# Annual salary plus bonus data for chief executive officers are presented in the business-Week 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.

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

#### Solutions

Chapter
Section
Chapter 8, Problem 52SE
Textbook Problem
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## Annual salary plus bonus data for chief executive officers are presented in the business-Week 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.

Expert Solution
To determine

Find the number of chief executive officers required to estimate the population mean annual salary provide at 95% confidence.

### Explanation of Solution

Calculation:

The given information is that the annual salary and the bonus data for chief executive officers are represents in business week pay survey. The sample standard deviation is \$675. The margin of error is 100.

The formula for sample size for an interval estimate of a population mean is,

n=(zα2)2σ2E2 .

From the “Table 8.1 value of zα2  ”, the value of z for 95% is 1.96.

The value of 95% confidence interval for population proportion is,

n=(1

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