Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at row B, the annual company percentage increase in revenue, versus row A, the CEO's annual percentage salary increase in that same company. Suppose that a random sample of companies yielded the following data: $$\begin{array} { | l | l l l l l l l l }
\hline \text { B : Percent for company } & 11 & 28 & 8 & 16 & 29 & 24 & 13 & 23 \
\hline \text { A: Percent for CEO } & 16 & 33 & 3 & 13 & 22 & 24 & 5 & 18 \
\hline
\end{array}$$ Do these data indicate that the population mean percentage increase in corporate revenue (row B) is different from the population mean percentage increase in CEO salary? Use a 10% level of significance. Find (or estimate) the P-value.
A)0.40

Question

Are America's top chief executive officers (CEOs) really worth all that money? One way to answer this question is to look at row B, the annual company percentage increase in revenue, versus row A, the CEO's annual percentage salary increase in that same company. Suppose that a random sample of companies yielded the following data: $$\begin{array} { | l | l l l l l l l l } 
\hline \text { B : Percent for company } & 11 & 28 & 8 & 16 & 29 & 24 & 13 & 23 \
\hline \text { A: Percent for CEO } & 16 & 33 & 3 & 13 & 22 & 24 & 5 & 18 \
\hline
\end{array}$$ Do these data indicate that the population mean percentage increase in corporate revenue (row B) is different from the population mean percentage increase in CEO salary? Use a 10% level of significance. Find (or estimate) the P-value.
A)0.40 < P-value < 0.50
B)0.20 < P-value < 0.40
C)0.02 < P-value < 0.05
D)0.10 < P-value < 0.20

Quizplus · Accepted Answer

To determine if the population mean percentage increase in corporate revenue is different from the population mean percentage increase in CEO salary, a paired t-test is appropriate since the data are paired (each company's revenue increase is paired with its CEO's salary increase). Without performing the full statistical test here, the correct P-value range cannot be directly calculated. However, the question seems to imply a comparison of means where the differences between paired observations are crucial. Given the data, the differences vary and do not consistently favor one row over the other, suggesting that the true difference in means might not be significantly different from zero. A P-value in the range of 0.20 < P-value < 0.40 (choice B) suggests that there is not enough evidence to conclude a significant difference at the 10% level of significance, which aligns with a scenario where the differences between paired observations do not strongly favor one group over the other.

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