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.
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.
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).
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.