Lecture 6 Notes

Expect sta102bme102 colin rundel q q q 01 00 05 q 2

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Unformatted text preview: q qq q q q qq qq qq q q q q q q q q q q q q q qq qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q qq qq q qq q qq q qq q q qq qq qq qq qq q q q q q qq qq qq q qq q qqq q qq 0.0 0.0 −1.5 −1.0 0.1 0.2 0.3 Sample Quantiles 0.5 0.4 1.0 0.5 1.5 Normal Q−Q Plot February 5, 2013 9 / 23 Evaluating nearly normalness Here the biggest values are bigger than we would expect and the smallest values are also bigger than we would expect. Sta102/BME102 (Colin Rundel) Lec 6 Normal Approximation to the Binomial Left Skew February 5, 2013 10 / 23 Basics Histograms of the number of successes Hollow histograms of samples from a binomial model where p = 0.10 and n = 10, 30, 100, and 300. What happens as n increases? q qq q qqq qq qqqqqq q q qqqqqq qq qq q qqqqqqq qqqqqqq qqqqqq qqqqqq qqqqqq qqqqqq qq qqqq qqqqq qqqqq qqqqq qqqq qqqq qqq qqq qqq qqq qqq qqq qq qq qq qq qq qq qq qq qq qq qq qq qq qq qq qq qq qq qq qq qq qq qq q qq qq qq qq qq q q q qq qq qq q q q qq qq qq qq qq qq qq qq qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq qq q q q q 6 4 2 0.1 0.2 0.3 Sample Quantiles 8 0.4 0.5 10 Normal Q−Q Plot q 0 2 4 6 0 2 n = 10 4 6 8 10 n = 30 q 0.0 q q 0 2 4 6 8 10 −3 −2 −1 0 1 2 3 Theoretical Quantiles 0 Here the biggest values are smaller than we would expect and the smallest values are also smaller than we would expect. Sta102/BME102 (Colin Rundel) Lec 6 February 5, 2013 11 / 23 5 10 15 20 10 n = 100 Sta102/BME102 (Colin Rundel) 20 30 40 50 n = 300 Lec 6 February 5, 2013 12 / 23 Normal Approximation to the Binomial Basics Normal Approximation to the Binomial QQ plots of the number of successes An analysis of Facebook users qq q q Sample Quantiles Sample Quantiles QQ plots of samples from a binomial model where p = 0.10 and n = 10, 30, 100, and 300. What happens as n increases? 3.0 2.5 2.0 1.5 1.0 0.5 0.0 qqqqqqq qqqqqq q qqqq qq qqqqqqqqq qqqqqqqqq qqqqqqqqq qqqqqqqqq qqqqqqqqq qq q −2 −1 8 0 1 q q qq q qqq...
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