Question

You wish to determine if there is a negative 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
67.2	118
53.8	131.4
68.2	321.5
60.5	-67.4
58.2	154.3
60.5	230.3
41.2	157.7
105.5	91
72.8	-80
80.9	-105.7
79.6	125.1
81.7	-58.5
67.5	70.3
48.5	-81
17.9	184.8
57.4	149.2
59	30.8
43.1	104.9
63.9	-75
81.4	-1.2
50.5	-58.2
90.9	-27.9
77	115.3
54.2	171.7
78.9	208.3
54.3	-6.6
37.6	116.5
33	113.7
75.9	61.9
108.2	-54.3
54.4	81.2
87.3	279.8
68	-68.2
61.1	143.4
78	137.5
82.1	184.1
43.5	439.4
82	16.3
89.4	226.7
94.7	166.1

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

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

Answer 1