Question

An IQ test is designed so that the mean is 100 and the standard deviation is 15 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of the residents of a state if you want to be​ 95% confident that the sample mean is within 4 IQ points of the true mean.

What is the required sample size?

Answer 1

55

Explanation:

`\displaystyle MOE = z\biggr((\sigma)/(√(n))\biggr)\\\\4=1.96\biggr((15)/(√(n))\biggr)\\\\4=(29.4)/(√(n))\\\\√(n)=(29.4)/(4)\\\\√(n)=7.35\\\\n=54.0225\\\\n\approx55\uparrow`

Make sure to always round up the required sample size to the nearest integer!