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=0.767, n=25
A) Critical values: r= ±0.487 , significant linear correlation
B) Critical values: r= ±0.396 , no significant linear correlation
C) Critical values: r= ±0.396 , significant linear correlation
D) Critical values: r= ±0.487 , no significant linear correlation

Question

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=0.767, n=25
A) Critical values:  r= ±0.487 , significant linear correlation
B) Critical values:  r= ±0.396 , no significant linear correlation
C) Critical values:  r= ±0.396 , significant linear correlation
D) Critical values:  r= ±0.487 , no significant linear correlation

Quizplus · Accepted Answer

For a sample size of n=25 and a significance level of 0.05, the critical value of r can be found in a table of critical values for Pearson's correlation coefficient. For n=25, the critical value of r is approximately ±0.396. Since the given r=0.767 is greater than 0.396, it represents a significant linear correlation.

Given the Linear Correlation Coefficient R and the Sample Size