Final answer:
A 95% confidence interval means we are 95% confident the interval captures the true population proportion if the sample is random and representative, but it may not be accurate if the sample is not randomly selected.
Step-by-step explanation:
When interpreting a 95% confidence interval like the one mentioned in the ESPN poll about the NFC East Division after Michael Vick broke his non-throwing hand, it is important to understand what the interval represents. If option B states that we are 95% confident that between about 22% and 28% of ESPN viewers thought the Eagles would still win the division, this suggests that we can be 95% confident that this range includes the true proportion of the population opinion if the sample is random and representative.
However, we must consider the method of data collection. The question suggests that the sample may not have been randomly selected, which is a potential source of bias. Therefore, in such cases, even a 95% confidence interval may not accurately reflect the underlying population's opinion, as indicated in option D. Proper random sampling is crucial for the validity of a confidence interval. Without it, confidence intervals may be misleading, as they assume a random sample to extrapolate results to the entire population.