Question

Annual salary plus bonus data for chief executive officers are presented in the BusinessWeek Annual Pay Survey. A preliminary sample showed that the standard deviation is $675 with data provided in thousands of dollars. How many chief executive officers should be in a sample if we want to estimate the population mean annual salary plus bonus with a margin of error of $100,000?

Answer 1

Answer: 176.

Explanation:

Formula to find the sample size is given by :-

`n=((z^*\cdot \sigma)/(E))^2`

, where
`\sigma` = Population standard deviation from prior study.

E = margin of error.

z* = Critical value.

As per given , we have

`\sigma=\$675000`

E= $100,000

We take 95% confidence interval.

Critical value (Two tailed)=
`z^*=1.96`

The required sample size =
`n=(((1.96)\cdot 675000)/(100000))^2`

`n=(13.23)^2\\\\ n=175.03299\approx176` [Round to next integer]

Hence, the required sample size = 176.