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:

B: Percent for company	5	8	13	16	14	20	4	13
A: Percent for CEO	2	-1	3	14	19	17	3	9

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 1% level of significance. Are the data statistically significant at level α? Will you reject or fail to reject the null hypothesis?

a. Since the interval containing the P-values has values that are smaller than the level of significance, the data are statistically significant and so we reject the null hypothesis.

b. Since the interval containing the P-values has values that are smaller than the level of significance, the data are not statistically significant and so we reject the null hypothesis.

c. Since the interval containing the P-values has values that are larger than the level of significance, the data are not statistically significant and so we fail to reject the null hypothesis.

d. Since the interval containing the P-values has values that are larger than the level of significance, the data are statistically significant and so we fail to reject the null hypothesis.

e. Since the interval containing the P-values has values that are larger than the level of significance, the data are not statistically significant and so we reject the null hypothesis.

Answer 1

Paired T-Test and CI: B:Percent for company, A: Percent for CEO

Paired T for B:Percent for company - A: Percent for CEO

N Mean StDev SE Mean
B:Percent for company 8 11.63 5.53 1.95
A: Percent for CEO 8 8.25 7.61 2.69
Difference 8 3.38 4.69 1.66

99% CI for mean difference: (-2.43, 9.18)
T-Test of mean difference = 0 (vs not = 0): T-Value = 2.04 P-Value = 0.081>0.01(=level of significance)

Option c. Since the interval containing the P-values has values that are larger than the level of significance, the data are not statistically significant and so we fail to reject the null hypothesis.