Question

We want to obtain a sample to estimate a population mean. Based on previous evidence, researchers believe the population standard deviation is approximately

. We would like to be 99.5% confident that the estimate is within 0.1 of the true population mean. How large of a sample size is required?
n=

Answer 1

5,144,079

Explanation:

`\displaystyle CI=\mu\pm z\biggr((\sigma)/(√(n))\biggr)\\\\CI_(99.5\%)=\mu\pm2.807\biggr((80.8)/(√(n))\biggr)\\\\0.1=2.807\biggr((80.8)/(√(n))\biggr)\\\\0.1√(n)=226.8056\\\\√(n)=2268.056\\\\n=5144078.01914\\\\n=5144079`

Thus, you would need a sample size of 5,144,079 to be 99.5% confident that the true population mean is ±0.1 away from it with a population standard deviation of 80.8 (aka. our margin of error).