Final answer:
±0.497 for the critical value of the correlation coefficient for a two-tailed test at α = 0.05 for a sample size of n = 20. Thus The correct option is Option C:
Step-by-step explanation:
For a two-tailed test with α = 0.05 and a sample size of n = 20, the critical value of the correlation coefficient can be found using the critical values table for Pearson's correlation. With α = 0.05 and n = 20, the critical value is approximately ±0.497.
In this case, the critical value for a two-tailed test at α = 0.05 and n = 20 can be obtained from statistical tables or software that provides critical values for correlation coefficients. When looking at the critical values table for Pearson's correlation coefficients, the value for α = 0.05 and a sample size of n = 20 is approximately ±0.497. This means that for a correlation coefficient outside the range of -0.497 to 0.497, we would reject the null hypothesis in favor of the alternative hypothesis at a significance level of 0.05 in a two-tailed test.
The critical values table helps in determining the threshold beyond which the calculated correlation coefficient would be considered significant at a given level of significance (α) and sample size (n). In this case, a critical value of ±0.497 signifies the boundaries for statistical significance in a two-tailed test for the correlation coefficient with a sample size of 20 at a significance level of 0.05. Thus The correct option is Option C: