Estimate a population mean: confidence interval for a simple random sample

Theory

To determine the confidence interval for a mean based on simple random sampling the following formula is used:

Where:

DE The standard error of the mean.

n The number of individuals sampled.

f The sampling fraction, that is the number of samples as a proportion of the total population size.

The confidence interval is calculated as follows:

Where:

p The mean estimated from a simple random sampling.

z The value obtained from the standard normal distribution. To each value of confidence there is a correspondent value of z. The levels of confidence more frequently used in biological studies are 90%, 95% and 99%. The values of z correspondent to them are 1.64, 1.96, and 2.58 respectively.

SE The standard error of the mean.


Instituto Nacional de Tecnología Agropecuaria	EpiCentre, IVABS, Massey University

DE	The standard error of the mean.
n	The number of individuals sampled.
f	The sampling fraction, that is the number of samples as a proportion of the total population size.

p	The mean estimated from a simple random sampling.
z	The value obtained from the standard normal distribution. To each value of confidence there is a correspondent value of z. The levels of confidence more frequently used in biological studies are 90%, 95% and 99%. The values of z correspondent to them are 1.64, 1.96, and 2.58 respectively.
SE	The standard error of the mean.