Chapter 18

Comparing two population means

1. Give examples of scientific questions that would warrant comparisons of two population means.
2. Recognize the Greek letter \(\delta\), the Greek analog to the Roman letter \(d\), which is used to indicate \(\delta\text{ifferences}\) between population parameters.
3. State a claim about two population means \(\mu_{X}\) and \(\mu_{Y}\) as an equality / inequality involving the difference \(\delta = \mu_{X} - \mu_{Y}\) between the population means.

Two-sample \(t\) procedures

1. State the test statistic used in the two-sample \(t\)-test.
2. Determine, qualitatively, whether an observed test statistic from the two-sample \(t\)-test provides evidence against a null hypothesis.
3. State the sampling distribution of the test statistic used in the two-sample \(t\)-test, and the assumptions that must hold for that sampling distribution to be correct.

Two-sample \(t\)-tests in R (Lecture Notes for Lecture 17)

1. Interpret the output of two.sample.t.test in MUsaic, including:
   • where \(t_{\text{obs}}\) is reported
   • where the estimated degrees of freedom for the \(t\)-distribution is reported
   • where the \(P\)-value for \(t_{\text{obs}}\) is reported
   • where the confidence interval is reported
2. Use two.sample.t.test to perform a two-sample \(t\)-test in R.
3. Use two.sample.t.test to construct a two-sided confidence interval for the population difference \(\delta\) in R.
4. Interpret a two-sided confidence interval for a population difference \(\delta\) in the context of a given problem.