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? (Note: The desired margin of error would be E=100 if the data are in thousands of dollars.) Use 95% confidence.

Answer 1

175

Explanation:

The sample size n in Simple Random Sampling is given by

`\bf n=(z^2s^2)/(e^2)`

where z = 1.96 is the z-score associated with a 95% confidence level ans s the standard deviation.

Replacing values

`\bf n=((1.96)^2(675)^2)/((100)^2)=175`

So, there should be 175 chief executive officers in a sample if we want to estimate the population mean annual salary plus bonus with a margin of error of $100,000