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Homework_05_Solutions

# Homework_05_Solutions - 1 Fish on Bicycles ^(a = x = 64 32...

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1. Fish on Bicycles (a) ˆ λ = ¯ x = 64 32 = 2 (b) [¯ x - t 31 ,. 975 × ¯ x 32 , ¯ x + t 31 ,. 975 × ¯ x 32 ] = [1 . 4901 , 2 . 5099] > qt(0.975,df=31) [1] 2.039513 Note that if you used the table with t 30 ,. 975 = 2 . 045, then the C.I. is (1.4888,2.5113) Note also that some of you may have interpolated between t 30 , 0 . 975 and t 35 , 0 . 975 us- ing the tables. Any of these methods is fine. (c) poisson.test(x=64,T=32)\$conf.int [1] 1.540244 2.553955 (d) The CI’s are fairly different. The CI in part (c) includes larger values of λ (lower limit of 1 . 54 compared to 1 . 49, upper limit of 2 . 55 compared to 2 . 51). They have similar widths, but the approximate CI is very slightly wider. Here we prefer the exact CI from (c) because we have a small sample n = 32 and the method used for part (b) doesn’t guarantee a good enough approximation with a sample size of only 32. (e) poisson.test(x=532,T=260)\$conf.int [1] 1.875953 2.227649 (f) They are very similar. We have a new sample size n = 260 which is large enough to provide a very good approximation. 2. Ozone Levels (a) Given that 1995 is a few years ago all of the data are a little ‘historic’, but it is

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Homework_05_Solutions - 1 Fish on Bicycles ^(a = x = 64 32...

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