Question

Annual salary plus bonus data for chief executive officers are presented in an annual pay survey. A preliminary sample showed that the standard deviation is $575 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. (Round your answer up to the nearest integer.)

chief executive officers

Answer 1

Solution

standard deviation =   =575

Margin of error = E = 100

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96 ( Using z table ( see the 0.025 value in standard normal (z) table corresponding z value is 1.96 )

sample size = n = [Z_/2* / E] ²

n = ( 1.96*575 / 100 )²

n =127

Sample size = n =127