Given a confidence interval for a population mean, how can you find the point estimate of the mean from the interval endpoints $a$ and $b$?

• A. Use only the upper endpoint: $b$
• B. Multiply the endpoints: $a\times b$
• C. Subtract the lower endpoint from the upper endpoint: $b-a$
• D. Calculate the average of the endpoints: $\frac{a+b}{2}$

Answer: (D)

Verified step by step guidance

1. Understand that a confidence interval for a population mean is typically given as an interval between two endpoints: the lower endpoint \( a \) and the upper endpoint \( b \).
2. Recall that the point estimate of the population mean is the best single estimate of the mean based on the sample data, which is usually the sample mean.
3. Recognize that the confidence interval is constructed symmetrically around the point estimate, so the point estimate lies exactly in the middle of the interval.
4. To find the point estimate from the endpoints \( a \) and \( b \), calculate the midpoint of the interval by averaging the two endpoints using the formula: \[\text{Point Estimate} = \frac{a + b}{2}\]
5. This average gives the best estimate of the population mean based on the confidence interval endpoints.