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.