To find the point estimate $\hat{p}$ for a population proportion given a confidence interval, you use the midpoint of the interval limits. The formula for the point estimate is:

$\hat{p} = \frac{\text{Lower Limit} + \text{Upper Limit}}{2}$

For this problem:

• Lower Limit = 0.753
• Upper Limit = 0.797

Calculating:

$\hat{p} = \frac{0.753 + 0.797}{2} = \frac{1.550}{2} = 0.775$

Answer:

The correct choice is 0.775.

Would you like more details, or do you have any questions?

1. What is a confidence interval?
2. How do you interpret a confidence interval in statistics?
3. Why is the midpoint used for finding the point estimate?
4. How does the width of the confidence interval affect the estimate?
5. What are common confidence levels in statistics?

Tip: Confidence intervals give a range that likely contains the true parameter, giving more information than a single estimate alone.