Question

The mean pay in 2008 Bh CEOsat the 500 biggest U.S. companies was 12.8 million dollars.”” Public outcry and stockholder complaints have forced compensation committees to reconsider senior executive salaries. A random sample of CEOs was obtained, and the total pay (in millions of dollars) for each is given in the following table.

10.1 4.3 13.8 5.1 13.0 21.2 4.5 10.5 17.6 10.1 6.5 9.9 13.3 20.4

Is there any evidence to suggest that the mean pay for CEOs has decreased? Use a = 0.05 and assume normality.

Answer 1

The null and alternative hypotheses are,

H0 : μ = 12.8

Ha : μ < 12.8

Using TI-83 plus calculator we get,

Test statistic = t = -0.916

p-value = 0.1882

t-critical value at significance level of 0.05 with degrees of freedom = 14 - 1 = 13 is, t_{​​​​​​crit} = -1.771

Excel Command : =TINV(0.10, 13) = 1.771

Since, test statistic = -0.916 > -1.771

We fail to reject the null hypothesis.

Conclusion : There is insufficient evidence to conclude that the mean pay for CEOs has decreased.