Minimum Sample Size
Population Size20000
Margin of Error0.15
Confidence0.95
Power0.5
Population Variance13
z(alpha/2) + z(beta)1.95996398454005
z(alpha) + z(beta)1.64485362695147
Minimum Sample Size (2 sided test)1997.89237596271
Minimum Sample Size (1 sided test)1449.94729245012


Minimum Sample Size (for Infinite Populations)
Population Sizeinfinite
Margin of Error0.15
Confidence0.95
Power0.5
Population Variance13
z(alpha/2) + z(beta)1.95996398454005
z(alpha) + z(beta)1.64485362695147
Minimum Sample Size (2 sided test)2219.50954084549
Minimum Sample Size (1 sided test)1563.20288458846


Minimum Sample Size (Unknown Population Variance)
Population Size20000
Margin of Error0.15
Confidence0.95
Power0.5
Population Varianceunknown
t(alpha/2) + t(beta)1.96115267419883
t(alpha) + t(beta)1.64590594250899
Minimum Sample Size (2 sided test)2000.07407518899
Minimum Sample Size (1 sided test)1451.66842651734


Minimum Sample Size
(Infinite Population, Unknown Population Variance)
Population Sizeinfinite
Margin of Error0.15
Confidence0.95
Power0.5
Population Varianceunknown
t(alpha/2) + t(beta)1.96103386679928
t(alpha) + t(beta)1.64582960687591
Minimum Sample Size (2 sided test)2221.93332211282
Minimum Sample Size (1 sided test)1565.05849925782