Question

Accounting and Machiavellianism. Refer to the Behavioral Research in Accounting(January 2008) study ofMachiavellian traits in accountants, Exercise 6.19 (p. 341),where a Mach rating score was determined for each ina sample of accounting alumni who work as purchasingmanagers. Suppose you want to reduce the width of the95% confidence interval for the true mean Mach ratingscore of all purchasing managers you obtained in Exercise 6.19b. How many purchasing managers should be includedin the sample if you desire a sampling error of only 1.5Mach rating points? Use$\mathbf{\sigma }\approx \mathbf{12}$ in your calculations.

Short answer

246 purchasing managers should be includedin the sample if you desire a sampling error of only 1.5

Step-by-step solution

Given information

Referring to Exercise 6.19 (p. 341),

 Step 2: Finding the sample size

Here the standard error is 1.5

The value of the standard deviation is 12

The critical value for a 95% confidence interval is$z_{\alpha /2}=z_{0.05/2}=z_{0.025}=1.96$

$\begin{array}{c}SE=z_{\alpha /2}\frac{\sigma }{\sqrt{n}}\\ n={z^2}_{\alpha /2}\frac{{\sigma }^2}{S{E}^2}\\ n={1.96}^2\times \frac{{12}^2}{{1.5}^2}\\ n=245.8624\\ n\simeq 246\end{array}$

246 purchasing managers should be includedin the sample if you desire a sampling error of only 1.5