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Chapter 10: Problem 5

Consider the following quote from the article "Review Finds No Link Between Vaccine and Autism" (San Luis Obispo Tribune, October 19,2005 ): "'We found no evidence that giving MMR causes Crohn's disease and/or autism in the children that get the MMR, said Tom Jefferson, one of the authors of The Cochrane Review. 'That does not mean it doesn't cause it. It means we could find no evidence of it." (MMR is a measlesmumps-rubella vaccine.) In the context of a hypothesis test with the null hypothesis being that MMR does not cause autism, explain why the author could not conclude that the MMR vaccine does not cause autism.

Short Answer

Expert verified
The author could not conclude that the MMR vaccine does not cause autism because in hypothesis testing, the inability to reject the null hypothesis (MMR does not cause autism in this context) is not the same as proving the null hypothesis. Not finding evidence that the vaccine causes autism is different from proving that the vaccine does not cause autism.

Step by step solution

01

Understand Null Hypothesis in Hypothesis Testing

In statistics, a hypothesis testing is conducted to examine and infer the validity of a statement or statistical question based on a sample data. In this set-up, there is a null hypothesis, the hypothesis that there is no significant difference exists and it is assumed to be true until statistical evidence nullifies it.
02

Comprehend the Purpose of the Author's Study

The author's study is trying to see if there is a link between the MMR vaccine and autism. Understand that if there was strong evidence present that showed MMR causes autism then the null hypothesis would have been rejected. However, this is not the case here.
03

Understand the Author's Conclusion

The author mentions that there was 'no evidence that giving MMR causes Crohn's disease and/or autism'. In terms of hypothesis testing, this means that they did not have the necessary evidence to reject the null hypothesis.
04

Realise the Limitations of Hypothesis Testing

The statement, 'That does not mean it doesn't cause it. It means we could find no evidence of it.', means that not rejecting the null hypothesis is not the same as accepting it. Hypothesis testing does not provide the capability to prove the null hypothesis, it only allows us to reject it with a certain level of confidence when we have enough evidences against it.

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Key Concepts

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

Null Hypothesis
In hypothesis testing, the null hypothesis is a foundational concept. It is essentially an assumption that there is no effect or no difference. For this specific example, the null hypothesis is that MMR vaccinations do not cause autism.
  • In practice, the null hypothesis serves as a default or starting point.
  • It is assumed to be true unless strong statistical evidence suggests otherwise.
Understanding this concept is crucial because it acts as the baseline we use to understand data findings. Rejecting or not rejecting the null hypothesis is dependent on the evidence gathered from observations or experiments conducted throughout the research process.
It's important to note that accepting a null hypothesis isn't the same as proving it true. Instead, it implies that there is not enough evidence to suggest otherwise.
Statistical Evidence
Statistical evidence plays a pivotal role in hypothesis testing. It refers to the data or information gathered and analyzed to support or refute a hypothesis. In the discussed research, statistical evidence was collected to determine if there is a link between the MMR vaccine and autism.
  • The findings did not show sufficient evidence to reject the null hypothesis.
  • This means the data failed to demonstrate that MMR causes autism, as per the information analyzed by the study's authors.
However, it's crucial to understand that failing to reject the null hypothesis due to lack of statistical evidence doesn't imply the non-existence of an effect or relationship. Instead, it simply signifies that there wasn't enough evidence in the gathered data to draw substantial conclusions against the null hypothesis.
Research Study
Research studies are methodically organized investigations designed to answer specific questions. For the MMR vaccine study, the focus was on identifying whether the vaccine has any causal link to autism.
  • The study utilizes data collection, analysis, and interpretation to seek an answer.
  • If the data had shown strong evidence that MMR causes autism, the null hypothesis would have been rejected.
Researchers follow scientific methods and statistical testing protocols to ensure the accuracy and reliability of their conclusions. The careful design and execution of a research study are vital to obtaining valid and meaningful results.
Vaccination and Autism
The connection鈥攐r lack thereof鈥攂etween vaccinations, such as the MMR vaccine, and autism has been a topic of interest and concern for some time. In this study, the researchers aimed to investigate any possible relationship between these vaccines and the development of autism.
  • The outcome was a finding of no significant evidence to establish a causal link.
  • This aligns with the consensus in the scientific community that vaccines, like MMR, do not lead to autism.
It's essential to approach such sensitive topics with scientific rigor and objective analysis. While the public may have concerns, scientific studies are conducted to provide evidence-based insights that help guide public health decisions.

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Most popular questions from this chapter

A certain university has decided to introduce the use of plus and minus with letter grades, as long as there is evidence that more than \(60 \%\) of the faculty favor the change. A random sample of faculty will be selected, and the resulting data will be used to test the relevant hypotheses. If \(p\) represents the proportion of all faculty that favor a change to plus-minus grading, which of the following pair of hypotheses should the administration test: $$ H_{0}: p=.6 \text { versus } H_{a}: p<.6 $$ or $$ H_{0}: p=.6 \text { versus } H_{a}: p>.6 $$ Explain your choice.

According to a Washington Post-ABC News poll, 331 of 502 randomly selected U.S. adults interviewed said they would not be bothered if the National Security Agency collected records of personal telephone calls they had made. Is there sufficient evidence to conclude that a majority of U.S. adults feel this way? Test the appropriate hypotheses using a .01 significance level.

Do state laws that allow private citizens to carry concealed weapons result in a reduced crime rate? The author of a study carried out by the Brookings Institution is reported as saying, "The strongest thing I could say is that I don't see any strong evidence that they are reducing crime" (San Luis Obispo Tribune, January 23 . 2003 ). a. Is this conclusion consistent with testing \(H_{0}:\) concealed weapons laws reduce crime versus \(H_{a}:\) concealed weapons laws do not reduce crime or with testing \(H_{0}:\) concealed weapons laws do not reduce crime versus \(H_{a}\) : concealed weapons laws reduce crime Explain. b. Does the stated conclusion indicate that the null hypothesis was rejected or not rejected? Explain.

Many older homes have electrical systems that use fuses rather than circuit breakers. A manufacturer of 40 -amp fuses wants to make sure that the mean amperage at which its fuses burn out is in fact \(40 .\) If the mean amperage is lower than \(40,\) customers will complain because the fuses require replacement too often. If the mean amperage is higher than \(40,\) the manufacturer might be liable for damage to an electrical system as a result of fuse malfunction. To verify the mean amperage of the fuses, a sample of fuses is selected and tested. If a hypothesis test is performed using the resulting data, what null and alternative hypotheses would be of interest to the manufacturer?

The mean length of long-distance telephone calls placed with a particular phone company was known to be 7.3 minutes under an old rate structure. In an attempt to be more competitive with other long-distance carriers, the phone company lowered long-distance rates, thinking that its customers would be encouraged to make longer calls and thus that there would not be a big loss in revenue. Let \(\mu\) denote the mean length of long-distance calls after the rate reduction. What hypotheses should the phone company test to determine whether the mean length of long-distance calls increased with the lower rates?
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