Question

1. In election polls, we often see confidence intervals reported. Suppose you see54% ± 3% support Tom (vs Jerry). Your friend has just finished taking statistics and says: based on this, there’s less than a 2.5% chance that Jerry wins. You’re perhaps a bit more skeptical. Why? Why isn’t that error (that you can imagine exists) part of the confidence interval?

Answer 1

A confidence interval is always reported with a certain level of confidence. Level of confidence means probability that true parameter lies in the mentioned confidence inyerval. Here confidence interval for votes in favour of Tom is 51% to 57%.

When your friend reports that Jerry has less than 2.5% chance of winning the election, it means that Tom has atleat 97.5% of winning the election. This means that level of confidence for votes in favour of Tom is 97.5%. This means that guessing in favour of Tom may still go wrong 2.5% of the times or in other words, votes in favour of Tom may still lie outside the predicted interval with probability 0.025 or 2.5%