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

  1. Define the Type II Error Rate for a hypothesis test.
  2. Recognize and use the convention of denoting the Type I Error rate by \(\alpha\) and the Type II Error Rate by \(\beta\).
  3. For a given hypothesis test and a specified alternative value, compute the Type I and Type II Error Rates for the hypothesis test.
  4. Define the power of a hypothesis test, and relate the power to the Type II Error Rate of the test.
  5. Define the effect size \(\Delta\) for a hypothesis test for the population mean of a Gaussian population.
  6. State how the power of a hypothesis changes with:

Section 9.2: Tests About a Population Mean

  1. Use the pwr.norm.test function from the R package pwr to perform power calculations for hypothesis tests for the population mean of a Gaussian population.
  2. Determine the distribution of the \(Z\)-statistic for a given hypothesis test for the population mean of a Gaussian population when \(\mu = \mu_{a} \neq \mu_{0}\).

Section 9.4: \(P\)-values

  1. Define the \(P\)-value for an observed test statistic.
  2. Compute the \(P\)-value for the observed test statistic in a hypothesis test for:
  3. Use a \(P\)-value to perform a hypothesis test at a significance level \(\alpha\).
  4. (In the best of all possible worlds:) Avoid common mis-definitions and mis-interpretations of the \(P\)-value.