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 increase for company 37 7 12 7 21 18 17 10

A: Percent increase for CEO 28 10 9 3 26 16 20 7

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? Assume that the distribution of differences is approximately normal, mound-shaped and symmetric. Use a 1% level of significance. Find (or estimate) the P-value.

Select one answer:

a. 0.02 < P-value < 0.05

b. 0.01 < P-value < 0.02

c. 0.25 < P-value < 0.50

d. P-value = 0.05

e. P-value = 0.25

Answer 1

Ho :   µd=   0
Ha :   µd ╪   0

Sample #1	Sample #2	difference , Di =sample1-sample2	(Di - Dbar)²
37	28	9.000	60.0625
7	10	-3.000	18.0625
12	9	3.000	3.0625
7	3	4.000	7.5625
21	26	-5.000	39.0625
18	16	2.000	0.5625
17	20	-3.000	18.0625
10	7	3.000	3.0625

	sample 1	sample 2	Di	(Di - Dbar)²
sum =	129	119	10	149.5

mean of difference ,    D̅ =ΣDi / n =   1.250                  
                          
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    4.6214                  
                          
std error , SE = Sd / √n =    4.6214   / √   8   =   1.6339      
                          
t-statistic = (D̅ - µd)/SE = (   1.25   -   0   ) /    1.6339   =   0.765
                          
Degree of freedom, DF=   n - 1 =    7                  

p-value =        0.46925   [excel function: =t.dist.2t(t-stat,df) ]

so, answer is c. 0.25 < P-value < 0.50