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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 μ 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., H0, Ha, μ, p, ˉx, s, n, ˆp, z, t, α).
Formulas/expressions you should understand when and how to use.
z=ˆp−p√p(1−p)/n t=ˉx−μs/√n np≥15, n(1−p)≥15