Given the linear correlation coefficient r and the sample si

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to sate whether or not the given r represents a significan linear correlation. Use a significance level of 0.05, r=0.127, n=15.

With the information above, can you find the critical values of r? Is r a representation of a significant linear correlation?

Solution

Given n=15(small sample), r=0.127, alpha=0.05, so at (15-2)=13 degrees of freedom, ttab=2.16.

Ho:the value of r=0.127 is not significant vs H1:the value of r=0.127 is significant. Then tcal=[(r*(n-2))/(1-r²)]=[(0.127*13)/((1-0.0161))=0.4579/0.9919=0.4616<2.16. Here tcal<ttab, so we accept null hypothesis, i.e.,Ho:the value of r=0.127 is not significant.