State how a \(P\)-value is defined for an observed test statistic and a given null hypothesis.
State the rejection rule for using the \(P\)-value of an observed test statistic to reject (or not) the null hypothesis at a given significance level \(\alpha\).

Define the two types of errors one can make in a hypothesis test, and state their names.
Relate the two types of errors that one can make in a hypothesis test to decisions in legal trials and during warfare.
Define the two error rates of a hypothesis test.
Recognize \(\alpha\) as indicating the Type I Error Rate of a hypothesis test.
Recognize the synonym of “significance level” for the Type I Error Rate \(\alpha\).
State which of the two error rates are explicitly controlled for in constructing a hypothesis test.
Define test statistic, and explain the distinction between a test statistic and an observed test statistic.
Define the rejection region of a hypothesis test, and state how the rejection region is used to make a conclusion about a null hypothesis.
State the 7 step procedure for testing a claim about a population using a hypothesis test that controls the Type I Error Rate.

State the test statistic that is used for a one-sample \(t\)-test, and give its sampling distribution when underlying the population is Normal and the null hypothesis is true.
State the left-sided, right-sided, and two-sided rejection regions for the one-sample \(t\) test.
Identify when a left-sided, right-sided, or two-sided rejection region is appropriate to test a given null hypothesis.
Construct a left-sided, right-sided, or two-sided rejection region given a claim about a population and a significance level \(\alpha\).
Determine whether an observed test statistic “falls in” a rejection region.
Determine the appropriate tail of the \(t\)-distribution to use to compute a \(P\)-value for a given null hypothesis.
Compute the \(P\)-value for an observed \(t\)-statistic, and use the \(P\)-value to conclude whether or not to reject a given null hypothesis.