PUB 550 Topic 3 DQ 1: Hypothesis Testing Steps

Give the six steps in order and state each precisely, because the errors here are usually in the wording rather than the sequence. State the null and alternative hypotheses; set the significance level; select the appropriate test and check its assumptions; compute the test statistic; compare it against the critical value or obtain the p-value; and decide whether to reject the null, then interpret that in the terms of the original question. Two points of precision matter. The alpha level is chosen before the data are examined, and choosing it afterwards destroys the error control the whole procedure exists to provide. And the decision is reject or fail to reject — never accept — because the test is constructed to control the risk of one kind of error, not to confirm the null. Say why the null is the one being tested as well, since students often state the two hypotheses correctly and then argue as though the alternative were on trial.

Then build the public health scenario so that it actually exercises the steps rather than illustrating them loosely. A workable one: a county introduces text message reminders for childhood immunisation appointments and wants to know whether on-time completion improved. The null is that the completion proportion is unchanged; the alternative is that it differs, and say whether you are testing one-tailed or two-tailed and why. The outcome is a proportion in two independent groups, so the test is a two-proportion z-test or a chi-square test of independence, and the assumption to check is expected cell counts. Then interpret in public health terms, which is what distinguishes this from a statistics exercise: a statistically significant increase of half a percentage point across a county may be real and still not justify the programme's cost, so report the difference in percentage points and the confidence interval alongside the p-value.