Minimum Sample Size
Population Size162
Margin of Error0.05
Confidence0.95
Power0.85
Population Variance13
z(alpha/2) + z(beta)2.99639737403384
z(alpha) + z(beta)2.68128701644526
Minimum Sample Size (2 sided test)161.443271229007
Minimum Sample Size (1 sided test)161.305320290795


Minimum Sample Size (for Infinite Populations)
Population Sizeinfinite
Margin of Error0.05
Confidence0.95
Power0.85
Population Variance13
z(alpha/2) + z(beta)2.99639737403384
z(alpha) + z(beta)2.68128701644526
Minimum Sample Size (2 sided test)46687.6655602079
Minimum Sample Size (1 sided test)37384.3603357012


Minimum Sample Size (Unknown Population Variance)
Population Size162
Margin of Error0.05
Confidence0.95
Power0.85
Population Varianceunknown
t(alpha/2) + t(beta)3.01465400407996
t(alpha) + t(beta)2.6942114723321
Minimum Sample Size (2 sided test)161.449971042731
Minimum Sample Size (1 sided test)161.311940988619


Minimum Sample Size
(Infinite Population, Unknown Population Variance)
Population Sizeinfinite
Margin of Error0.05
Confidence0.95
Power0.85
Population Varianceunknown
t(alpha/2) + t(beta)2.99645969972532
t(alpha) + t(beta)2.68134215476456
Minimum Sample Size (2 sided test)46689.6078068054
Minimum Sample Size (1 sided test)37385.8979047706