Question

The Pearson correlation coefficient for a relationship between two variables from a data sample of n = 11 was found to be r ~ - 0.603. Is this relationship statistically significant at the a = 0.05 level?

Critical Values of the Pearson Correlation Coefficient
n a = 0.05 a = 0.01
4 0.950 0.990
5 0.878 0.959
6 0.811 0.917
7 0.754 0.875
8 0.707 0.834
9 0.666 0.798
10 0.632 0.765
11 0.602 0.735
12 0.576 0.708

A) Yes, the linear relationship between the variables is statistically significant at the 0.05 level of significance, because |r| > critical value.
B) No, the linear relationship between the variables is not statistically significant at the 0.05 level of significance, because /r| ≤ critical value.
C) No, the linear relationship between the variables is not statistically significant at the 0.05 level of significance, because r ≤ 0.
D) Yes, the linear relationship between the variables is statistically significant at the 0.05 level of significance, because r > 0.

Answer 1

[AI-generated answer — Bot GPT 3.5]

A) Yes, the linear relationship between the variables is statistically significant at the 0.05 level of significance, because |r| > critical value.

Since the absolute value of r is 0.603, which is greater than the critical value of 0.602 for n = 11 at the 0.05 level of significance, the relationship between the two variables is considered statistically significant.