91Ó°ÊÓ

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"10 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 which effects are significant, all evidence points to the fact that exercise is good for the brain. Several tests involving these studies are described. In each case, define the relevant parameters and state the null and alternative hypotheses. (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 (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 (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

Step by step solution

01

Define Hypothesis for Scenario (a)

For scenario (a), the relevant parameter could be the average levels of BMP in the brains of mice. The null hypothesis (\(H_0\)) would be that exercise does not affect the average levels of BMP in the brains of mice, stating that there is no difference between the average BMP levels of exercising and sedentary mice. The alternative hypothesis (\(H_A\)) would be that exercise affects the average levels of BMP in the mice brains, stating that exercising mice have lower levels of BMP on average than sedentary mice.

02

Define Hypothesis for Scenario (b)

For scenario (b), the relevant parameter could be the average levels of noggin in mice's brains. The null hypothesis (\(H_0\)) would be that exercise doesn't affect the average levels of noggin in the mice brains, stating there is no difference between the average noggin levels in exercising and sedentary mice. The alternative hypothesis (\(H_A\)) would be that exercise affects the average levels of noggin in the brains of the mice, stating that exercising mice have higher levels of noggin in the brain on average than sedentary mice.

03

Define Hypothesis for Scenario (c)

For scenario (c), the relevant parameters is the correlation between the level of BMP and the level of noggin in the brains of mice. The null hypothesis (\(H_0\)) would be that there's no correlation between the level of BMP and the level of noggin. The alternative hypothesis (\(H_A\)) would be that there is a negative correlation between the level of BMP and the level of noggin in the brains of mice.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Null and Alternative Hypotheses

In the realm of statistics, understanding the null and alternative hypotheses is fundamental to hypothesis testing. When researchers want to check the validity of a claim or assess the effect of an intervention, such as exercise on brain function, they begin by setting up these hypotheses.

The null hypothesis (\(H_0\)), is the default assumption that there is no effect or no difference; it serves as a benchmark for comparing the observed data. In our example regarding exercise and brain function in mice, the null hypothesis asserts that exercise does not influence the average levels of BMP or noggin in the brain.

Conversely, the alternative hypothesis (\(H_A\) or \(H_1\) corresponds to the research hypothesis and reflects the effect or difference that the study aims to investigate, such as lower BMP levels or higher noggin levels in exercising mice.

Importance of Clear Definitions

Clear definitions of these hypotheses are crucial for designing the experiment and interpreting results. If the results gathered from an experiment with mice suggest that exercising mice indeed have different levels of these brain proteins compared to sedentary ones, researchers may reject the null hypothesis in favor of the alternative.

Binary Nature of Hypotheses

It's essential to note that these hypotheses are mutually exclusive—only one can be true in the context of the study. Moreover, they must be formulated before any data collection to avoid bias and ensure the integrity of the research process.

Correlation in Statistics

Correlation holds immense significance in statistics as it gauges the strength and direction of a relationship between two variables. When we speak of correlation, particularly in scientific research, we are often probing how closely two variables move in relation to one another.

In the context of the brain function study, researchers might investigate the correlation between BMP and noggin levels in mice brains. If a negative correlation is present, as one variable increases (BMP), the other (noggin) tends to decrease, and vice versa. Detecting such patterns is fundamental to understanding biological interactions and can provide insights into mechanisms through which exercise impacts brain function.

Distinguishing Correlation from Causation

Importantly, correlation does not imply causation. Just because two things are correlated, it doesn't necessarily mean that one causes the other. There could be other lurking variables or the possibility of a coincidental relationship. In our mice example, even if a negative correlation between BMP and noggin is found, further experimentation is necessary to determine if exercise directly causes the changes observed.

Effect of Exercise on Brain Function

Delving into the biological effects of exercise on the brain, it is fascinating to observe how physical activity can influence cognitive function and structural brain changes. Research, like the mouse study in the exercise, suggests that exercise can boost brain health by modifying protein levels that regulate brain development and neuronal activity—a topic of great interest in both neuroscience and psychology.

Proteins like BMP and noggin serve as biological indicators of brain health. Variations in their levels could impact how brain cells function and communicate, suggesting that increasing physical activity might lead to improved cognitive abilities through biological pathways.

Practical Implications for Humans

Exploring the effects observed in mice may also have implications for human health. Exercise is often touted for its myriad benefits on physical health, but studies like the one described could pave the way to understanding how lifestyle choices like regular physical activity could have a similarly profound impact on our mental acuity and neuroplasticity—the brain's ability to reorganize itself by forming new neural connections.