Question

If [0.34,0.57] is a realization of a (non-asymptotic, for some fixed n) 95% confidence interval for an unknown parameter p, then which of the following is true?

The probability that the unknown parameter p is in this interval is

≥0.025

≥0.05

≥0.95

None of the above, because p and [0.34,0.57] are both deterministic.

Answer 1

We have a 95% confidence interval with lower bound = 0.34 and upper bound = 0.57

We know that with a 95% confidence interval, we have 95% confidence that the unknown population parameter p is between the lower bound and upper bound, i.e. between 0.34 and 0.57.

Important thing to notice is that we are only confident, but there is not a 95% chance or probability of getting the p value within 0.34 and 0.57 range.

Therefore, we are not sure whether the probability is 0.025, 0.05 or 0.95.

So, answer is None of the above,