Carrying out a Hypothesis Test

General Structure

  • Come up with the null hypothesis.
  • Come up with the alternative hypothesis.
  • Decide what significance level is to be used and obtain the critical region.
  • Collect data.
  • Select which type of hypothesis test will be used.
  • Work out the test statistic.
  • From the information obtained, choose which hypothesis to accept.

Why are these steps important?

Come up with the Null and Alternative Hypothesis

This is easy yet necessary. In particular the specific wording of the alternative hypothesis tells us whether we need to perform a one-tailed or two-tailed test.

Decide which Significance Level to use

It is essential that the level of significance is decided before the data is collected. If we decide the significance level after the data is collected, we may pick a stronger/weaker level based on the data in order to prove our point.

Work out the Critical Region

The critical region tells us what values of the test statistic will result in the null hypothesis being rejected hence the alternative hypothesis being accepted and depends on the chosen significance level.

Work out the Test Statistic

It is through calculating the test statistic and seeing whether or not it is in the critical region that lets us know which hypothesis to accept.

Decision

If the test statistic is in the confidence interval then accept $H_0$. If the test statistic is in a critical region then accept $H_1$.

External Resources

See Also

Null and Alternative Hypotheses

Critical Region and Confidence Interval

Selecting a Hypothesis Test