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

Class Examples

Class Examples

Class Examples

Class Examples

Class Examples

Class Examples

Class Examples

Class Examples