Chapter 14

Statistical estimation (and Lecture 11 Lecture Notes)

1. Distinguish between a descriptive statistic and an inferential statistic, and state what they characterize about a sample or a population.
2. Describe the “black box” model of statistical inference.
3. State the three main types of inferential statistics we will discuss in this course.
4. Define point estimator.
5. Distinguish between a point estimator as a procedure and a point estimate as a number.
6. Discuss the main properties of the sample mean of a random sample from a population as a point estimator for the population’s mean.

Margin of error and confidence level (and Lecture 11 Lecture Notes)

1. State the standard error for the sample mean of a simple random sample.
2. Explain why the standard error of the sample mean is so-named.
3. Determine the probability that the sample mean is within a specified error from the population mean.
4. Define a probability \(c\) margin of error for a sample mean.
5. Compute a probability \(c\) margin of error for a sample mean using a critical value from the standard Normal distribution.
6. Relate body probabilities \(c\) to tail probabilities \(\alpha\).
7. Relate the critical values \(z_{\alpha}\) of a standard Normal distribution to its quantiles, and compute such a critical value using R.

Chapter 17

The \(t\) distributions (and Lecture 11 Lecture Notes)

1. Explain why the standard error of the sample mean is not useful in practice.
2. State and compute an estimate of the standard error of the sample mean.
3. Compare and contrast \(Z\)-scores and \(T\)-scores.
4. Explain what a \(T\)-score indicates about an observed sample mean.
5. Compute the \(T\)-score of an observed sample mean given the relevant information about the population and sample.