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Unformatted text preview: FINAL EXAM STAT 101, Instructors: A. Wyner, A. Rakhlin December 15, 2009 Student Name: Section: Instructions • Use the space provided to answer questions. You can use the back of these pages as scratch paper. • You must show work and give explanations (except for the multiple-choice questions). • Rules of uniformity: One-sided letter crib sheet, calculator ok (even with statistical functions and graphing), otherwise closed notes, closed book. • No cell phones visible! • Rules of Fairness: – Complete this exam entirely on your own. Do not acquire information from other stu- dents or the outside in any form. – Do not take copies of this exam out of this room. – You have two hours for this exam. Any student observed continuing to write after time has been called will be documented and points will be deducted. • Rules of Consideration: – Be considerate to others by not causing commotion and distraction. – If you finish early, leave quietly; avoid slamming doors. Honor code applies to the above Rules. Your signature: About this test: When more than one choice seems reasonable, pick the one that is best. STOP WAIT UNTIL YOU ARE INSTRUCTED TO PROCEED. 19 questions for a total of 100 points. STAT 101 Final Exam 1. (2 points) If the sample size n is large and p is the population proportion, the sampling distri- bution of the proportion is approximately (a) Binomial Bin (1 / 2 ,p ) (b) Normal N ( p,SD ( X i )) (c) Normal N ( p,p (1- p ) /n ) (d) Normal N (ˆ p, ˆ p (1- ˆ p ) /n ) (e) Normal N ( p, p p (1- p ) /n ) 2. (2 points) The Central Limit Theorem asserts that for i.i.d. random variables X 1 ,...,X n (a) The histogram of the data closely resembles the probability distribution of X i when n is large. (b) The histogram of the data closely approximates the mean of the population when n is large. (c) The sampling distribution of the mean is approximately normal when n is large. (d) The sampling distribution of the mean resembles the probability distribution of X i . 3. (2 points) The probability distribution for the average of 9 i.i.d. normal N (2 , 3 2 ) random variables X 1 ,...,X 9 is best described as (a) Approximately N (2 , 3 2 ) (b) Exactly N (2 , 3) (c) Exactly N (1 / 9 , 3 2 / 9) (d) Exactly N (2 , 1) (e) Can only be determined if the distribution of X i is known since the smaple size n is only 9....
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- Fall '08