Question

how do we test hypotheses concerning the linear correlation coefficient?

Answer 1

Hypothesis test for the linear correlation coefficient is completed using the t test statistic

For null hypothesis, we always assume that the population correlation or rho is equal to 0

For alternate hypothesis, we can assume it to be two tailed, left tailed or right tailed based on the requirement of hypothesis testing

We have the sample size n value and sample correlation coefficient r value

then we use the following formula to solve for test statistic t

t = (r*(sqrt{n-2))/sqrt{1-r^2}.........sqrt means square root

Then we find the p value corresponding to the test statistic and compare it with the significance level

if p value is less than significance level, then there is a significant correlation

if p value is equal or greater than significance level, then there is no significant correlation