You would like to construct a 99% confidence interval to estimate the population mean score on a nationwide examination in psychology, and for this purpose we choose a random sample of exam scores. The sample we choose has a mean of 512 and a standard deviation of 77. (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, based on the sample, is the sample mean itself. 

In this case, the sample mean is \( \bar{x} = 512 \). Therefore, the best point estimate for the population mean is **512**.

Would you like to see how to construct the 99% confidence interval using this information? If so, I can walk you through the steps.

Here are some related questions:
1. What is a confidence interval and why is it important in statistics?
2. How do you calculate the margin of error for a confidence interval?
3. What is the formula for a confidence interval for the population mean when the population standard deviation is unknown?
4. How does the sample size affect the width of a confidence interval?
5. What is the difference between a 95% and a 99% confidence interval?
6. How do you determine the critical value (z-score) for a 99% confidence interval?
7. What assumptions must be met to construct a confidence interval for the mean?
8. How does the standard deviation of the sample influence the confidence interval?

**Tip:** When estimating a population mean, the larger the sample size, the more precise your confidence interval will be.

Learn how to construct a 99% confidence interval to estimate the population mean score on a nationwide psychology examination. Includes steps on calculating point estimates, understanding confidence intervals, and interpreting statistical significance.

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