**Steps
in Statistical Hypothesis Testing**

** Step 1:** State the null hypothesis, H

** Step 2:** State the size(s) of the sample(s). This
represents the amount of evidence that is being used to make a decision. State
the significance level, a, for the test. The significance level is the probability of
making a Type I error. A Type I error is a decision in favor of the alternative
hypothesis when, in fact, the null hypothesis is true. A Type II error is a
decision to fail to reject the null hypothesis when, in fact, the null
hypothesis is false.

** Step 3:** State the test statistic that will be
used to conduct the hypothesis test (the appropriate test statistics for the
different kinds of hypothesis tests are given in the tables of the reference
page, “Statistical Inference for Values of Population Parameters”). The
following statement should appear in this step: “The test statistic is _________ , which under H

** Step 4:** Find the critical value for the test. This
value represents the cutoff point for the test statistic. If the null
hypothesis were true, there would be only a probability of a of
obtaining a value of the test statistic that would be at least this extreme. If
the value of the test statistic computed from the sample data is beyond the
critical value, the decision will be made to reject the null hypothesis in
favor of the alternative hypothesis.

** Step 5:** Calculate the value of the test
statistic, using the sample data. (If you are using Excel or SAS, or some
similar computer package, you will calculate the value of the test statistic,
along with a p-value.)

** Step 6:** Decide, based
on a comparison of the calculated value of the test statistic and the critical
value of the test, whether to reject the null hypothesis in favor of the
alternative. (If you have a calculated p-value, then decide based on a
comparison of the p-value with a. If the p-value is less than a, reject H

If the decision is to reject H_{0}, the statement of
the conclusion should read as follows: “We reject H_{0} at the (value of a) level of significance. There is sufficient evidence to
conclude that (statement of the alternative hypothesis).”

If the decision is to fail to reject H_{0}, the
statement of the conclusion should read as follows: “We fail to reject H_{0}
at the (value of a) level of significance. There
is not sufficient evidence to conclude that (statement of the alternative
hypothesis).”