91Ó°ÊÓ

To find the critical values for the given significance levels (\(\alpha=0.05\) and \(\alpha=0.01\)) and sample size (number of pairs of ranks, n = 12), you should consult a table of critical values for Spearman's rank correlation coefficient (\(r_s\)). This table usually lists the critical values for a two-tailed test, so you will need to find the one-tailed critical values by halving the significance levels: a. For \(\alpha=0.05\), the one-tailed significance level is \(\frac{0.05}{2} = 0.025\). b. For \(\alpha=0.01\), the one-tailed significance level is \(\frac{0.01}{2} = 0.005\). Now look up the critical values in the \(r_s\) table using the one-tailed significance levels and the number of pairs of ranks (12). You will find the following critical values: a. For \(\alpha=0.05\) (0.025 in one-tailed test), the critical value is approximately \(\pm0.576\) b. For \(\alpha=0.01\) (0.005 in one-tailed test), the critical value is approximately \(\pm0.760\)

Now that you have the critical values, you can determine the rejection regions for negative rank correlation: a. For \(\alpha=0.05\), the rejection region for negative rank correlation (given by \(r_s<0\)) is \(r_s<-0.576\). If the calculated \(r_s\) is less than -0.576, you can reject the null hypothesis in favor of the alternative hypothesis (negative rank correlation) at the 0.05 significance level. b. For \(\alpha=0.01\), the rejection region for negative rank correlation (given by \(r_s<0\)) is \(r_s<-0.760\). If the calculated \(r_s\) is less than -0.760, you can reject the null hypothesis in favor of the alternative hypothesis (negative rank correlation) at the 0.01 significance level.