Question

Explain why the evaluation of a confidence interval is equivalent to a statistical test?

Answer 1

The evaluation of a confidence interval is equivalent to a statistical test.

Suppose we want to test about a population parameter (say, mean) and we got a confidence interval [a,b] for mean at some level of significance let's say (alpha).

Now, we can test the hypothesis about the mean at alpha level of significance. Then,

If the sample mean lies outside the interval, we can reject the null hypothesis

If the sample mean lies in the interval, we do not reject the null hypothesis