/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 53 Multiple Sclerosis and Sunlight ... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Multiple Sclerosis and Sunlight It is believed that sunlight offers some protection against multiple sclerosis (MS) since the disease is rare near the equator and more prevalent at high latitudes. What is it about sunlight that offers this protection? To find out, researchers \({ }^{15}\) injected mice with proteins that induce a condition in mice comparable to MS in humans. The control mice got only the injection, while a second group of mice were exposed to UV light before and after the injection, and a third group of mice received vitamin D supplements before and after the injection. In the test comparing UV light to the control group, evidence was found that the mice exposed to UV suppressed the MS-like disease significantly better than the control mice. In the test comparing mice getting vitamin D supplements to the control group, the mice given the vitamin \(\mathrm{D}\) did not fare significantly better than the control group. If the p-values for the two tests are 0.472 and 0.002 , which p-value goes with which test?

Short Answer

Expert verified
The p-values correspond to the following tests: The p-value 0.002 is for the test comparing UV light to the control group and the p-value 0.472 is for the test comparing vitamin D supplements to the control group.

Step by step solution

01

Interpret p-values

The p-value is a statistical concept that measures the strength of evidence in support of a null hypothesis or basically to deny the experiment hypothesis. A p-value less than 0.05 means there is strong evidence against the null hypothesis or that you reject the null hypothesis. A p-value higher than 0.05 means there is weak evidence against the null hypothesis or you fail to reject the null hypothesis.
02

Match the p-values to the tests

From the experiment it is known that the mice exposed to UV light had a significantly better result in contrast to the control group. Also, it is known that the mice given the vitamin D didn't fare significantly better than the control group. Hence, based on the p-value interpretations, the lower p-value (0.002) which equates to a significant result should be for the UV light group and the higher p-value (0.472) which equates to an insignificant result should be for the Vitamin D group.

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Key Concepts

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

Null Hypothesis
The null hypothesis is a cornerstone concept in statistical hypothesis testing. It's a default position that suggests there is no effect or no difference in the context of scientific research. For instance, if researchers are studying the impact of sunlight on MS, the null hypothesis would be that sunlight does not affect the progression or suppression of MS.
In the experiment with mice, the null hypothesis might be stated as 'UV light or vitamin D supplements do not suppress MS-like conditions in mice.' Researchers then use statistical tests to challenge this hypothesis. The goal is to gather evidence from data to either support or reject the null hypothesis. When results significantly deviate from what the null hypothesis predicts, researchers may conclude that their findings provide evidence of an effect, subsequently leading to the rejection of the null hypothesis.
Understanding the null hypothesis is crucial for interpreting p-values. It serves as the basis for determining whether the experimental results are due to chance or if they reflect the actual effect of the treatment or condition under investigation.
Statistical Significance
Statistical significance is a term used to indicate that the result of a statistical test is unlikely to have occurred by random chance. This is determined by calculating a p-value, which is the probability of observing the results (or more extreme results) if the null hypothesis were true.
A commonly accepted threshold for declaring statistical significance is a p-value of 0.05 or less. This means there's less than a 5% probability that the results are due to random chance. In the context of the MS and sunlight study, the p-value of 0.002 suggests a statistically significant difference between the control group and the mice exposed to UV light. This would lead researchers to reject the null hypothesis and conclude that UV light has a protective effect against the development of an MS-like condition.

Importance of the 0.05 Threshold

The 0.05 threshold isn't a magical number but a convention that has been accepted in the scientific community. It's important to understand that 'statistical significance' doesn't necessarily equate to 'practical significance.' Even if a result is statistically significant, it's essential to consider whether the effect size is meaningful in a practical sense.
Research Methodology
Research methodology encompasses the techniques, strategies, and methods employed by researchers to systematically solve a research problem. It involves the whole process—from defining research questions and hypotheses to data collection and analysis.
In our example with the sunlight and MS study, the research methodology included experimental design involving control groups and test groups (mice exposed to UV light and mice given vitamin D supplements), which is a common design in biomedical research. The dependability of the research findings relies heavily on the choice of methodology, including how the experiment is controlled, how samples are selected, and how data is analyzed.

Experimental Controls and Validity

Good research methodology is also key in maintaining the validity of the experiment. The use of control mice ensures that results can be attributed to the treatments rather than other confounding variables. For instance, the improved condition of the UV light group as compared to the control group strengthens the researchers' conclusions that UV light may have a protective effect against MS-like conditions.

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Most popular questions from this chapter

In Exercises 4.5 to 4.8 , state the null and alternative hvpotheses for the statistical test described. Testing to see if there is evidence that the mean of group \(\mathrm{A}\) is not the same as the mean of group \(\mathrm{B}\).

State the null and alternative hvpotheses for the statistical test described. Testing to see if there is evidence that the correlation between two variables is negative

Are You "In a Relationship"? A new study \(^{45}\) shows that relationship status on Facebook matters to couples. The study included 58 college-age heterosexual couples who had been in a relationship for an average of 19 months. In 45 of the 58 couples, both partners reported being in a relationship on Facebook. In 31 of the 58 couples, both partners showed their dating partner in their Facebook profile picture. Men were somewhat more likely to include their partner in the picture than vice versa. However, the study states: "Females' indication that they are in a relationship was not as important to their male partners compared with how females felt about male partners indicating they are in a relationship." Using a population of college-age heterosexual couples who have been in a relationship for an average of 19 months: (a) A \(95 \%\) confidence interval for the proportion with both partners reporting being in a relationship on Facebook is about 0.66 to \(0.88 .\) What is the conclusion in a hypothesis test to see if the proportion is different from \(0.5 ?\) What significance level is being used? (b) A 95\% confidence interval for the proportion with both partners showing their dating partner in their Facebook profile picture is about 0.40 to 0.66. What is the conclusion in a hypothesis test to see if the proportion is different from \(0.5 ?\) What significance level is being used?

Exercises 4.117 to 4.122 give null and alternative hypotheses for a population proportion, as well as sample results. Use StatKey or other technology to generate a randomization distribution and calculate a p-value. StatKey tip: Use "Test for a Single Proportion" and then "Edit Data" to enter the sample information. Hypotheses: \(H_{0}: p=0.6\) vs \(H_{a}: p>0.6\) Sample data: \(\hat{p}=52 / 80=0.65\) with \(n=80\)

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

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