Final answer:
A confidence interval represents the range of values that is believed to contain the true population parameter with a certain level of confidence, such as 97% or 95%. The width of the confidence interval depends on the confidence level, with higher confidence requiring a wider interval. Factors outside of sampling error can also impact survey results and are not covered by the margin of error.
Step-by-step explanation:
The reported confidence interval for the risk of death from vascular causes gives a range within which we expect the true risk level to fall, with a certain level of confidence. For example, a 97 percent confidence interval means that, were we to take 100 different samples and compute a confidence interval from each sample, we would expect approximately 97 of those intervals to contain the true risk factor.
When you construct a confidence interval, you adjust the width of the interval according to your desired level of confidence. The higher the confidence level, such as 99 percent versus 90 percent, the wider the interval since you are including more of the possible sample variations. Conversely, a lower confidence level results in a narrower interval, reflecting less certainty that the interval contains the true value.
Factors besides sampling error—like the method of data collection or the survey design—can affect survey outcomes and are not accounted for in the margin of error. These should be considered when interpreting confidence intervals and their implications.