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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.

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rodolforodriguezr

Answer:

175

Step-by-step explanation:

The sample size n in Simple Random Sampling is given by

[tex]\bf n=\frac{z^2s^2}{e^2}[/tex]

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

Replacing values

[tex]\bf n=\frac{(1.96)^2(675)^2}{(100)^2}=175[/tex]

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

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