Question

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" 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 a random sample of companies yielded the following data:

B: Percent increase for company	30	22	22	18	6	4	21	37
A: Percent increase for CEO	16	14	24	14	-4	19	15	30

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 5% level of significance. Solve the problem using the critical region method of testing. (Let d = B − A. Round your answers to three decimal places.)

test statistic	=
critical value	=

Answer 1

here we want to test the

null hypothesis H0:=0 (  increase in corporate revenue is same)

alternate hypothesis Ha: (  increase in corporate revenue different or not same)

we use paired t-test and statisitc t=/sd/(sqrt(n))=4/(8.9602/sqrt(8))=1,2627 with n-1=8-1=7 fg

critical t=t(0.05/2,7)=2.3646

since the calculated t=1.2627 is less than critical t=2.3646, so we fail to reject H0(or accept H0) and conclude that increase in corporate revenue same or not different.

B	A	d=B-A
30	16	14
22	14	8
22	24	-2
18	14	4
6	-4	10
4	19	-15
21	15	6
37	30	7
	n=	8
	mean=	4.0000
	sd=	8.9602
	SE=sd/sqrt(n)=	3.1679
	t=	1.2627
	critical t=	2.3646
two tailed	p-value=	0.2471
one tailed	p-value=	0.1236