Download STEPS IN STATISTICAL HYPOTHESIS TESTING

STEPS IN STATISTICAL HYPOTHESIS TESTING
Step 1: State the null hypothesis, H0, and the alternative hypothesis, Ha. The alternative
hypothesis represents what the researcher is trying to prove. The null hypothesis represents the
negation of what the researcher is trying to prove. (In a criminal trial in the American justice
system, the null hypothesis is that the defendant is innocent; the alternative is that the defendant
is guilty; either the jury rejects the null hypothesis if they find that the prosecution has presented
convincing evidence, or the jury fails to reject the null hypothesis if they find that the
prosecution has not presented convincing evidence).
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, , 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 on the reverse side
of this handout). The following statement must appear in this step: “The test statistic is
_________, which under H0 has a _____________ probability distribution (with _____ degrees
of freedom).”
Step 4: Find the rejection region of the test, using the form of the alternative hypothesis from
Step 1, the value of  from Step 2, and the distribution of the test statistic from Step 3.
Step 5: Choose the random sample(s) from the population(s). Calculate the value of the test
statistic, and the p-value for the test, using the gathered data.
Step 6:
Compare the calculated p-value to the chosen level of significance. If the p-value is less than ,
then the null hypothesis will be rejected, and the alternative hypothesis will be affirmed. If the
p-value is greater than , the null hypothesis will not be rejected.
If the decision is to reject H0, the statement of the conclusion should read as follows: “We reject
H0 at the _____ level of significance. There is sufficient evidence to conclude that (statement of
the alternative hypothesis).”
If the decision is to fail to reject H0, the statement of the conclusion should read as follows: “We
fail to reject H0 at the_____ level of significance. There is not sufficient evidence to conclude
that (statement of the alternative hypothesis).”1
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Note: It is not correct to say that we accept the null hypothesis, or that we conclude that the
null hypothesis is true. We never attempt to prove a null hypothesis. We either disprove it, or
we fail to disprove it.