The analysis involves assessing the strength and direction of a correlation, stating and testing the null hypothesis via p-value and t-value comparison, to determine if the correlation is statistically significant and not due to random chance.
Understanding Correlation and Hypothesis Testing
When analyzing the correlation evaluated in cell A15, it can be categorized as weak, moderate, or strong depending on its value. If the correlation is positive, as assessed in cell A15, it indicates that as one variable increases, the other variable tends to increase as well. The result in cell A23 indicates the direction of this association.
The null hypothesis usually states that there is no effect or no association; in the context of correlation, the null hypothesis (stated in cell A25) would assert that there is no correlation between the variables. If the p-value in cell A16 is less than the chosen level of significance (α, often set to 0.05), we would reject the null hypothesis as it suggests that the observed correlation is not due to random chance.
Comparing the t-value in cell A17 to the table t-value in cell A18 assists in determining if the observed correlation is statistically significant. If the t-value is greater than the critical value from the table (considering the appropriate degrees of freedom and level of significance), it provides evidence against the null hypothesis, leading us to reject it. However, without the specific numbers, we cannot determine the appropriate conclusion for Exercises 4 and 5.