Question

The data below show the wages earned by six workers at three differe C). The firms 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 variable 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). 1. nt firms (A, B, and firm wagc audits accountant 14 19 15 12 16
a) What are the mean, variance, and standard deviation of wages? b) What are the mean, variance, and standard deviation of number of audits? c) Make a scatter plot with audits on the horizontal axis and wages on the vertical axis. Dod d) e) the relationship between wages and audits appear to be positive or negative? What is the covariance of wages and audits? Is this consistent with part c)? What is the correlation of wages and audits?
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The following analysis relates to estimation of mean, variance and standard deviation of wage and audit and then estimation of covariance and correlation between them

The mean of audits is: Sum(audit) Nimber of Observations Mean aidit- 1.333333 The variance of audits is: Tariance audit- NumbThe relationship between wage and audit appears to be negative. As the audit increases, the wage appears to decline. d) The covariance of wages and audits is: Σ(wage, _ mean-wage )(audit-mean-audit) wage mecm_ wage(ait-mecn_aclit)+...+(wage 11-14.5)61333333). +1614(2-1.333333) -5.83333-0.3333-6-0.66667 +0.833333+1 Cov calit, wage)-- Niamber_of_observations -meam_wage) (caucitmen _aicit) --1.83333 Yes, the value of covariance is negative and is consistent with negative relationship that appear in wage-audit plot. e) The correlation of the wage and audits is: Cov(aidit,wage) Standa d deviation wage Standarddeviationaudit Corelation(cudit,wage)- -1.83333 2.6299561.105542 --0.63055

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