Question

A study is conducted in a company that employs 800 engineers. A random sample of 50 engineers reveals that the average sample age is 34.3 years. Historically, the population standard deviation of the age of the company’s engineers is approximately 8 years. Construct a 98% confidence interval to estimate the average age of all the engineers in this company

Answer 1

$\mu=34.3,\sigma=8,n=50$

$Z_\frac{\alpha}{2}=Z_\frac{0.02}{2}=Z_{0.01}=2.33$

$CI=[34.3±2.33\frac{8}{\sqrt{50}}]]$

$=[34.3±2.64]$

$=[31.66,36.94]$