Question

An online poll at a Web site asked: A nationwide ban of the diet supplement ephedra went into effect recently. The herbal stimulant has been linked to 155 deaths and many more heart attacks and strokes. Ephedra manufacturer NVE Pharmaceuticals, claiming that the FDA lacked proof that ephedra is dangerous if used as directed, was denied a temporary restraining order on the ban yesterday by a federal judge. Do you think that ephedra should continue to be banned nationwide? \(65 \%\) of 17,303 respondents said "yes." Comment on each of the following statements about this poll: a) With a sample size that large, we can be pretty certain we know the true proportion of Americans who think ephedra should be banned. b) The wording of the question is clearly very biased. c) The sampling frame is all Internet users. d) Results of this voluntary response survey can't be reliably generalized to any population of interest.

Short answer

a) Sample may not be representative; b) Question is biased; c) Limited to online users; d) Results can't be generalized.

Step-by-step solution

Analyze Statement a

Statement a claims that a large sample size of 17,303 respondents provides certainty about the true proportion of Americans' opinions. A large sample size generally reduces sampling error, but this assumes the sample is representative of the population. Since the respondents are self-selected from an online poll, this may not accurately reflect the true opinions of all Americans, due to selection bias.

Evaluate Statement b

Statement b assesses whether the wording of the question is biased. The question mentions serious negative health impacts of ephedra, which could influence respondents, creating bias as it potentially leads respondents towards a 'yes' answer. This suggests that the wording is biased, affecting the survey's reliability.

Consider Statement c

Statement c asserts that the sampling frame is all Internet users. Since the poll was conducted online, only individuals who have access to the internet and chose to visit the website were included. Thus, the sampling frame is indeed all internet users, but more accurately, it may only include visitors to the specific website running the poll.

Assess Statement d

Statement d discusses the limitations of the poll's results. As a voluntary response survey, it is subject to self-selection bias, as those with strong opinions are more likely to respond. Without random sampling, these results cannot reliably be generalized to the whole population of Americans.

Key concepts

Sampling Bias

Sampling bias occurs when the sample collected is not representative of the larger population. In the case of the online poll about the ephedra ban, the sample consists of individuals who have chosen to visit the specific website and participate in the survey. This creates a problem because the survey respondents may not reflect the views of the general population accurately.

A few reasons sampling bias might arise include:

• Restricted access to the survey to only certain groups, like internet users on a particular site
• Specific characteristics of participants, such as their interests in health topics or their likelihood to engage with online polls

Without ensuring that all segments of the population have an equal chance of being included in the sample, the results are susceptible to skewing, which means what the survey shows might not hold true for the whole country.

Voluntary Response

Voluntary response in surveys refers to the principle that participants choose to respond on their initiative. This is distinct from random sampling, where individuals are randomly selected to represent the entire population.

Voluntary response surveys often suffer from biases because they tend to attract individuals with strong opinions on the topic. In our case with the ephedra poll, those who chose to express their opinion might feel strongly about health supplements' regulation.

• This might mean that the results are slanted towards a more extreme viewpoint, either for or against the ephedra ban
• Individuals with a neutral stance or who are indifferent might have chosen not to participate, causing a gap in the dataset

Thus, a voluntary response poll, such as this, does not accurately measure the balance of opinions in the entire population and must be interpreted with caution.

Survey Design

The design of a survey significantly affects its reliability and validity. Survey design includes how questions are worded, the medium through which the survey is delivered, as well as the sample population.

In the poll regarding the ephedra ban, the question was crafted to potentially influence the participants' answers by including emotive language about health risks and legal actions. Such wording can lead to biased results, as respondents might be swayed to agree with the implied message of the question.

• To enhance reliability, questions should be neutral and not suggest any specific reaction
• Moreover, ensuring a diverse mode of distribution can help in reaching a broader audience, reducing internet-specific demographic limitations

Good survey design is crucial to gaining insights that can be generalized to the broader population, which was not the case here.

Self-Selection Bias

Self-selection bias arises when individuals select themselves into a group, causing a biased sample and therefore affecting the survey results’ generalizability. This bias is prevalent in situations such as the ephedra poll, where the respondents have opted themselves into taking the survey.

Self-selection bias can manifest as:

• A sample that only represents individuals with high engagement or strong views on the surveyed topic
• Exclusion of individuals who might have moderate opinions or are indifferent, skewing the results towards more extreme positions

To mitigate such bias, a survey should ideally employ random sampling methods, where participants are randomly selected, ensuring more balanced and representative results across different demographics and viewpoints in the population.