Sample Size Formula

confidence (percent)

90

standard deviation σ

1.

margin of error E

0.3

2

Z

α/2

σ

E

=

2

1.6451.

0.3

=

30.0616

The minimum sample size needed is 31.

This Demonstration calculates the sample size (an integer) that produces a sample mean within the given margin of error. For a confidence level of

100(1-α)%

,

Z

α/2

is the

1-α/2

quantile of a standard normal distribution.

Details

The minimum sample size formula can be found in most elementary statistics texts. The formula appears in M. Sullivan, Fundamentals of Statistics, 2nd ed., Upper Saddle Creek, NJ: Pearson Education, Inc., 2008 p. 414.

External Links

Sample (Wolfram MathWorld)

Sample Size (Wolfram MathWorld)

Permanent Citation

David Gurney

"Sample Size Formula"
http://demonstrations.wolfram.com/SampleSizeFormula/
Wolfram Demonstrations Project
Published: March 7, 2011