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	21	10	15	23	15	29	20	30
A: Percent increase for CEO	17	1	11	28	16	34	12	22

​

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 5% level of significance. What is the alternate hypothesis?

​

Answer 1

µd = µB - µA

null hypothesis,Ho :   µd=   0
alternate hypothesis,Ha :   µd ╪   0

Sample #1	Sample #2	difference , Di =sample1-sample2	(Di - Dbar)²
21	17	4.000	1.5625
10	1	9.000	39.0625
15	11	4.000	1.5625
23	28	-5.000	60.0625
15	16	-1.000	14.0625
29	34	-5.000	60.0625
20	12	8.000	27.5625
30	22	8.000	27.5625

	sample 1	sample 2	Di	(Di - Dbar)²
sum =	163	141	22	231.5

mean of difference ,    D̅ =ΣDi / n =   2.7500
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    5.7508
std error , SE = Sd / √n =    5.7508   / √   8   =   2.0332      
                          
t-statistic = (D̅ - µd)/SE = (   2.75   -   0   ) /    2.0332   =   1.353
                          
Degree of freedom, DF=   n - 1 =    7                  
  
p-value =        0.2183 [excel function: =t.dist.2t(t-stat,df) ]               
Conclusion:     p-value>α , Do not reject null hypothesis                      

There is not enough evidence to conclude that  population mean percentage increase in corporate revenue (row B) is different from the population mean percentage increase in CEO salary