Question

A sociologist believes that there is a relationship between number of friends an elderly person has and their perceived level of stress.

Participant	# of Friends (Y)	Stress Level (X)
A	10	1
B	3	7
C	12	2
D	11	3
E	6	5
F	8	4
G	14	1
H	9	2
I	10	3
J	2	10

*higher scores of the measure of stress (from 1 to 10) indicate more stress.

Use this information to answer questions 3 and 7.

Question 3

What is the correlation coefficient?

Question 4

Use Table R to find the critical value for the correlation coefficient.

Question 5

The correlation coefficient is significantly different from zero, meaning there is a significant linear relationship (correlation) between x and y.

Group of answer choices

True

False

Question 6

What is the relationship?

Group of answer choices

negative; moderate

negative; strong

positive; moderate

positive; weak

Question 7

Compute the coefficient of determination.

Answer 1

3.

X	Y
1	10
7	3
2	12
3	11
5	6
4	8
1	14
2	9
3	10
10	2

Also, the following calculations are needed to compute the correlation coefficient:

	X	Y	X*Y	X2	Y2
	1	10	10	1	100
	7	3	21	49	9
	2	12	24	4	144
	3	11	33	9	121
	5	6	30	25	36
	4	8	32	16	64
	1	14	14	1	196
	2	9	18	4	81
	3	10	30	9	100
	10	2	20	100	4
Sum =	38	85	232	218	855

The correlation coefficient r is computed using the following expression:

where

In this case, we get that

Therefore, the sample correlation coefficient is computed as follows

4.

The critical value for the correlation coefficient is 0.632.

The sample size is n = 10, so then the number of degrees of freedom is df = n-2 = 10 - 2 = 8

The corresponding critical correlation value rc​ for a significance level of α=0.05, for a two-tailed test is:

rc ​= 0.632

5.

The following needs to be tested:

H0​ : ρ = 0

HA ​: ρ 0

The corresponding critical correlation value rc​ for a significance level of α=0.05, for a two-tailed test is:

rc​ = 0.632

Observe that in this case, the null hypothesis H0​:ρ=0 is rejected if ∣r∣>rc​=0.632.

We have that ∣r∣=0.921>rc​=0.632, from which is concluded that the null hypothesis is rejected.

True, the correlation coefficient is significantly different from zero, meaning there is a significant linear relationship (correlation) between x and y.

6.

The relationship is negative, strong.

7.

Coefficient of determination =