An R Introduction to Statistics

Sampling Size of Population Proportion

The quality of a sample survey can be improved by increasing the sample size. The formula below provide the sample size needed under the requirement of population proportion interval estimate at (1 − α) confidence level, margin of error E, and planned proportion estimate p. Here, zα∕2 is the 100(1 − α∕2) percentile of the standard normal distribution.

2 n = (zα∕2)-p(1−-p) E2

Problem

Using a 50% planned proportion estimate, find the sample size needed to achieve 5% margin of error for the female student survey at 95% confidence level.

Solution

Since there are two tails of the normal distribution, the 95% confidence level would imply the 97.5th percentile of the normal distribution at the upper tail. Therefore, zα∕2 is given by qnorm(.975).

> zstar = qnorm(.975) 
> p = 0.5 
> E = 0.05 
> zstar^2 ∗ p ∗ (1−p) / E^2 
[1] 384.15

Answer

With a planned proportion estimate of 50% at 95% confidence level, it needs a sample size of 385 to achieve a 5% margin of error for the survey of female student proportion.

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