## Related questions with answers

Total 2005 CE0 compensation for the largest U.S. companies by revenue is reported in the following frequency distribution, along with some summary statistics. Total compensation includes salary, bonuses, stock and incentives, the potential value of stock options, and gains from stock options exercised.

$\begin{array}{|l|c|} \hline \begin{array}{l} \text { Total Compensation } \\ \text { (in millions of \$) } \end{array} & \text { Frequency } \\ \hline \text { Less than } 5 & 43 \\ \hline 5 \text { up to } 10 & 65 \\ \hline 10 \text { up to } 15 & 32 \\ \hline 15 \text { up to } 20 & 38 \\ \hline 20 \text { or more } & 60 \\ \hline & n=238 \\ \hline \end{array}$

Other summary statistics for CEO compensation (in millions of $) are as follows:$

$\begin{array}{|c|c|c|c|c|} \hline \text { Mean } & \text { Median } & \begin{array}{c} \text { Standard } \\ \text { Deviation } \end{array} & \text { Skewness } & \text { Kurtosis } \\ \hline 19.03 & 11.02 & 27.61 & 5.26 & 35.53 \\ \hline \end{array}$

$a. Conduct a goodness-of-fit test for normality of CEO compensation at the 1% significance level.

b. Conduct the Jarque-Bera test at the 1$ significance level.

c. Does total compensation of CEOs for the largest U.S. companies not follow the normal distribution?

Solution

Verified$\bold{a.)}$ We specify the competing hypotheses for the data. First is the null hypotheses $H_0$

$H_0:\text{The total compensation follows the normal distribution.}$

and next is the alternative hypotheses $H_a$

$H_a:\text{The total compensation follows the normal distribution.}$

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