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; strong

positive; moderate

positive; weak

negative; moderate

Question 7

Compute the coefficient of determination.

Answer 1

Q3)

We know that correlation between X and Y is given by:

So correlation between x and y is -0.9214983

Q4)

Here we need to find the critical value of t distribution.

here it will be t distribution will follow t distribution with n-2 = 10-2 = 8 df

so critical value of t distribution with 8 df and is given by:

tcritical, 0.05/2 = 2.306004 (Calculated in R)

Code of R is attached herewith

Q5)

Steps to do correlation analysis:

Step 1

where is the population correlation coefficent.

Here the criteria for the decision is that if calculated |t| is more than tabulated t then we have enough evidence to reject the null hypothesis.

So if |t| > tcritical, 0.05/2 = 2.306004

Then we have enough evidence to reject H0

Step 4:

So the test statistic is given by:

where rxy is sample correlation.

t = -6.7109

And here

|t| > tcritical

which implies that we do have enough evidence to reject H0

i.e., correlation between x and Y is there.

So Answer is True.

Q6)

Since we can see that correlation between both of them is -0.9214983 which implies that their is strong negative correlation between Friends and stress level.

So option negative; strong is correct.

Q7)

As we know that  coefficient of determination is given by the square of correlation coefficient.

So

So Coefficient of determination is  0.8491591

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