Section 9.1: Tests of a Hypothesis Based on a Single Sample

  1. Identify the two types of errors that we can make while performing a statistical hypothesis test with regards to rejecting / not rejecting the null hypothesis.
  2. Give the standard names for the two types of errors from the previous learning objective.
  3. Define the Type I and Type II error rates of a hypothesis testing procedure.
  4. State which of the two error rates we control by fixing \(\alpha\) for a hypothesis test.
  5. Explain the analogy between Type I and Type II errors and convictions in the US criminal justice system.
  6. Define test statistic.
  7. Explain how the three test statistics from Sections 9.2 and 9.3 measure the discrepancy between the null hypothesis and the data.
  8. Distinguish between a test statistic, which gives the procedure for testing a statistical hypothesis, and the observed test statistic, which is the application of that procedure to a particular sample.
  9. Define the rejection region of a statistical hypothesis test.
  10. Explain the rationale behind the procedure for constructing the rejection region for a hypothesis test of significance level \(\alpha\).
  11. Construct rejection regions for one-sided and two-sided alternative hypotheses.
  12. State and follow the “hypothesis testing recipe” given a claim about a population to test.

Section 9.2: Tests About a Population Mean

  1. State an appropriate test statistic to test a claim about the population mean of a Gaussian population with known population standard deviation.
  2. State an appropriate test statistic to test a claim about the population mean of a Gaussian population with unknown population standard deviation.
  3. Identify when the \(Z\) or \(T\) statistics are appropriate to test a claim about the mean of a population.
  4. Perform a level \(\alpha\) hypothesis test for a claim about a population mean.

Section 9.3: Tests Concerning a Population Proportion

  1. State an appropriate test statistic to test a claim about the success probability / population proportion from a binomial experiment.
  2. Identify when the \(Z\) statistic is appropriate to test a claim about the success probability of a binomial experiment.
  3. Perform a level \(\alpha\) hypothesis test for a claim about a binomial success probability or population proportion.