Using techniques from an earlier section, we can find a confidence interval for μ_{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
d
of the differences and the sample standard deviation s_{d}. If d has a normal distribution or is moundshaped, or if n ≥ 30, then a confidence interval for μ_{d} is as follows.
d − E < μ_{d} < d + E
where E =
t_{c}
s_{d}  

c = confidence level (0 < c < 1)
t_{c} = critical value for confidence level
c and d.f. = n − 1
B: Percent increase for company 
14  18  24  18  6  4  21  37 
A: Percent
increase for CEO 
29  26  19  14 
−4 
19  15  30 
(a) Using the data above, find a 95% confidence interval for the mean difference between percentage increase in company revenue and percentage increase in CEO salary. (Round your answers to two decimal places.)
lower limit  
upper limit 
(b) Use the confidence interval method of hypothesis testing 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.
Since μ_{d} = 0 from the null hypothesis is not in the 95% confidence interval, do not reject H_{0} at the 5% level of significance. The data indicate a difference in population mean percentage increases between company revenue and CEO salaries.Since μ_{d} = 0 from the null hypothesis is in the 95% confidence interval, reject H_{0} at the 5% level of significance. The data do not indicate a difference in population mean percentage increases between company revenue and CEO salaries. Since μ_{d} = 0 from the null hypothesis is in the 95% confidence interval, do not reject H_{0} at the 5% level of significance. The data do not indicate a difference in population mean percentage increases between company revenue and CEO salaries.Since μ_{d} = 0 from the null hypothesis is not in the 95% confidence interval, reject H_{0} at the 5% level of significance. The data indicate a difference in population mean percentage increases between company revenue and CEO salaries.
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