Chapter 14

Hypothesis testing

1. Identify what types of quantities a statistical hypothesis always addresses.
2. Identify the population parameter from a statistical claim.
3. Given a claim about a population parameter \(\theta\) as a “word problem,” write the claim as \(\theta \, \, \square \, \, \theta_{0}\) where the “box” \(\square\) contains one of \(=, \neq, \leq, \geq, <,\) or \(>\) and \(\theta_{0}\) is the claimed value of the population parameter.
4. Define null hypothesis and alternative hypothesis.
5. Given a claim in the form \(\theta \, \, \square \, \, \theta_{0}\), identify whether the claim is a null hypothesis or an alternative hypothesis.
6. Given a claim in the form \(\theta \, \, \square \, \, \theta_{0}\), identify the associated null and alternative hypotheses for the claim.
7. Recognize the symbols \(H_{0}\) (“H-naught”) and \(H_{a}\) (“H-a”) as denoting the null and alternative hypotheses, respectively.
8. Explain why it never (no really, never) makes sense to frame a statistical hypothesis in terms of a sample statistic.

Tests for a population mean

1. Given a claim about a population mean \(\mu_{X}\) as a “word problem,” write the claim as \(\mu_{X} \, \, \square \, \, \mu_{0}\) where the “box” \(\square\) contains one of \(=, \neq, \leq, \geq, <,\) or \(>\) and \(\mu_{0}\) is the claimed value of the population mean.
2. Given a claim about a population mean \(\mu_{X}\) as a “word problem,” determine the corresponding null and alternative hypotheses.
3. State a reasonable test statistic for testing a claim about a population mean.

Chapter 14

The one-sample \(t\) test

1. Explain why a \(T\)-score can be used to test a claim about a population mean.
2. Compute the observed \(T\)-score, denoted \(t_{\text{obs}}\), from a “word problem” about a population mean.
3. Given an observed sample mean, sample standard deviation, and sample size, and a pair of null / alternative hypotheses, determine whether the observed sample mean provides evidence against the null hypothesis (equivalently, for the alternative hypothesis).
4. State the sampling distribution of the \(T\)-score under the null hypothesis when the population distribution is Normal (or approximately so).