Question

Each of 100 laboratory rats has available both plain water and a mixture of water and caffeine in their cages. After 24 hours, two measures were recorded for each rat: the amount of caffeine the rat consumed, X, and the rat's blood pressure, Y. The correlation between X and Y was 0.428. Which of the following conclusions is justified on the basis of this study?
A. The correlation between X and Y in the population of rats is also 0.428
B. If the rats stop drinking the water/caffeine mixture, this would cause a reduction in their blood pressure.
C. About 18 percent of the variation in blood pressure can be explained by a linear relationship between blood pressure and caffeine consumed.
D. Rats with lower blood pressure do not like the water/caffeine mixture as much as do rats with higher blood pressure.
E. Since the correlation is not very high, the relationship between the amount of caffeine consumed and blood pressure is not linear.

Answer 1

Answer:

C. About 18 percent of the variation in blood pressure can be explained by a linear relationship between blood pressure and caffeine consumed.

Explanation:

Here, r = 0.428

∴ We can say it will give a positive curve, as 0.428 indicates it is a positive correlation.

Though the amount of correlation is low, still it is positive and more than 0.4

So, nearly about 18% of the variation in the blood pressure can be observed by the consumption of caffeine water. As consumption of caffeine water and blood pressure is both increasing so we can say that r= 0.428 will give a positive linear curve.