Question

a researcher investigated the relationship between monthly income and years of service in a company. using the data from 20 workers, the computed correlation coefficient was found to be 0.25. is the computed r significant at 0.05 level of significance? 

Answer 1

$T=r\frac{\sqrt{n-2}}{\sqrt{1-r^2}}=0.25\frac{\sqrt{20-2}}{\sqrt{1-0.25^2}}=1.09545\sim t_{n-m-1}=t_{17}\\P\left( \left| T \right|>1.09545 \right) =2F_{t,17}\left( -1.09545 \right) =2\cdot 0.1443=0.2886$

Here m is the number of variables, m=2.

Since the P-value is greater than the significance level, the coefficient is not significant.