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Gossets student-t model What happens to quantitative samples when n is small?

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Gossets student-t model What does the CLT say? The Bean Machine Vocab A1

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William Gosset

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Vocab A2 Gosset-t ?

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Vocab A3 Vocab A4 degrees of freedom (df) Because of extra variation when using sample s for in the sampling dist. (for quantitative data) a different set of models was needed. All models differ a little based on the sample size or n called degrees of freedom (df) as n approaches then t approaches normal. Student-t a family of distributions df = n – 1

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Vocab A5 Student-t Assumptions / conditions Independence: data values independent – or reasonable to assume Randomization: data from random sample or randomized experiment 10% : when we dont have replacement, cant sample more than 10% Nearly normal : data come from dist. unimodal and symmetric (make histogram) - the smaller the sample the more closely it should follow a normal model

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Vocab A6 Student-t One sample t-interval for the mean y ± t * n-1 SE( y ) t* depends on your confidence level and the df.

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Vocab A7 Vocab A8 Student-t One sample t-test for the mean the t-value

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P(-1.96 < z < 1.96) =.95. Shape of t Distributions for n = 3 and n = 12.

P(-1.96 < z < 1.96) =.95. Shape of t Distributions for n = 3 and n = 12.

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