Ch 10: One- and Two-Sample Tests of Hypotheses

p-value

a number between 0 and 1 that quantifies how confidence we can be a random variable is different from our null hypothesis

p-value vs. classic hypothesis training

classic: compares critical value to Sample Z

-p-value: use Sample Z as critical value, then calculate its areas and compare to alpha

general steps for classic hypothesis

-identify key statistics (mean, sample mean, standard deviation, etc)

-find Sample Z

-find critical value of population using α (graphing helps)

-compare Sample Z to critical value and see if H_a is true

general steps for p-value

-same steps as classic hypothesis

-make Sample Z the critical value and find its area on Z/T table (p-value)

-compare with given α and see if it’s less than

upper limit p-value

-upper limit: P(Z > whatever) == 1 - [table_entry]

lower limit p-value

-lower limit: P(Z < whatever) == [table_entry]

two-tailed p-value

-two-tailed: P(Z ≠ whatever) == 2*(Z > whatever)

Type I Error (α)

probability of rejecting H₀ when H₀ is actually true

Type II Error (β)

probability of accepting H₀ when H₀ is actually false