Question

What is the relationship between the size of a confidence interval and its level of confidence (ex, 95% or 99%) .

"The larger the interval, the more useful it is" "The smaller the interval, the more confident you are" "The larger the interval, the less confident you are'. "The larger the interval, the more confident you are

Answer 1

We have to find the relation between the size of the confidence interval and its level of confidence.

Now, we know from our study of confidence intervals that the width of the interval is directly proportional to the z-value ( or t value or chi squared value depending on the distribution of the test statistic ), which in turn is directly proportional to the level of confidence.

This means that, the more confident we want to be on our interval, higher would be the z-value etc., and therefore we would have a larger interval of confidence.

Thus, the correct answer is

option (D) The larger the interval, the more confident you are.