Question at position 2 The website of a city newspaper places opinion poll questions next to many of its news stories. Simply click your response to join the sample. One of the questions was “Do you plan to diet this year?” More than 30,000 people responded, with 88% saying “Yes.” Which of the following is true?About 88% of all residents of the city plan to diet this year.The poll used a voluntary response sample and the proportion of all city residents who plan to diet this year is likely to be less than 88%. The poll used a voluntary response sample and the proportion of all city residents who plan to diet this year is likely to be greater than 88%. The poll used a convenience sample and the proportion of all city residents who plan to diet this year is likely to be greater than 88%. The poll used a convenience sample and the proportion of all city residents who plan to diet this year is likely to be less than 88%.

Question

Question at position 2  The website of a city newspaper places opinion poll questions next to many of its news stories. Simply click your response to join the sample. One of the questions was “Do you plan to diet this year?” More than 30,000 people responded, with 88% saying “Yes.” Which of the following is true?About 88% of all residents of the city plan to diet this year.The poll used a voluntary response sample and the proportion of all city residents who plan to diet this year is likely to be less than 88%. The poll used a voluntary response sample and the proportion of all city residents who plan to diet this year is likely to be greater than 88%. The poll used a convenience sample and the proportion of all city residents who plan to diet this year is likely to be greater than 88%. The poll used a convenience sample and the proportion of all city residents who plan to diet this year is likely to be less than 88%.

BlackTom AI · Accepted Answer

The scenario involves collecting opinions via a voluntary response sample attached to a news site. This type of sampling is prone to bias because people who feel strongly about a topic are more likely to respond, while those with weaker opinions may skip it. Now, evaluate each option:

Option 1: About 88% of all residents of the city plan to diet this year.
This statement claims the sample proportion directly reflects the population proportion. It ignores potential sampling bias. Since the data come from voluntary responses, it is not reasonable to assume the sample perfectly matches the population; therefore this option is not the most defensible conclusion.

Option 2: The poll used a voluntary response sample and the proportion of all city residents who plan to diet this year is likely to be less than 88%.
Reasoning: Because the sample is voluntary, those who plan to diet (a potentially more motivated or opinionated group) might be more inclined to respond, inflating the observed 88%. If the sample inflates the proportion, the true population proportion would be lower than 88%. This aligns with typical bias expectations for voluntary response samples in surveys about personal behaviors. Hence this statement is plausible.

Option 3: The poll used a voluntary response sample and the proportion of all city residents who plan to diet this year is likely to be greater than 88%.
This would be true if the voluntary-response bias caused the sample to oversample those who plan to diet and overstate the true population proportion. However, given the common tendency of voluntary response samples to overrepresent opinions on the topic (which can inflate estimates), this option could be plausible in some contexts, but the stated 88% specifically being driven higher than the population is not the most directly supported conclusion without additional data, and the test framing often emphasizes the lower than 88% outcome when response bias is present.

Option 4: The poll used a convenience sample and the proportion of all city residents who plan to diet this year is likely to be greater than 88%.
Here, mislabeling the sampling method as convenience rather than voluntary response is inaccurate given the description (voluntary response via clicking a response). Additionally, even if it were convenience, the expectation about the direction of bias would depend on who is more accessible and willing to respond, not a guaranteed greater-than-88% figure. Since the method is identified as voluntary response, this option misstates both the sampling method and the likely bias direction.

Option 5: The poll used a convenience sample and the proportion of all city residents who plan to diet this year is likely to be less than 88%.
Similar to Option 4, this incorrectly classifies the sampling method and incorrectly constrains the bias direction without basis from the described voluntary-response setup. It also contradicts the typical bias pattern for voluntary responses in opinion polls on personal health behaviors.

In summary, recognizing the voluntary-response nature of the poll helps explain why the observed 88% might overstate the true population proportion, making the population proportion likely to be less than 88%. This aligns with the idea that those strongly in favor of dieting may be overrepresented in voluntary responses, producing an inflated sample proportion relative to the population.

Similar Questions

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