Documentation for

Confidence Interval for a sample mean

Minn M. Soe, MD, MPH, MCTM : msoe@sph.emory.edu

Kevin M. Sullivan, PhD, MPH, MHA: cdckms@sph.emory.edu

This module calculates the confidence interval for a sample mean. First, the user is prompted to enter the sample mean, standard deviation, sample size, population size from which the sample was taken (if known) and desired confidence interval.

Although default values are provided, the user can change these parameter values as required.

As the confidence interval of sample mean takes into account "correction factor for finite population", population size needs to be entered. If population size is unknown or can not be estimated, set the value at 999,999,999. Please note that the sample size should be less than or equal to population size. Likewise, confidence intervals ranging from 20% - 99.99% can be entered, specifically, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 98, 99, 99.5, 99.8, 99.9, 99.95, 99.98 & 99.99.

The output from the default example is as below:

The interpretation is that we are 95% confident that the true mean of cholesterol in the population is captured between 146.725 mg% and 153.275 mg%. The confidence interval values shown in the first row of results are based on z-score according to large sample size theory (>30). If the sample size is small, confidence intervals based on t-test should be chosen. In our example, there is not much difference between the results based on z-test and t-test, because of large sample size (n=268). Currently, all confidence intervals calculated are two-sided confidence intervals. The formulae for the methods are provided below.

Formulae

The notation for the formulae are:

= standard error

= standard deviation of a sample

N = population size

n = sample size

= confidence limit

= sample mean

Z1-α/2 = the two-sided Z value (eg. Z=1.96 for 95% confidence interval).

tn-1,α/2 = the two-sided t value with df = n-1

Acknowledgement:

Default values are derived from an example of Epitable in EPI6 (DOS version).

References:

"Normal approximation" method described in Bernard PM, Lapointe C, Measures Statistiques en e'pide'miologie, Presses de L' Universite' du Que'bac, 1987, pp 277-282.