Answer to Question #248980 in Statistics and Probability for Yeee

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

$n=50 \\ \bar{x}=34.3 \\ \sigma = 8$

Two-sided confidence interval:

$CI = (\bar{x} - \frac{Z_c \times \sigma}{\sqrt{n}}, \bar{x} + \frac{Z_c \times \sigma}{\sqrt{n}})$

For 98 % confidence interval

$Z_c=2.326 \\ CI = (34.3 - \frac{2.326 \times 8}{\sqrt{50}}, 34.3 + \frac{2.326 \times 8}{\sqrt{50}}) \\ =(34.3 -2.63, 34.3 + 2.63) \\ = (31.67, 36.93)$