Question

Machiavellian describes negative character traits that include manipulation cunning, duplicity, deception, and bad faith. A Machiavellian (“Mach”)rating score was determined for each in a random sample of 122 purchasing managers, with the following results: ?̅=99.6,?=12.6. A director of purchasing at a major firm claims that the true mean Mach rating score of all purchasing managers is 85.

A. Give the rejection region for the test using ?=0.10.

Answer 1

Solution:

Given the true mean value, sample mean and standard error, we can find the test statistic as follows:

Test statistic = (sample mean - true mean value)/(standard error/n1/2)

z-statistic = (99.6 - 85)/(12.6/1221/2)

z-statistic = 14.6/(12.6/11.045) = 12.809

With significance level of 0.10, critical value z0.10/2 = z0.05 = 1.645

As z-statistic is much greater than critical value of z (12.809 > 1.645), we reject the claim.

To answer the question, rejection region is any statistic value greater than 1.645.