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In: Math

Are America's top chief executive officers (CEOs) really worth all that money? One way to answer...

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?

Solutions

Expert Solution

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


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