Question

Let xbe the average number of employees in a group health insurance plan, and let y be the average administrative cost as a percentage of claims. Suppose a random sample of employees gave the following information.

x	2	8	14	32	73
y	50	45	35	28	16

Given that the value of r is –0.949, should y increase as xincreases, does the value of r imply that y should tend to increase, decrease, or remain the same? Explain.

Answer 1

Given that,

X be the average number of employees in a group health insurance plan.

Y be the average administrative cost as a percentage of claims.

And correlation between them is r = - 0.949

That is there is strong negative correlation between X and Y.

Therefore, as the average number of emploees in agroup health insurance plan increase the average administrative cost (percentage of claims) decreases.

That is as X increase Y should decrease because there is negative correlation between X and Y.

and value of r imply that Y should tend to decrease.

Note:

Negative correlation: Negative correlation is a relationship between two variables in which one variable increases as the other decreases, and vice versa.

Therefore as X increase, Y should decreases.