Question

A 0.05 significance level is being used to test a correlation between two variables. If the linear correlation coefficient r is found to be 0.591 and the critical values are r = ±0.878, what can you conclude?

Answer 1

Null hypothesis:
`\rho =0`

Alternative hypothesis:
`\rho \\eq 0`

The statistic to check the hypothesis is given by:

`t=(r √(n-2))/(√(1-r^2))`

And is distributed with n-2 degreed of freedom. df=n-2

For this case since the calculated values is on the interval (-0.878, 0.878) we can FAIL to reject the null hypothesis and on this case the correlation would be not significant at 5% of significance

Explanation:

In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:

Null hypothesis:
`\rho =0`

Alternative hypothesis:
`\rho \\eq 0`

The statistic to check the hypothesis is given by:

`t=(r √(n-2))/(√(1-r^2))`

And is distributed with n-2 degreed of freedom. df=n-2

For this case since the calculated values is on the interval (-0.878, 0.878) we can FAIL to reject the null hypothesis and on this case the correlation would be not significant at 5% of significance