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Unformatted text preview: AMS572.01 Midterm Exam Fall, 2009 Name: ________________________________ ID: _____________________ Signature: _________________________ Instruction: This is a close book exam. Anyone who cheats in the exam shall receive a grade of F. Please provide complete solutions for full credit. The exam goes from 12:50-2:10pm. Good luck! 1. (for all) To study the effectiveness of wall insulation in saving energy for home heating, the energy consumption (in MWh) for 5 houses in Bristol, England, was recorded for two winters; the first winter was before insulation and the second winter was after insulation: House 1 2 3 4 5 Before 12.1 10.6 13.4 13.8 15.5 After 12.0 11.0 14.1 11.2 15.3 (a) Please provide a 95% confidence interval for the difference between the mean energy consumption before and after the wall insulation is installed. What assumptions are necessary for your inference? (b) Can you conclude that there is a difference in mean energy consumption before and after the wall insulation is installed at the significance level 0.05? Please test it and evaluate the p-value of your test. What assumptions are necessary for your inference? (c) Please write the SAS program to perform the test and examine the necessary assumptions given in (b). SOLUTION: This is inference on two population means, paired samples. (a). 36 . = d , s d = 1.30 CI: ) 97 . 1 , 25 . 1 ( 5 30 . 1 776 . 2 36 .- = (b). : = d H , : d H (1) 0.36 0 0.619 1.30/ 5 d d t s n-- = = 1, /2 4,0.025 2.776 n t t - = = Since 0.619 t is smaller than 4,0.025 2.776 t = , we cannot reject H . (2) 2 ( 0.619) 0.57 p value P T- = In the exam, since you do not have access to the statistical software such as R, you can only estimate the range of the p-value based on your t-table. You thus estimate p-value > 2*0.1=0.2 based on the t-table you were given. Assumptions for (a) and (b): the paired differences follow a normal distribution. (c) The SAS program is: Data energy; Input before after @@; Diff=before - after; Datalines; 12.1 12.0 10.6 11.0 13.4 14.1 13.8 11.2 15.5 15.3 ; Run; Proc univariate data = energy normal; Var Diff; Run; 2A (for AMS students). Suppose we have two independent random samples from two normal populations: ( 29 1 2 1 2 1 , , , ~ , n X X X N K , and ( 29 2 2 1 2 2 , ,...
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This note was uploaded on 01/31/2011 for the course AMS 572 taught by Professor Weizhu during the Fall '10 term at SUNY Stony Brook.
- Fall '10