Question

Using techniques from an earlier section, we can find a confidence interval for μd. Consider a...

Using techniques from an earlier section, we can find a confidence interval for μd. Consider a random sample of n matched data pairs A, B. Let d = BA 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 sd. If d has a normal distribution or is mound-shaped, or if n ≥ 30, then a confidence interval for μd is as follows.

dE < μd < d + E

where E = tc

sd
 n

c = confidence level (0 < c < 1)

tc = 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 μd = 0 from the null hypothesis is not in the 95% confidence interval, do not reject H0 at the 5% level of significance. The data indicate a difference in population mean percentage increases between company revenue and CEO salaries.Since μd = 0 from the null hypothesis is in the 95% confidence interval, reject H0 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 μd = 0 from the null hypothesis is in the 95% confidence interval, do not reject H0 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 μd = 0 from the null hypothesis is not in the 95% confidence interval, reject H0 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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