Question

The accompanying data represent the total compensation for 12 randomly selected chief executive officers​ (CEOs) and the​ company's stock performance.

Company   Compensation   Return
A   14.98   74.48
B   4.61   63.62
C   6.15   148.21
D   1.11   30.35
E   1.54   11.94
F   3.28   29.09
G   11.06   0.64
H   7.77   64.16
I   8.23   50.41
J   4.47   53.19
K   21.39   21.94
L   5.23   33.68

​(a) Treating compensation as the explanatory​ variable, x, use technology to determine the estimates of β0 and β1.

The estimate of β1 is −0.217.

​(Round to three decimal places as​ needed.)

The estimate of beta 0β0 is 50.1

​(Round to one decimal place as​ needed.)

​(b) Assuming that the residuals are normally distributed​, test whether a linear relation exists between compensation and stock return at the α=0.01level of significance. What are the null and alternative​ hypotheses?

B. H0​: β1=0 H1​: β1≠0 Your answer is correct.

Compute the test statistic using technology. -0.10​

(Round to two decimal places as​ needed.)

Compute the​ P-value using technology.

0.919

​(Round to three decimal places as​ needed.)

State the appropriate conclusion. Choose the correct answer below.

A.

Reject H0. There is sufficient evidence to conclude that a linear relation exists between compensation and stock return.

B.

Reject H0. There is not sufficient evidence to conclude that a linear relation exists between compensation and stock return.

C.

Do not reject H0. There is sufficient evidence to conclude that a linear relation exists between compensation and stock return.

D.

Do not reject H0. There is not sufficient evidence to conclude that a linear relation exists between compensation and stock return.

Answer 1

Part a) and b) are correct.

Now we have to make conclusion.

Here p-value = 0.919 and  = 0.01

Decision rule : if p-value , we reject the null hypothesis H0, otherwise we fail to reject H0

Our p-value = 0.919 > 0.01

So we fail to reject the null hypothesis H0 .

Conclusion : Do not reject H0 . There is There is not sufficient evidence to conclude that a linear relation exists between compensation and stock return.