Question

Consider the example below. Let’s suppose that we construct a confidence interval for the popularity of candidate A and from a sample we find she’s preferred by 48% of the voters with a margin of error of 3%. The confidence interval is then (46%, 51%) We then construct a confidence interval for candidate B and from the sample we find she’s preferred by 51% with the same margin of error. The confidence interval in this case is (48%, 54%) Based on these two interval estimates, do we have evidence to suggest that candidate B is ahead?

Answer 1

To determine whether the two group means are different, we often compare the confidence intervals for those groups. If those intervals overlap, we conclude that the difference between groups is not statistically significant. If there is no overlap, the difference is significant. Here, the two confidence intervals overlap with each other (Since, upper bound for candidate A i.e. 51% lies on the confidence interval for B or the lower bound for candidate B i.e. 48% lies on the confidence interval for A). Hence, we have not enough evidence to suggest that candidate B is ahead.