Step 1 :The question is asking about the correlation coefficient, denoted as 'r', between the average number of employees in a group health insurance plan (x) and the average administrative cost as a percentage of claims (y). The correlation coefficient measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a strong negative relationship, 1 indicates a strong positive relationship, and 0 indicates no relationship.
Step 2 :In this case, we need to calculate the correlation coefficient 'r' between x and y to determine the relationship. If 'r' is positive, as x increases, y should also increase. If 'r' is negative, as x increases, y should decrease. If 'r' is zero, there is no linear relationship between x and y, so we cannot predict the behavior of y as x increases.
Step 3 :Let's calculate 'r' using the given data. The data for x is [2, 8, 14, 32, 73] and for y is [50, 45, 35, 28, 16].
Step 4 :The correlation coefficient 'r' is calculated to be approximately -0.95, which is close to -1. This indicates a strong negative linear relationship between x and y.
Step 5 :Therefore, as x increases, y should tend to decrease.
Step 6 :Final Answer: \(\boxed{\text{As x increases, y should tend to decrease.}}\)