Question

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 mound-shaped, or if n ≥ 30, then a confidence interval for μ_d is as follows.

d − E < μ_d < d + E

where E = t_c

sd

n

c = confidence level (0 < c < 1)

t_c = critical value for confidence level c and d.f. = n − 1

B: Percent increase for company	28	16	26	18	6	4	21	37
A: Percent increase for CEO	25	24	24	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 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 μ_d = 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 μ_d = 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 μ_d = 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.

Answer 1

for 95% CI; and 7 degree of freedom, value of t=			2.365
therefore confidence interval=sample mean -/+ t*std error
margin of errror          =t*std error=		7.015
lower confidence limit                     =		-5.89
upper confidence limit                    =		8.14

b)

Since μ_d = 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.