Question

Annual salary plus bonus data for chief executive officers are presented in a magazine Annual Pay Survey. A preliminary sample showed that the standard deviation is $673 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 to next whole number.

Answer 1

Solution :

Given that,

standard deviation = = 673

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 = 1.960

Sample size = n = ((Z_/2 * ) / E)²

= ((1.960 * 673) / 100)²

= 173.9972

= 174

Sample size = 174