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.

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.)

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