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	2	5	29	8	21	14	13	12
A: Percent for CEO	-1	5	21	13	12	18	9	8

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. Will you use a left tailed, right tailed, or two tailed test?

Answer 1

paired t test

Ho :   µd=   0
Ha :   µd ╪   0 (two tailed test)

mean of difference ,    D̅ =ΣDi / n =   2.375                  
                          
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    5.097                  
                          
std error , SE = Sd / √n =    5.0973   / √   8   =   1.8022      
                          
t-statistic = (D̅ - µd)/SE = (   2.375   -   0   ) /    1.8022   =   1.3179
                          
Degree of freedom, DF=   n - 1 =    7                  
t-critical value , t* =    ±   3.4995   [excel function: =t.inv.2t(α,df) ]               
                          
p-value =        0.2290 [excel function: =t.dist.2t(t-stat,df) ]               
Decision:   p-value>α , Do not reject null hypothesis                      

There is no enough evidence to conclude that the population mean percentage increase in corporate revenue (row B) is different from the population mean percentage increase in CEO salary