Chapter 10.1, Problem 18P

Expand Your Knowledge: Confidence Intervals for ${\mu }_{\text{d}}$ Using techniques from Section 8.2, we can find a confidence intervals for ${\mu }_{\text{d}}$. Consider a random sample of n matched data pairs A, B. Let d = B – A be a random variable representing the difference between the values in a matched data pair. Compute the sample mean $\bar{d}$ of the differences and the sample standard deviation $s_d$. If d has a normal distribution or is mound-shaped, or if $n\ge 30$, then a confidence interval for ${\mu }_{\text{d}}$ is

$\begin{array}{l}\bar{d}-E<{\mu }_d<\bar{d}+E\\ \text{where}E=t_c\frac{S_d}{\sqrt{n}}\\ c=\text{confidence}\text{level}\left(0<c<1\right)\\ t_c=\text{critical}\text{value}\text{for}\text{confidence}\text{level}c\text{and}d.f.=n-1\end{array}$

Using the data of Problem 9, find a 95% confidence interval for the mean difference between percentage increase in company revenue and percentage increase in CEO salary.

Use the confidence interval method of hypothesis testing outlined in Problem 25 of Section 8.2 to test the hypothesis that population mean percentage increase in company revenue is different from that of CEO salary. Use a 5% level of significance.