Question

Test the claim that the correlation between two variables is zero when a sample of 19 points has the correlation coefficient of 0.46. Test with alpha = 0.01.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 0

H_a :    0

r = 0.46

n = 19

degrees of freedom = n - 2 =

Test statistic = t

=

= 0.46 * (17) / (1 - 0.46²)

= 2.1336

Test statistic = 2.136

= 0.01

Critical value = 2.898

Test statistic < Critical value

Fail to reject the null hypothesis at the 1% level of significance .