Given a set of data with a correlation coefficient of 0.89 and a sample size of 20, is the correlation significant?
Answer
Step 4: Compare the value of t obtained with the critical t-value in the t-distribution table for degrees of freedom n-2 = 18 and significance level of 0.05, usually, the critical t-value is approximately 2.101.
Step 1 ：Step 1: Compute the test statistic using the formula: \(t = r \sqrt{\frac{n-2}{1-r^2}}\)
Step 2 ：Step 2: Substitute the given values into the formula: \(t = 0.89 \sqrt{\frac{20-2}{1-0.89^2}}\)
Step 3 ：Step 3: Solve the expression to find the value of t
Step 4 ：Step 4: Compare the value of t obtained with the critical t-value in the t-distribution table for degrees of freedom n-2 = 18 and significance level of 0.05, usually, the critical t-value is approximately 2.101.
