Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of
0)05. $$r = - 0.816 , n = 5$$
A) Critical values: $r = \pm 0.878$, no significant linear correlation
B) Critical values: $r = \pm 0.878$, significant linear correlation
C) Critical values: $r = 0.950$, significant linear correlation
D) Critical values: $r = \pm 0.950$, no significant linear correlation

Question

Quizplus · Accepted Answer

The critical values are calculated as $r = \pm t_{\alpha/2, n-2}\sqrt{\frac{1-r^2}{n-2}}$, where $t_{\alpha/2, n-2}$ is the critical value of the t-distribution with $n-2$ degrees of freedom and a significance level of $\alpha/2$. For a significance level of 0.05 and $n = 5$, the critical values are $r = \pm 0.878$. Since the given $r$ value of -0.816 is within these critical values, it does not represent a significant linear correlation.

Given the Linear Correlation Coefficient R and the Sample Size r=−0.816,n=5r = - 0.816 , n = 5r=−0.816,n=5

Given the Linear Correlation Coefficient R and the Sample Size $r = - 0.816 , n = 5$