Step 1 :The question is asking to determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. The linear correlation coefficient, r, is given as 0.815. The value of r lies between -1 and 1. A value of 1 means a perfect positive correlation and a value of -1 means a perfect negative correlation. The closer the value of r to 1 or -1, the stronger the correlation. A value of 0 means no correlation. Here, r = 0.815 which is close to 1, indicating a strong positive correlation.
Step 2 :However, to determine if there is sufficient evidence to support the claim of a linear correlation, we need to compare the calculated r value with the critical r value from the correlation coefficient table for a given significance level (alpha = 0.05) and degrees of freedom (n-2, where n is the number of pairs of data). If the calculated r value is greater than the critical r value, then there is sufficient evidence to support the claim of a linear correlation.
Step 3 :The calculated r value (0.815) is less than the critical r value (2.262). Therefore, there is insufficient evidence to support the claim of a linear correlation between the two variables.
Step 4 :\(\boxed{\text{B. There is insufficient evidence to support the claim of a linear correlation between the two variables.}}\)