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? Select one: a. two tailed test b. right tailed test c. left tailed test

Answer 1

From the given data we have:

company	CEO	difference
2	-1	3
5	5	0
29	21	8
8	13	-5
21	12	9
14	18	-4
13	9	4
12	8	4
mean (Xd-bar)=		2.375
standard deviation =		5.097

sample size,n = 8

sample mean,dbar = 2.375

standard deviation,Sd = 5.097

alpha,a = 0.01

.Hypotheses:

H0: u_d = 0

H1: u_d is not equal to 0

This is two tailed test

.Test statistic,

t = dbar/(Sd/sqrt(n))

t = 1.32

.critical value = +/- t(a/2,n-1) = +/- t(0.025, 7)

critical value = +/- 3.50

.So the non-critical region is interval between the interval (-3.50 , 3.50)

Here we can see the test statistic t lies inside the interval hence H0 can not be rejected.

Conclusion:

There is not sufficient evidence to support the claim.Hence we can conclude that these data do not indicate that the population mean percentage increase in corporate revenue (row B) is different from the population mean percentage increase in CEO salary