Hypothesis Testing - My Notes

General Univariate Population

mu = pop'n average

SD = pop'n SD

Sample n units from population

y_bar = sample average

SD_hat = sample SD

SE_hat = SD_hat/sqrt(n) if n is large

SE_hat_hat = SD_hat/sqrt(n-1) if n is small

Null hypothesis H0: mu=V (where V is some actual number)

Alternative hypothesis depends on the problem, either: Ha: mu < V   or Ha: mu > V

Large n: form z-score = (y_bar - V)/SE_hat

Small n: form t-sscore = (y_bar - V)/SE_hat_hat

Large n: Use normal table to find area under normal curve for z-score (that's the p-value)

Small n: Use t table to find p-value

Binary (0 or 1) Population

pi = pop'n proportion

SD = pop'n SD = sqrt( pi * (1-pi) )

Sample n units from population, and only do this stuff if n is large!

p = sample proportion

SE = SD/sqrt(n)

(NOTE: in binary case here, the SD and SE are NOT estimated;

We're assuming the null hypothesis is true, which means we know what pi really is,

which means that we know what SD and SE really are!!!

This is different from the general univariate case!!!)

Null hypothesis H0: pi=V (where V is some actual number)

Alternative hypothesis depends on the problem, either: Ha: pi < V   or Ha: pi > V

Form z-score = (p - V)/SE (where SE is calculated using the value V in place of pi)

Use normal table to find area under normal curve for z-score (that's the p-value)