Final answer:
The margin of error reflects how much the poll results might differ from the actual population opinion. If researchers state a ±3 percent margin at a 95% confidence level, it means the true proportion is likely within 3 percentage points of the observed proportion.
Step-by-step explanation:
The margin of error in a poll reflects the range within which the true value in the population is expected to fall, given the sample results, with a specified level of confidence. In the student's poll, where 560 people were asked if they liked dogs and 87 said they did, the margin of error with a 95% confidence level is not provided directly.
However, if the margin of error given by a group of researchers is ±3 percent, it means that we can be 95% confident that the true population proportion who like dogs is within 3 percentage points above or below the observed sample proportion.
To find the margin of error for the student's poll, we need to know the confidence level and use the appropriate formula. But since we already have the information from the researchers, the margin of error would likely be close to the ±3 percent given the similar size of the sample to the typical size where this margin was deemed acceptable.