Question

At the .01 significance level, does the data below show significant correlation?

x	y
5	22.78
6	21.22
7	20.96
8	26.8
9	24.34
10	15.28
11	12.82
12	10.86
13	9.2

• Yes, significant correlation
• No

**Please explain why its yes/no

Answer 1

We have to test the hypothesis

Whether or not correlation coefficient is significant?

i.e. Null Hypothesis- ( i.e. Two variables X and Y are independent.)

against

Alternative Hypothesis- (i.e. Two variables are dependent.)

Where is the population correlation coefficient between X and Y.

Significance correlation coefficient is tested by t-test.

The value of the test statistic is given by

r = sample correlation coefficient between X and Y.

By using R

> x= 5:13
> y=c(22.78,21.22,20.96,26.8,24.34,15.28,12.82,10.86,9.2)
> r=cor(x,y)
> r
[1] -0.8147932

from R-output the value of sample correlation coefficient r = -0.8148.

Since there is negative correlation between X and Y.

Value of test statistic is

t = -3.7183

Alpha : level of significance = 0.01

Since value of test is -3.7183 and test is two-tailed, p-value is obtained by

by using R

> p=2* pt(-3.7183,7)
> p
[1] 0.007472764

p-value = 0.0075.

Decision : Since p-value < level of significance, we reject the null hypothesis at 1% level of significance.

Conclusion: There is sufficient evidence support to claim that the correlation coefficient is significant.