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### Step-by-Step Procedure for Testing the Significance of Correlation Coefficient (Numerical Approach) The correlation coefficient, denoted as \( r \), measures the strength and direction of the linear relationship between two variables. To determine whether this correlation is statistically significant, we perform a hypothesis test. #### Step 1: Define the Hypotheses - Null Hypothesis (\( H_0 \)): There is no correlation between the two variables, i.e., \( \rho = 0 \). - Alternative Hypothesis (\( H_1 \)): There is a significant correlation, i.e., \( \rho \neq 0 \). #### Step 2: Compute the Correlation Coefficient \( r \) The Pearson correlation coefficient is given by: \[ r = \frac{n \sum xy _______ _________ ______ ____ ________ __________ _____ _________ _______.
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