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	28	28	12	18	6	4	21	37
A: Percent increase for CEO	22	25	14	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. (Let d = B ? A.)

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: ?_d = 0; H₁: ?_d > 0H₀: ?_d > 0; H₁: ?_d = 0     H₀: ?_d ? 0; H₁: ?_d = 0H₀: ?_d = 0; H₁: ?_d ? 0H₀: ?_d = 0; H₁: ?_d < 0

(b) What sampling distribution will you use? What assumptions are you making?

The Student's t. We assume that d has an approximately uniform distribution.The Student's t. We assume that d has an approximately normal distribution.     The standard normal. We assume that d has an approximately uniform distribution.The standard normal. We assume that d has an approximately normal distribution.

What is the value of the sample test statistic? (Round your answer to three decimal places.)


(c) Find the P-value. (Round your answer to four decimal places.)

Answer 1

SolutionA:

alpha=5%=0.05

NUll Hypothesis is

H0:

Alternative Hypothesis:

H1:

?d = 0; H1: ?d ? 0

Solutionb:

since sample sizes are less than30

use t distribution assuming normal

The Student's t. We assume that d has an approximately normal distribution.

use eexcel data data analysis>t test assuming unequal variance.

t-Test: Two-Sample Assuming Unequal Variances
	B:percent increase for company	A:percent icrease for CEO
Mean	19.25	16.875
Variance	133.3571429	103.5536
Observations	8	8
Hypothesized Mean Difference	0
df	14
t Stat	0.436431668
P(T<=t) one-tail	0.334589434
t Critical one-tail	1.761310136
P(T<=t) two-tail	0.669178868
t Critical two-tail	2.144786688

t=0.436

Solutionc:

p=0.6692