are asked for a probability that cannot be calculated by hand, you can express your answer either in terms of normal probabilities (e.g. P (Z < . . .), P (Z > . .
Research methods: background and review
Kerby Shedden
Department of Statistics, University of Michigan
April 7, 2011
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Author(s): Kerby Shedden, Ph.D., 2010 License: Unless otherwise noted, this
Author(s): Kerby Shedden, Ph.D., 2010 License: Unless otherwise noted, this material is made available under the terms of the Creative Commons Attribution Share Alike 3.0 License: http:/creativecommon
Election polls
For each race, we have one or more polls reported as X 2SE, or with a margin of error of ME." Typical ME's are 0.03-0.04. In "X our notation, ME = 2SE. The data underlying X are X1 , .
Statistics 403 Exam 1
October 27, 2009 Instructions: You may not use notes, books, formula cards, etc. You may use a calculator, but only for arithmetic. If you are asked for a probability that cannot
Statistics 403 Midterm Exam October 26th, 2010 1. Answer the questions given below for the following probability distribution (your answers may depend on a and p): x -a P (X = x) p/2 0 1-p a p/2
(a) W
Statistics 403 Final Exam December 17, 2010 1. We are planning a study in which our goal will be to accurately estimate a treatment effect, expressed as the difference in mean responses between treate
Statistics 403 Exam 2
December 21, 2009 Instructions: You may not use notes, books, formula cards, etc. You may use a calculator, but only for arithmetic. If you are asked for a probability that canno
Statistics 403 Exam 2
December 9, 2008 Instructions: You may not use calculators, notes, books, formula cards, etc. If you are asked for a probability that cannot be calculated by hand, you can expres
Author(s): Kerby Shedden, Ph.D., 2010 License: Unless otherwise noted, this material is made available under the terms of the Creative Commons Attribution Share Alike 3.0 License: http:/creativecommon
Author(s): Kerby Shedden, Ph.D., 2010 License: Unless otherwise noted, this material is made available under the terms of the Creative Commons Attribution Share Alike 3.0 License: http:/creativecommon