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Understand what might be reasonable null and alternative hypotheses for a given problem (note that for alternative hypotheses there may be more than one “right answer” since we have a choice between one-sided and two-sided hypotheses/tests).
Understand the roles of the null and alternative hypotheses in a statistical test.
Be able to correctly compute the appropriate test statistic (i.e., \(z\) or \(t\)) for a statistical test.
Understand the definition of a p-value — it is a probability, but a probability of what?
Understand how to compute a p-value based on a \(z\) or \(t\) test statstic.
Understand the decision rule for whether or not to reject a null hypothesis.
Understand what is meant by statistically significant and how it relates to the decision made be a statistical test.
Understand how to conduct a statistical test concerning \(\mu\) using a confidence interval.
Understand simple versus composite hypotheses.
How do we conduct a statistical test with a composite null hypothesis?
Understand how to conduct a sign test — mainly how do we compute the p-value for the test?
What are type I and type II errors?
What is the probability of making a type I error (assuming the null hypothesis is true)?
How does increasing/decreasing the significance level affect the probabilities of type I and type II errors (assuming such an error is possible)?
What is meant by the power of a statistical test?
What can be done to increase the power of a statistical test?
As usual, be comfortable with notation (e.g., \(H_0\), \(H_a\), \(\mu\), \(p\), \(\bar{x}\), \(s\), \(n\), \(\hat{p}\), \(z\), \(t\), \(\alpha\)).
Formulas/expressions you should understand when and how to use.
\[ z = \frac{\hat{p}-p}{\sqrt{p(1-p)/n}} \] \[ t = \frac{\bar{x}-\mu}{s/\sqrt{n}} \] \[ np \ge 15, \ \ \ n(1-p) \ge 15 \]