Question

If you were given a choice:

Wide confidence interval with a small confidence level
Wide confidence interval with a large confidence level

Narrow confidence interval with a small confidence level
Narrow confidence interval with a large confidence level

Which would you choose? Why? Provide at least one hypothetical example.

Answer 1

I would choose a Narrow confidence interval with a large confidence level

A narrower confidence interval may be more precise but, when calculated the same way, such as the 95% method, they all have the same accuracy. They capture the true value the same proportion of the time.

Also, just because it's narrow doesn't mean you're less likely to encounter a sample that falls within that narrow confidence interval. A narrow confidence interval can be achieved one of three ways. The experimental method or nature of the data could just have very low variance. The confidence interval around the boiling point of tap water at sea level is pretty small, regardless of the sample size, that is why we chose higher confidence interval. The confidence interval around the average weight of people might be rather large because people are very variable but one can make that confidence interval smaller by just acquiring more observations. In that case, as you gain more certainty about where you believe the true value is, by collecting more samples and making a narrower confidence interval( with higher confidence level), then the probability of encountering an individual in that confidence interval does go up..