Minimum Sample Size
Population Size20000
Margin of Error1
Confidence0.95
Power0.95
Population Variance13
z(alpha/2) + z(beta)3.60481761149153
z(alpha) + z(beta)3.28970725390294
Minimum Sample Size (2 sided test)167.524599553321
Minimum Sample Size (1 sided test)139.712450162488


Minimum Sample Size (for Infinite Populations)
Population Sizeinfinite
Margin of Error1
Confidence0.95
Power0.95
Population Variance13
z(alpha/2) + z(beta)3.60481761149153
z(alpha) + z(beta)3.28970725390294
Minimum Sample Size (2 sided test)168.931230157553
Minimum Sample Size (1 sided test)140.688259612961


Minimum Sample Size (Unknown Population Variance)
Population Size20000
Margin of Error1
Confidence0.95
Power0.95
Population Varianceunknown
t(alpha/2) + t(beta)3.62836756369638
t(alpha) + t(beta)3.31182580008083
Minimum Sample Size (2 sided test)169.701962637866
Minimum Sample Size (1 sided test)141.584151666959


Minimum Sample Size
(Infinite Population, Unknown Population Variance)
Population Sizeinfinite
Margin of Error1
Confidence0.95
Power0.95
Population Varianceunknown
t(alpha/2) + t(beta)3.62816902032638
t(alpha) + t(beta)3.31167025401027
Minimum Sample Size (2 sided test)171.126935720729
Minimum Sample Size (1 sided test)142.573078326854