Question

Exercise and the Brain

It is well established that exercise is beneficial for our bodies. Recent studies appear to indicate that exercise can also do wonders for our brains, or, at least, the brains of mice. In a randomized experiment, one group of mice was given access to a running wheel while a second group of mice was kept sedentary. According to an article describing the study, "The brains of mice and rats that were allowed to run on wheels pulsed with vigorous, newly born neurons, and those animals then breezed through mazes and other tests of rodent IQ"¹ compared to the sedentary mice. Studies are examining the reasons for these beneficial effects of exercise on rodent (and perhaps human) intelligence. High levels of BMP (bone-morphogenetic protein) in the brain seem to make stem cells less active, which makes the brain slower and less nimble. Exercise seems to reduce the level of BMP in the brain. Additionally, exercise increases a brain protein called noggin, which improves the brain’s ability. Indeed, large doses of noggin turned mice into “little mouse geniuses”, according to Dr. Kessler, one of the lead authors of the study. While research is ongoing in determining how strong the effects are, all evidence points to the fact that exercise is good for the brain. Several tests involving these studies are described. In each case, state the null and alternative hypotheses. Your answers should be an expression composed of symbols:

¹Reynolds G., "Phys Ed: Your Brain on Exercise," The New York Times, July 7, 2010.

(a) Testing to see if there is evidence that mice allowed to exercise have lower levels of BMP in the brain on average than sedentary mice.

Let group 1 be the exercising mice and let group 2 be the sedentary mice.

(b) Testing to see if there is evidence that mice allowed to exercise have higher levels of noggin in the brain on average than sedentary mice.

Let group 1 be the exercising mice and let group 2 be the sedentary mice.

(c) Testing to see if there is evidence of a negative correlation between the level of BMP and the level of noggin in the brains of mice.

Answer 1

a) Testing to see if there is evidence that mice allowed to exercise have lower levels of BMP in the brain on average than sedentary mice

Here, the test is one - tailed

Null hypothesis : The average level of BMP ( bone-morphogenetic protein ) in the brain of mice and rats who were kept sedentary is mu ( say any value )

Alternate hypothesis : The average level of BMP ( bone-morphogenetic protein ) in the brain of mice and rats who were given access to a running wheel is mu1 ( say ) and mu1 < mu

b)Testing to see if there is evidence that mice allowed to exercise have higher levels of noggin in the brain on average than sedentary mice

Null hypothesis : The average level of noggin in the brain of mice and rats who were kept sedentary is mu ( say any value )

Alternate hypothesis : The average level of noggin in the brain of mice and rats who were given access to a running wheel is mu1 ( say ) and mu1 > mu

c) Testing to see if there is evidence of a negative correlation between the level of BMP and the level of noggin in the brains of mice

Null hypothesis : The correlation among the level of BMP and the level of noggin in the brains of mice is zero

Alternate hypothesis : The correlation among the level of BMP and the level of noggin in the brains of mice is less than zero