Explain the difference between a hypothesis test and a confi

Explain the difference between a hypothesis test and a confidence interval. How are they similar?

Solution

A hypothesis test determines the critical value of a test statistic to a certain level of significance to determine if the observation obtained is rare enough to reject a null hypothesis.

A confidence interval is an interval of the considered \"usual values\" of the sample statistic according to the confidence level, if the null hypothesis is true.

They are similar in the sense that a confidence interval can be used to test a hypothesis. We can do so by inspecting if the sample statistic lies inside the confidence interval.