Sampling Size of Population Mean
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 mean interval estimate at (1 −α) confidence level, margin of error E, and population variance σ2. Here, zα∕2 is the 100(1 − α∕2) percentile of the standard normal distribution.
Problem
Assume the population standard deviation σ of the student height in survey is 9.48. Find the sample size needed to achieve a 1.2 centimeters margin of error 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).
Answer
Based on the assumption of population standard deviation being 9.48, it needs a sample size of 240 to achieve a 1.2 centimeters margin of error at 95% confidence level.
