Question

An IQ test is designed so that the mean is 100 and the standard deviation is 16 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95​% confidence that the sample mean is within 3 IQ points of the true mean. Assume that sigma σ equals=16 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.

a) The required sample size is ??

​

Answer 1

A % confidence interval for population mean is given by

where n= sample size, population standard deviation 16  

here so 1.96 (using standard normal table)

According to the given question ​​ So n=109.27

So required sample size=109

This is a reasonable s​​​​ample size for a real-world calculation because we need a sample size n for such a calculation.

thank you.