Question

Machiavellian describes negative character traits that include manipulation, cunning, duplicity, deception, and bad faith. A Machiavellian (Mach) rating score was determined for each person in a sample of accounting alumni who work as purchasing managers. Scores range from a low of 40 to a high of 160, with the theoretical neutral Mach rating score of 100. Suppose you want to reduce the width of a 95% confidence interval for the true mean Mach rating score of all purchasing managers. How many purchasing managers should be included in the sample if you desire a sampling error of only 1.4 Mach rating points? Use σ ≈ 14 in your calculations.

Answer 1

Solution :

Given that,

Population standard deviation = = 14

Margin of error = E = 1.4

At 95% confidence level the z is,

= 1 - 95%

= 1 - 0.95 = 0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96  

sample size = n = [Z/2* / E] 2

n = [1.96 * 14 / 1.4 ]2

n = 384.16

Sample size = n = 385