Question

The data below show the wages earned by six workers at three different firms (A, B, and C). The firm's name is shown in column 1 and the workers' wages in column 2. The third column shows the number of times that each firm has been audited for financial fraud while the worker was employed at the firm. The fourth column is a binary varia indicating whether or not the employee works at the accounting department. In the following questions you may check your work using a calculator but must show how you set up the expression you are solving (i.e. show your work). . firm wage audits accountant 14 19 15 12 16

Answer 1

a) Here receiving more audits does not indicate either increase or decrease in wages for employees. From the given table, when there is 3 audits, the wage is 11, for 2 audits the wage is 14 & 16 respectively, for 1 audit the wage is 12 and for no audit, the wage is 15 and 19 respectively. Therefore, there is no direct or inverse relationship between the wages of employees and number of audits.

b) For workers in accounting department,when there is no audit, the wages for employees is 19, when there is 1 audit, the wage is 12 and when there is 3 audits, the wage is 11. Therefore, for workers in accounting department, increase in audits indicate decrease in wage for workers.

c) The mean value of audits( $\bar{X}$$\bar{}$$\bar{}$$\bar{}$) for workers employed in accounting department = (3+0+1)/3=4/3=1.33

The mean value of wage ($\bar{Y}$) for workers employed in accounting department = (19+12+11)/3=14

The formula for covariance is

Cov(X,Y) = $\Sigma$(X-$\bar{X}$)(Y-$\bar{Y}$)/n-1

Here $\Sigma$(X-$\bar{X}$)(Y-$\bar{Y}$)= (3-1.33)(11-14) +(0-1.33)(19-14) +(1-1.33)(12-14)=-11

Therefore, Cov(X,Y) = -11/(3-1)= -.5.5

The negative covariance indicate inverse relationship between audits and wage of workers employed in accounting department, This means when number of audits increases, the wage will decrease and when number of audits decreases, the wage will increase.

d) The answer in part b) is not consistent with answer in part a) because there seems no relationship between number of audits and wages of workers in part a) but in part (b) the increase in audits results decrease in wage of workers employed in accounting department. If we compare the relationship between number of audits and wages of workers in accounting department in part (a), there appears inverse relationship between the two variables.