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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 in $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 :

JeanaShupp

Answer: 176

Step-by-step explanation:

As per given , we have

A preliminary sample showed that the standard deviation in $675. (provided in thousands of dollars)

Best estimated standard deviation : [tex]\sigma=675[/tex] (provided in thousands of dollars)

Critical value for 95 % confidence interval : [tex]z_{\alpha/2}=1.96[/tex]

Margin of error : E= 100 (provided in thousands of dollars)

Now, the formula to find the sample size :

[tex]n=(\dfrac{z_{\alpha/2}\cdot \sigma}{E})^2\\\\ =(\dfrac{(1.96)(675)}{100})^2=175.0329\approx176[/tex]

Hence, the number of chief executive officers should be in a sample = 176

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