Question: Expand Your Knowledge: Sample Size and Significance of Correlation

In this problem we use Table 4-4 to explore the significance of r based on different sample sizes.

a.) Is a sample correlation coefficient r = 0.820 significant at the a = 0.01 level based on a sample size of n = 7 data pairs? What about n = 9 data pairs? What about n = 9 data pairs?

b.) Is a sample correlation coefficient r = 0.40 significant at the a = 0.05 level based on a sample size of n = 20 data pairs? What about n = 27 data pairs?

c.) Is it true that in order to be significant, an r value must be larger than 0.90? Larger than 0.70? Larger than 0.50? What does sample size have to do with the significance of r? Explain.