STA_100_Winter_2011_Midterm_Exam_II_Solutions - STA 100...

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STA 100: Midterm II Wednesday, February 16th, 8.00-8.50am For all questions you must show your work. This enables us to understand your thought process, give partial credit and prevent cheating. You should answer all of the problems in this exam. I This exam has 9 pages, including one page of instructions (this page), 6 pages of questions and 2 pages of probability tables. The exam has 3 problems. II Write your answer in the blank space provided below each sub-problem. The space provided should be more than enough (e.g., if you find yourself needing a lot more space than provided you should be concerned with the approach you’re using). If you do need more space, then please use the back of the corresponding page and clearly indicate that you have done so. III The sub-problems are arranged in a logical order and thus you should try to complete them in the order given. However, you should not ‘get stuck’ on a sub-problem if you are unable to complete it. You should move on and try to complete the rest by assuming any given results in the preceding parts are true even if you cannot establish or prove them. IV When asked to provide a numerical answer, indicate how you arrive at the answer. This makes it possible for us to render you partial credit even if you made an arithmetic error. V Use of a calculator is fine but no connection to the internet can be used. You are allowed to bring one page (double-sided) of notes into the exam. All other materials are prohibited. VI Please ask if you are unsure of the meaning of a particular problem. This exam is to be done alone, with no help from any other individuals. Thank you for your cooperation! Print your name below and sign: NAME(PRINT): SIGNATURE: For Grading Only: Question Score 1 /30 2 /35 3 /35 Total /100 1
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1. Back at the Costa Rican sloth sanctuary (from Midterm I), you are again asked to analyze some data about injuries to the sloths. Recall that the number of injured sloths in a given month was assumed to follow a Binomial distribution with n = 200 and probability of injury, p i.e., X Bin( n,p ), where X = number of sloths injured in a given month. (a) (2 points) In your first month at the sanctuary, 6 out of the 200 sloths were injured. Estimate p . We estimate ˆ p = 6 200 = 0 . 03 . (b) (12 points) Provide a 95% CI for p . Using the usual formula, a 95% CI for p is given by: ˆ p - t n - 1 , 1 - α/ 2 p ˆ p (1 - ˆ p ) n , ˆ p + t n - 1 , 1 - α/ 2 p ˆ p (1 - ˆ p ) n ! ± 0 . 03 - 1 . 97 × 0 . 03 × 0 . 97 200 , 0 . 03 + 1 . 97 × 0 . 03 × 0 . 97 200 ² = (0 . 006 , 0 . 054) , where we looked up t 199 , 0 . 975 = 1 . 972 in our t - tables. In other words, we are 95% confident that the monthly injury probability is between 0 . 6% and 5 . 4% (where ‘confident’ is used in the tech- nical statistical sense – it does not imply that there is a probability of 0.95 that p is in the interval).
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STA_100_Winter_2011_Midterm_Exam_II_Solutions - STA 100...

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