Minimum Sample Size
Population Size21
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)20.919347380442
Minimum Sample Size (1 sided test)20.8993727041744


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 Size21
Margin of Error0.15
Confidence0.95
Power0.15
Population Varianceunknown
t(alpha/2) + t(beta)3.15063540721813
t(alpha) + t(beta)2.78930035298091
Minimum Sample Size (2 sided test)20.927023953073
Minimum Sample Size (1 sided test)20.9069813718543


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