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
20
10
6
18
6
4
21
37
A: Percent
increase
for CEO
20
29
23
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
= ±
Interpret your conclusion in the context of the application.
Fail to reject the null hypothesis, there is sufficient evidence
to claim a difference in population mean percentage increases for
corporate revenue and CEO salary.Reject the null hypothesis, there
is insufficient evidence to claim a difference in population mean
percentage increases for corporate revenue and CEO
salary. Fail to reject the null hypothesis,
there is insufficient evidence to claim a difference in population
mean percentage increases for corporate revenue and CEO
salary.Reject the null hypothesis, there is sufficient evidence to
claim a difference in population mean percentage increases for
corporate revenue and CEO salary.
Compare your conclusion with the conclusion obtained by using
the P-value method. Are they the same?
The conclusions obtained by using both methods are the same.We
reject the null hypothesis using the critical region method, but
fail to reject using the P-value
method. We reject the null hypothesis using
the P-value method, but fail to reject using the
critical region method.