Chapter 4.1, Problem 22P

Expand Your Knowledge: Sample Size and Significance of

Correlation In this problem, we use Table 4-6 to explore the significance of r based on different sample sizes. See Problem 21.

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

(b) Is a sample correlation coefficient r = 0.40 significant at the $\alpha =0.05$ 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.