Build the method
If the research question is whether a process increases a success proportion beyond 0.30, use Ha:p>0.30. A two-sided alternative asks a different question about either direction. Switching after examining the observed rate invalidates the planned interpretation of the error threshold.
Worked example
A p-value of 0.02 for an upper-tail test means that, assuming the null model and other conditions, a statistic at least as large as observed has probability 0.02. It is not the probability that the null is true, and 0.98 is not the probability that the alternative is true.
Compare the alternatives
At a prespecified significance level of 0.05, p=0.02 leads to rejection; p=0.08 does not. For the latter, write insufficient evidence of increased population support, rather than proof of no increase. A nonsignificant result can reflect limited precision as well as a small effect.
Avoid a specific trap
An interval from 0.56 to 0.70 puts every reported plausible proportion above one half. It does not prove the true proportion is above one half, and it does not supply an exact p-value. Test–interval equivalence requires matching parameter, method, sidedness and levels; the common unpooled proportion interval and null-based test are not exactly interchangeable.
Transfer check with explanation
Transfer: a random observational poll can support population generalization when its design and response quality are adequate. It cannot establish that a policy causes support. State what the data identify, even when a small p-value makes a stronger causal story tempting.
Before data collection, an investigator asks whether a new process increases the population success proportion above 3/10. Which alternative matches the question?
- Translate the research direction before examining the observed sample.
- An increase means the population proportion exceeds the benchmark.
- Why an alternative fails: Reverse the prespecified direction of improvement.
Compare the other answer choices
Reverse the prespecified direction of improvement.
Use a two-sided change question instead of the prespecified increase question.
Describe a sample statistic rather than the population parameter in the alternative.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
AP Statistics Course and Exam Description, effective Fall 2026