The formula to calculate critical values for correlation coefficient hypothesis tests is not that messy. First, determine the significance level and the type of test (1- or 2-tailed). Then, find the corresponding critical t value using n2\displaystyle {n}-{2} degrees of freedom. Take this value and plug it into the equation
r=tt2+n2\displaystyle {r}=\frac{{t}}{{\sqrt{{{t}^{{2}}+{n}-{2}}}}}
The advantage of this formula is that it allows you to find more critical values than those listed in some tables. In particular, you can find one- and two-tailed critical values and for different significance levels.

You wish to conduct a hypothesis test to determine if a bivariate data set has a significant negative correlation among the two variables. That is, you wish to test the claim that Ha:ρ<0\displaystyle {H}_{{a}}:\rho<{0}. You have a data set with 143 subjects, in which two variables were collected for each subject. You will conduct the test at a significance level of α=0.01\displaystyle \alpha={0.01}.

Find the critical value for this test (use the formula given above).
rc.v. = \displaystyle

Report answers accurate to three decimal places.