Hypothesis Testing of Single Mean and Single Proportion: Summary of Formulas
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Hypothesis Testing of Single Mean and Single Proportion: Summary of Formulas
1.9
2008/06/06 17:43:25 GMT-5
2012/06/10 16:33:42.362 GMT-5
Barbara
Illowsky
Barbara Illowsky, Ph.D.
illowskybarbara@deanza.edu
Maxfield Foundation
Maxfield Foundation
cnx@cnx.org
Susan
Dean
Susan Dean
deansusan@deanza.edu
Connexions
Connexions
cnx@cnx.org
sdean billowsky
sdean billowsky cnxorg
MaxfieldFoundation
elementary
statistics
Mathematics and Statistics
en
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 not rejecting the null hypothesis when the null hypothesis is false.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's-t test.
- Single population proportion: Normal test.