**Instructions:** Enter the sample correlation \(r\), sample size \(n\) and the significance level \(\alpha\), and the solver will test whether or not the correlation coefficient is significantly different from zero using the critical correlation approach.

#### More About Significance of the Correlation Coefficient

The sample correlation \(r\) is a statistic that estimates the population correlation, \(\rho\). On typical statistical test consists of assessing whether or not the correlation coefficient is significantly different from zero.

There are least two methods to assess the significance of the sample correlation coefficient: One of them is based on the critical correlation. Such approach is based upon on the idea that if the sample correlation \(r\) is large enough, then the population correlation \(\rho\) is different from zero.

In order to assess whether or not the sample correlation is significantly different from zero, the following t-statistic is obtained

\[ t = r\sqrt{ \frac{n-2}{1-r^2}} \]If the above t-statistic is significant, then we would reject the null hypothesis \(H_0\) (that the population correlation is zero). You can also the critical correlation approach, with the same purpose of assessing whether or not the sample correlation is significantly different from zero, but in that case by comparing the sample correlation with a critical correlation value.

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