Gosset’s student-t model
What happens to quantitative samples when n is small?
Gosset’s student-t modelWhat does the CLT say?
The Bean Machine
Vocab A1
William Gosset
Vocab A2
Gosset-t ?
Vocab A3Vocab A4
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-ta family of distributions
df = n – 1
Vocab A5
Student-tAssumptions / conditions
Independence: data values independent – or reasonable to assume Randomization: data from random sample or randomized experiment 10% : when we don’t have replacement, can’t 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
Vocab A6
Student-tOne sample t-interval for the mean
y ± t*n-1 SE( y )
t* depends on your confidence level and the df.
𝑆𝐸 (𝑦 )=𝑠(𝑦 )√𝑛
Vocab A7Vocab A8
Student-tOne sample t-test for the mean
the t-valuet-value
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