10 Statistical Inference - Statistical Inference More...

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Statistical Inference More discussion on material covered in D&B Chapters 8 and 9
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Weights of Bears { The health of the bear population in Yellowstone National Park is monitored by periodic measurements taken from anesthetized bears. A sample of 54 bears has a mean weight of 182.9 pounds. The sample standard deviation is estimated to be 121.8 pounds. Use a 0.05 significance level to test the claim that the population mean of all such bear weights is different than 200 pounds. { Bear.t.test.ssc
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Most statisticians are familiar with conversations that start: { Q: What is the purpose of your analysis? { A: I want to do a significance test. { Q: No, I mean what is the overall objective? { A (with puzzled look): { I want to know if my results are significant. { And so on. ..." (Chatfield 1991)
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Hypothesis Testing { Formulate a hypothesis { Conduct an experiment { Test for significance { Don’t stop here! { Draw conclusions { Make predictions { Ask more questions
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One Tailed vs. Two Tailed z Tests Z P(Z) -3 -2 -1 0 1 2 3 0.0 0.1 0.2 0.3 0.4 qnorm(.975) 1.959964 qnorm(.95) 1.644854 qnorm(.05) 1.644854
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One Tailed vs. Two Tailed t Tests Z P(Z) -3 -2 -1 0 1 2 3 0.0 0.1 0.2 0.3 0.4 qnorm(0.975) 1.959964 qt(0.975,df=300) 1.967903 qt(0.975,df=30) 2.042272 qt(0.975,df=3) 3.182446
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Difference in the Mean vs. Difference in the … Variance x px 0 5 10 15 20 0.0 0.02 0.04 0.06 0.08 0.10 X = 0:20 Px = dchisq(x,10) plot(x,px, type='l',lwd=3) More on this later…
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x px 0 5 10 15 20 0.0 0.02 0.04 0.06 0.08 0.10 0.12 Normal vs.Other Distributions x = 0:20 px = dpois(x,10) plot(x,px, type='b',lwd=3)
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The Standardized Normal Distribution x x z z z x z e z f σ μ π σμ = = = = 2 2 2 2 1 ) 1 , 0 | ( Z P(Z) -3 -2 -1 0 1 2 3 0.0 0.1 0.2 0.3 0.4
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Using the Standard Normal in Hypothesis Testing Actual al Hypothetic 2 1 ) 1 , 0 | ( 1 0 2 1 1 0 0 0 2 2 x o x z z z s x z s x z e z f μ π σμ = = = = = Z P(Z) -3 -2 -1 0 1 2 3 0.0 0.1 0.2 0.3 0.4
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This note was uploaded on 11/12/2009 for the course BTRY 3010 at Cornell University (Engineering School).

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10 Statistical Inference - Statistical Inference More...

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