You would like to construct a 99% confidence interval to estimate the population mean annual income for people over age 40 in your state. You choose a random sample of such incomes and compute the mean of the sample as 40,281.5 dollars with a standard deviation of 7715.0 dollars.
(a) What is the best point estimate, based on the sample, to use for the population mean?

The best point estimate for the population mean is simply the sample mean. The sample mean is the most accurate estimate of the population mean based on the available data.

Given:
- Sample mean $\bar{x} = 40,281.5$ dollars

Thus, the best point estimate for the population mean is **40,281.5 dollars**.

Would you like to continue with the calculation of the 99% confidence interval or do you have any questions on this? 

### Related Questions:
1. How do you calculate the margin of error for a confidence interval?
2. What is the significance of using a 99% confidence level instead of 95%?
3. How do you determine the sample size needed for a specific margin of error?
4. What are the assumptions underlying the use of a confidence interval?
5. How does the standard deviation impact the width of the confidence interval?
6. What would be the confidence interval if the standard deviation was smaller?
7. How does increasing the sample size affect the confidence interval?
8. What is the difference between a confidence interval and a prediction interval?

**Tip:** Remember that the confidence interval provides a range within which we expect the population parameter to lie, with a certain level of confidence.

Learn how to construct a 99% confidence interval to estimate the population mean annual income for people over age 40 in your state. Given a sample mean of $40,281.5 and a standard deviation of $7,715.0, understand the process and significance of confidence intervals.

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