Q 8.29 - Elementary Statistics

Question

What is meant by saying that a $1-\alpha$ confidence interval is

a. exact?

b. approximately correct?

Step-by-Step Solution

Answer

a. By exact, we mean that confidence level is exactly equal to $1-\alpha$.

b. By approximately correct, we mean that confidence intervals are approximately correct.

Step 1: Given Information

We are given that confidence interval is $1-\alpha$.

Step 2: Meaning of exact confidence level

$100(1-\alpha )\%$ exact confidence interval means that confidence level is exactly equal to $1-\alpha$. It mean the probability that population parameter unknown value is within confidence limits and is $1-\alpha$ exactly.

Step 3: Meaning of approximately correct confidence level

It signifies that confidence level is equal to $1-\alpha$ approximately. It means that probability unknown parameter is within confidence limits is approximately equal to $1-\alpha$. This confidence is approximately correct.