Question

You wish to determine if there is a linear correlation between the two variables at a significance level of α=0.005α=0.005. You have the following bivariate data set.

x	y
13.6	126.6
33.5	42.2
17.6	78.5
39	32.7
33	61.5
47.1	25.1
41.4	34.7
74	-41
68.7	-3
41.2	59.9
27.1	89.2
27.2	78.7
-19.8	179.9
62.7	-1.1
21	112.8
40.6	32.6
27.3	63.2
27.6	59.6
31.4	52.7
56.6	9.1
55	28.6
40.5	46.3
17.9	91.8
52.1	-6.6
38	21.3
24.5	75.1
19.6	80.6
74.8	-55.6
44.9	12.5
51.1	25.1

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

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

Answer 1

Correlation ( r ) = -0.955