Question

You wish to determine if there is a positive linear correlation between the two variables at a significance level of α=0.01α=0.01. You have the following bivariate data set.

x	y
54.5	82.1
45.8	20.9
46.4	22.7
44.8	-5.5
38.8	-5.4
35.4	83.5
44.3	96.3
25	-45.1
47.8	29.8
48.8	6
49.9	40.6
50.2	62.7
42.1	20.4
32.3	-40.2
45.1	30.5
49.3	3.4
29.4	27.7
44	2.3
39.2	18.2
37.5	1
44.1	27.1
50.6	-41.3
42.9	90.5
39.2	4.5
40.2	-60.7
34	-39.3
50	107
39.3	-36.4
38.4	39.8
40.8	13.8
49.1	86.8
42.3	41.5
28.2	22

What is the correlation coefficient for this data set?
r =

To find the p-value for a correlation coefficient, you need to convert to a t-score:

t=√r2(n−2)1−r2t=r2(n-2)1-r2

This t-score is from a t-distribution with n–2 degrees of freedom.

What is the p-value for this correlation coefficient?
p-value =

Your final conclusion is that...

• There is insufficient sample evidence to support the claim the there is a positive correlation between the two variables.
• There is sufficient sample evidence to support the claim that there is a statistically significant positive correlation between the two variables.

Note: In your calculations, round both r and t to 3 decimal places in ALL calculations.

Answer 1

We have given the below data and we have to compute correlation coefficient between x and y .

x	y
54.5	82.1
45.8	20.9
46.4	22.7
44.8	-5.5
38.8	-5.4
35.4	83.5
44.3	96.3
25	-45.1
47.8	29.8
48.8	6
49.9	40.6
50.2	62.7
42.1	20.4
32.3	-40.2
45.1	30.5
49.3	3.4
29.4	27.7
44	2.3
39.2	18.2
37.5	1
44.1	27.1
50.6	-41.3
42.9	90.5
39.2	4.5
40.2	-60.7
34	-39.3
50	107
39.3	-36.4
38.4	39.8
40.8	13.8
49.1	86.8
42.3	41.5
28.2	22

•