Section 10.1: \(z\) Tests and Confidence Intervals for a Difference Between Two Population Means

1. Distinguish between inferential questions about a single population and about two populations.
2. Given a claim about two population, identify relevant population parameters and state the claim as an equality / inequality involving the population parameters.
3. State a point estimator for the difference between two population means, given a sample from each population.
4. Determine the mean and variance of the point estimator \(D = \bar{X} - \bar{Y}\).
5. Compute the mean and variance of sums and differences of two or more independent random variables.
6. Determine the distribution of the sum or difference of two independent Gaussian random variables.
7. State the \(Z\)-statistic for a two-sample test for the difference between two population means, including its sampling distribution under the null hypothesis when the populations are Gaussian.
8. Construct confidence intervals and upper/lower confidence bounds for the difference between two population means when the population standard deviations are known.
9. Perform a hypothesis test for a claim about the difference between two population means when the population standard deviations are known.

Section 10.2: The Two-Sample \(t\) Test and Confidence Interval

1. State the \(T\)-statistic for a two-sample test for the difference between two population means, including its approximate sampling distribution under the null hypothesis when the populations are Gaussian.
2. Construct confidence intervals and upper/lower confidence bounds for the difference between two population means when the population standard deviations are unknown.
3. Perform a hypothesis test for a claim about the difference between two population means when the population standard deviations are unknown.
4. Use the R function two.sample.t.test() to perform a two-sample \(t\)-test using summarized data.