The accompanying table shows the earnings per share (in dollars) and the dividends per share (in dollars) for
6
companies in a recent year. Complete parts (a) through (d) below.

Click here to view the data table.

Earnings per share, x

Dividends per share, y

1.2

0.95

4.3

0.38

3.58

2.4

8.56

1.12

1.92

0.75

3.17

1.43

Click here to view the table of critical values for the Pearson correlation coefficient.

n alpha=0.05 alpha=0.01
4 0.95 0.99
5 0.878 0.959
6 0.811 0.917
7 0.754 0.875
8 0.707 0.834
9 0.666 0.798
10 0.632 0.765
11 0.602 0.735
12 0.576 0.708
13 0.553 0.684
14 0.532 0.661
15 0.514 0.641
16 0.497 0.623
17 0.482 0.606
18 0.468 0.59
19 0.456 0.575
20 0.444 0.561
21 0.433 0.549
22 0.423 0.537
23 0.413 0.526
24 0.404 0.515
25 0.396 0.505
26 0.388 0.496
27 0.381 0.487
28 0.374 0.479
29 0.367 0.471
30 0.361 0.463
35 0.334 0.43
40 0.312 0.403
45 0.294 0.38
50 0.279 0.361
55 0.266 0.345
60 0.254 0.33
65 0.244 0.317
70 0.235 0.306
75 0.227 0.296
80 0.22 0.286
85 0.213 0.278
90 0.207 0.27
95 0.202 0.263
100 0.197 0.256

(a) Display the data in a scatter plot. Choose the correct graph below.

A.

B.

C.

D.

The graphs are on the Image. choose the correct graph

(b) Calculate the sample correlation coefficient r.

r=

Round to three decimal places as needed.

(c) Describe the type of correlation, if any, and interpret the correlation in the context of the data. Pick the correct answer. A to G which one is right?

There is

▼

a.a moderate negative

b.a strong negative

c.a perfect negative

d.a moderate positive

e.a perfect positive

f.a strong positive

g.no

linear correlation.

(d)
Interpret the correlation. Choose the correct answer below.

A.

As companies' earnings per share increase, their dividends per share tend to increase.

B.

Increases in companies' earnings per share cause their dividends per share to increase.

C.

As companies' earnings per share increase, their dividends per share tend to decrease.

D.

Increases in companies' earnings per share cause their dividends per share to decrease.

E.

Based on the correlation, there does not appear to be a linear relationship between companies' earnings per share and their dividends per share.

F.

Based on the correlation, there does not appear to be any relationship between companies' earnings per share and their dividends per share.

(E)
(d) Use the table of critical values for the Pearson correlation coefficient to make a conclusion about the correlation coefficient. Let α=0.01.

Pick A or B and find the critical value

The critical value is= .Therefore, there

▼
A.is

b.is not

sufficient evidence at the
1%
level of significance to conclude that

▼

A.there is no correlation

B.there is a significant linear correlation

between companies' earnings per share and their dividends per share.

(Round to three decimal places as needed.)

Question

The accompanying table shows the earnings per share (in dollars) and the dividends per share (in dollars) for

6

companies in a recent year. Complete parts (a) through (d) below.

Click here to view the data table.

Earnings per share, x	Dividends per share, y
1.2	0.95
4.3	0.38
3.58	2.4
8.56	1.12
1.92	0.75
3.17	1.43

Click here to view the table of critical values for the Pearson correlation coefficient.

n alpha=0.05 alpha=0.01
4 0.95 0.99
5 0.878 0.959
6 0.811 0.917
7 0.754 0.875
8 0.707 0.834
9 0.666 0.798
10 0.632 0.765
11 0.602 0.735
12 0.576 0.708
13 0.553 0.684
14 0.532 0.661
15 0.514 0.641
16 0.497 0.623
17 0.482 0.606
18 0.468 0.59
19 0.456 0.575
20 0.444 0.561
21 0.433 0.549
22 0.423 0.537
23 0.413 0.526
24 0.404 0.515
25 0.396 0.505
26 0.388 0.496
27 0.381 0.487
28 0.374 0.479
29 0.367 0.471
30 0.361 0.463
35 0.334 0.43
40 0.312 0.403
45 0.294 0.38
50 0.279 0.361
55 0.266 0.345
60 0.254 0.33
65 0.244 0.317
70 0.235 0.306
75 0.227 0.296
80 0.22 0.286
85 0.213 0.278
90 0.207 0.27
95 0.202 0.263
100 0.197 0.256

(a) Display the data in a scatter plot. Choose the correct graph below.

A.

B.

C.

D.

The graphs are on the Image. choose the correct graph

(b) Calculate the sample correlation coefficient r.

r=

Round to three decimal places as needed.

(c) Describe the type of correlation, if any, and interpret the correlation in the context of the data. Pick the correct answer. A to G which one is right?

There is

▼

a.a moderate negative

b.a strong negative

c.a perfect negative

d.a moderate positive

e.a perfect positive

f.a strong positive

g.no

linear correlation.

(d)

Interpret the correlation. Choose the correct answer below.

A.

As companies' earnings per share increase, their dividends per share tend to increase.

B.

Increases in companies' earnings per share cause their dividends per share to increase.

C.

As companies' earnings per share increase, their dividends per share tend to decrease.

D.

Increases in companies' earnings per share cause their dividends per share to decrease.

E.

Based on the correlation, there does not appear to be a linear relationship between companies' earnings per share and their dividends per share.

F.

Based on the correlation, there does not appear to be any relationship between companies' earnings per share and their dividends per share.

(E)

(d) Use the table of critical values for the Pearson correlation coefficient to make a conclusion about the correlation coefficient. Let α=0.01.

Pick A or B and find the critical value

The critical value is= .Therefore, there

▼

A.is

b.is not

sufficient evidence at the

1%

level of significance to conclude that

▼

A.there is no correlation

B.there is a significant linear correlation

between companies' earnings per share and their dividends per share.

(Round to three decimal places as needed.)

Accepted Answer

Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…