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
101.8	97.3
72.4	18.1
94.1	94.4
43.8	-23.5
84.5	84.5
68.1	27.2
51.3	3.9
88.6	87.8
77	53.1
56.9	13.7
72.7	29.5
74.1	36.7
112.3	112.7
70.9	40.1

What is the correlation coefficient for this data set?
       r =
(report answer accurate to at least 3 decimal places)

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−2n-2 degrees of freedom.

What is the p-value for this correlation coefficient?
       p-value =
(report answer accurate to at least 4 decimal places)

Your final conclusion is that...

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

Answer 1

Correlation ( r ) = 0.963

Test statistic :

t = r sqrt (n-2/( 1-r2 ))

t =   11.30

p value :

with t = 11.30 , df = 10

we get

p value = 0

Decision : p value < l.o.s

              i.e., 0 < 0.005

so reject H0

Conclusion :

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