Section 6.3: Estimating a Population Mean: \(\sigma\) Known

1. Explain how a point estimator is related to a population characteristic.
2. Give examples of point estimators for population parameters, like the population mean and standard deviation.
3. Compare and contrast an interval estimator and a point estimator.
4. Explain what a margin of error \(E\) corresponds to in an interval estimator.
5. Give the \(100c\%\) confidence interval / interval estimator for the population mean \(\mu\) when the population standard deviation \(\sigma\) is known.
6. State under what assumptions the confidence interval / interval estimator from the previous item is appropriate.
7. Relate the confidence level \(c\) to the size \(\alpha\) of a hypothesis test for the population mean.
8. State what quantity a confidence interval / interval estimator is for. That is, what are we confident about / what are we constructing an interval estimator for?
9. Explain what the \(100c\%\) confidence level indicates about a confidence interval / interval estimator in a way that a layperson would understand.
10. Give the sample size \(n\) that is necessary to achieve a margin of error \(E\) for the population mean \(\mu\) when the population standard deviation \(\sigma\) is known.
11. Describe (qualitatively) the interaction between the the sample size \(n\), population standard deviation \(\sigma\), confidence level \(c\), and margin of error \(E\) in the confidence interval / interval estimator for the population mean \(\mu\).
12. Use a \(100c\%\) confidence interval for the population mean \(\mu\) when the population standard deviation \(\sigma\) is known to perform a size \(\alpha = 1 - c\) two-tailed hypothesis test for \(\mu\) when the population standard deviation \(\sigma\) is known.

Section 6.4: Estimating a Population Mean: \(\sigma\) Unknown

1. Give the \(100c\%\) confidence interval / interval estimator for the population mean \(\mu\) when the population standard deviation \(\sigma\) is unknown.
2. State under what assumptions the confidence interval / interval estimator from the previous item is appropriate.
3. Use a \(100c\%\) confidence interval for the population mean \(\mu\) when the population standard deviation \(\sigma\) is unknown to perform a size \(\alpha = 1 - c\) two-tailed hypothesis test for \(\mu\) when the population standard deviation \(\sigma\) is unknown.