Question

n = 68, ¯x=75, and σ = 8. The sample population is normally distributed. Find the 99% interval estimate for µ.

Answer 1

The formula to calculate a confidence interval for a population mean is as follows:

$CI=\bar{x}\pm z\cdot\cfrac{\sigma}{\sqrt{n}},$

where:

• $\bar{x}=75$ : sample mean
• z:  the chosen z-value, for a 99% confidence interval z = 2.576
• $\sigma=8$ :  sample standard deviation
• n = 68:  sample size.

So,

$CI=75 \pm 2.576\cdot\cfrac{8}{\sqrt{68}}=\\= 75\pm2.50=(72.5, 77.5).$