Final answer:
The actual percentage of voters who support the issue is likely between 47% and 57%, considering the stated 52% result with a margin of error of +5. The margin of error indicates the range within which the true value is expected to lie and is central to the assessment of a poll's reliability.
Step-by-step explanation:
When a poll indicates that 52% of voters say they plan to vote for an issue with a margin of error of +5 percentage points, this means that if the poll's results are accurate, the actual percentage of voters who support the issue will likely fall within the range of 47% to 57%. This range is found by subtracting and adding the margin of error to the reported percentage (52% - 5% and 52% + 5%). Therefore, the correct answer to the question is: a) The actual percentage is between 47% and 57%.
The margin of error is crucial in determining the reliability of a poll. It reflects the uncertainty inherent in sampling and can vary based on the sample size and the confidence level used by the pollsters. A higher confidence level typically results in a wider margin of error, indicating less precision. Conversely, a larger sample size can lead to a smaller margin of error, suggesting greater precision in the results.
If a poll had an 8 percent margin of error, this would indicate that the actual vote percentage could be 8 percentage points higher or lower than the stated figure. So, the actual support for the candidate could range from 35% to 51%. The acceptability of the margin of error depends on the context and how the results will be used. Typically, margins of error around 3-5 percent are common for political polls.