Final answer:
The question asks about the Wilcoxon Signed-Rank Test, where you compare Tobtained with Tcritical to decide on the null hypothesis. If Tobtained <= Tcritical, the null hypothesis is not rejected, indicating no significant correlation. Examples of deciding based on critical values and p-values are provided.
Step-by-step explanation:
The question pertains to the Wilcoxon Signed-Rank Test, a non-parametric statistical test used to compare two related samples to assess whether their population mean ranks differ. To determine whether to reject the null hypothesis, the test statistic (Tobtained) is compared to the critical value (Tcritical). If Tobtained is less than or equal to Tcritical, you do not reject the null hypothesis as it indicates that there is not enough evidence to suggest that the variables are significantly correlated.
For example, if the critical value for α = 0.05 for a two-tailed test using the t-distribution with 29 degrees of freedom is 2.045, and your Tobtained is less than this, you would fail to reject the null hypothesis. Conversely, if the p-value is less than α, such as 0.0396 when α = 0.05, this indicates that the null hypothesis should be rejected, as there is strong evidence against it.