STA_100_Winter_2011_Midterm_Exam_II_Solutions

# STA_100_Winter_2011_Midterm_Exam_II_Solutions - STA 100...

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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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