Minimum Sample Size
Population Size20
Margin of Error0.15
Confidence0.95
Power0.15
Population Variance13
z(alpha/2) + z(beta)2.99639737403384
z(alpha) + z(beta)2.68128701644526
Minimum Sample Size (2 sided test)19.9270145669085
Minimum Sample Size (1 sided test)19.9089344378691


Minimum Sample Size (for Infinite Populations)
Population Sizeinfinite
Margin of Error0.15
Confidence0.95
Power0.15
Population Variance13
z(alpha/2) + z(beta)2.99639737403384
z(alpha) + z(beta)2.68128701644526
Minimum Sample Size (2 sided test)5187.51839557866
Minimum Sample Size (1 sided test)4153.81781507792


Minimum Sample Size (Unknown Population Variance)
Population Size20
Margin of Error0.15
Confidence0.95
Power0.15
Population Varianceunknown
t(alpha/2) + t(beta)3.15919306311097
t(alpha) + t(beta)2.79521046526987
Minimum Sample Size (2 sided test)19.934318686463
Minimum Sample Size (1 sided test)19.9161757474701


Minimum Sample Size
(Infinite Population, Unknown Population Variance)
Population Sizeinfinite
Margin of Error0.15
Confidence0.95
Power0.15
Population Varianceunknown
t(alpha/2) + t(beta)2.99695850394025
t(alpha) + t(beta)2.68178345519841
Minimum Sample Size (2 sided test)5189.46149184076
Minimum Sample Size (1 sided test)4155.35611144386