Final answer:
The margin of error of ± 3% at a 95% confidence level in a survey means we can be 95% confident that the true proportion of American support for marijuana legalization is within 3% of the reported 41%.
Step-by-step explanation:
The given margin of error in this survey tells us that there is a 95% confidence level that the true proportion of the entire American adult population that supports the legalization of marijuana is within 3% of the 41% figure reported by the survey. This means the actual support could realistically fall between 38% and 44%. The margin of error does not suggest that the results are incorrect by 3%, that any answers were fake, or provide certainty about the exact proportion; rather, it offers a range where the true value is likely to be found.
Surveys with a lower margin of error are usually more predictive of the actual opinion. It's important to consider that factors not accounted for by the margin of error, such as the survey's methodology, could affect the outcomes. A Pew Research Center survey in 2010 showed varying support for marijuana legalization and it's been observed that different polling methods may cause variation in responses.
If there was a change in the confidence level, say from 99 percent to 90 percent, the margin of error would also change, likely becoming smaller, resulting in a narrower confidence interval but less certainty.