Question

Critical Values for the Correlation Coefficient      
n   alpha = .05   alpha = .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
25   0.396   0.505
30   0.361   0.463
35   0.335   0.43
40   0.312   0.402
45   0.294   0.378
50   0.279   0.361
60   0.254   0.33
70   0.236   0.305
80   0.22   0.286
90   0.207   0.269
100   0.196   0.256
Note: To test H subscript 0: rho equals 0 against H subscript 1: rho not equal to 0, reject H subscript 0 if the absolute value of r is greater than the critical value in the table.      

For a sample of eight bears, researchers measured the distances around the bears' chests and weighed the bears. Minitab was used to find that the value of the linear correlation coefficient is r=0.969. Using a = 0.05, determine if there is a linear correlation between chest size and weight. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size? Click here to view a table of critical values for the correlation coefficient. a. Is there a linear correlation between chest size and weight? O A. Yes, because the test statistic falls between the critical values of - 0.707 and 0.707. O B. Yes, because the absolute value of the test statistic exceeds the critical value of 0.707. O C. No, because the absolute value of the test statistic exceeds the critical value of 0.707. O D. The answer cannot be determined from the given information. b. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size? (Round to three decimal places as needed.)

Answer 1

Solution:

n = 8

r = 0.969

Using claim , we can say that the test is TWO TAILED

$\alpha$ = 0.05

Now,

d.f = n - 2 = 8 - 2 = 6

a) Use the critical values table of Pearson correlation , the critical values are

-0.707 and 0.707

Rejection region is < -0.707 or > 0.707

r = 0.998 falls in rejection region.

So , significant correlation present.

Answer for part a is

Yes , the absolute value of the test statistic exceeds the critical of 0.707

Option A is correct.

b)

Proportion of variation explained

= r²

= 0.969²

= 0.939