Answer to Question #169487 in Statistics and Probability for Sunera

Question

A survey of 20 Sri Lankan companies indicated that the average annual income of company secretaries was Rs.120 000. Assuming that the population standard deviation is Rs.7500 and that the annual incomes are normally distributed, calculate the 90% confidence interval estimate of the average annual income of all company secretaries.

Answer 1

We have that:

$n=20$

$\bar x=120000$

$\sigma=7500$

$\alpha=0.1$

The 90% confidence interval estimate of the average annual income of all company secretaries is calculated by the formula:

$\bar x \pm Z_{\frac{\alpha}{2}}\frac{\sigma}{\sqrt n}=\bar x\pm Z_{0.05}\frac{\sigma}{\sqrt n}=120000\pm 1.64\cdot \frac{7500}{\sqrt {20}}=120000\pm 2750$

So the 90% confidence interval estimate of the average annual income of all company secretariess is (117250; 122750).