Hypothesis Testing of Single Mean and Single Proportion: Summary of Formulas
1.5
2008/06/06 17:43:25 GMT-5
2008/07/18 10:34:03.713 GMT-5
Barbara
Illowsky
illowskybarbara@deanza.edu
Susan
Dean
deansusan@deanza.edu
Connexions
cnx@cnx.org
elementary
statistics
Ho and Ha are contradictory.
If Ho has:
equal (=)
greater than or equal to
(≥)
less than or equal to (≤)
then Ha has:
not equal (≠)
or
greater than
(>) or
less than (<)
less than (<)
greater than (>)
If
α
≤
p-value, then do not reject
H
o
.If
α
>
p-value, then reject
H
o
.α is preconceived. Its value is set before
the hypothesis test starts.
The p-value is calculated from the data.α = probability of a Type I error = P(Type I error)
= probability of rejecting the null hypothesis when the null hypothesis is true.β = probability of a Type II error = P(Type II error) = probability of rejecting the null hypothesis when the null hypothesis is true.If there is no given preconceived α, then use α=0.05.Types of Hypothesis Tests- Single population mean, known population variance (or standard deviation): Normal
test.
- Single population mean, unknown population variance (or standard deviation):
Student-t test.
- Single population proportion: Normal test.