Hypothesis Test Logic
A free Statistics and Data Analysis lesson from the “Inference and Conclusions” unit, with a worked example and practice problems including step-by-step solutions.
A hypothesis test starts with a null claim, then asks whether the sample result would be unusual if that claim were true. The goal is evidence-based decision making, not proof with certainty. This lesson builds the habit of reading the context first, choosing the right statistical tool, calculating carefully, and then writing what the result means. By the end, students should be able to do the computation and explain why that computation answers the question.
What you'll learn
- State null and alternative hypotheses
- Describe evidence against the null
- Connect test statistics to unusual sample results
Worked example
Problem. A test begins by assuming a tutoring program has no effect, then checks whether the sample result is unusual under that assumption. What is the starting assumption called?
- The null hypothesis is the default claim being tested.
- The data are judged against that starting claim.
Answer: null hypothesis
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Practice case A: What is the role of the null hypothesis?
Choices: the default claim being tested · the strongest possible conclusion · the sample size · the final proof of causation
Show solution
- The null is the starting claim.
- Evidence is measured against it.
Answer: the default claim being tested
2. Practice case B: In a test, the claim researchers look for evidence toward is:
Choices: the exact sample order · the control group only · the response rate · the competing claim suggested by evidence
Show solution
- The alternative is what evidence may support.
- It competes with the null.
Answer: the competing claim suggested by evidence
3. Practice case C: A small p-value gives evidence:
Choices: that the sample was biased · that no context is needed · against the null hypothesis · for proving the null
Show solution
- Small p-values mean the data would be unusual if the null were true.
- That is evidence against the null.
Answer: against the null hypothesis
4. Practice case D: If the evidence is not strong enough, the correct decision is:
Choices: the sample size is zero · there is not enough evidence against the null · the null is proven true · the alternative is proven false forever
Show solution
- Failing to reject is not proof that the null is true.
- It means the data are not convincing enough.
Answer: there is not enough evidence against the null
5. Practice case E: What should a test conclusion avoid?
Choices: proof with certainty · evidence-based decision making · a comparison to a null claim · a conclusion with context
Show solution
- Hypothesis tests weigh evidence.
- They do not prove claims with absolute certainty.
Answer: proof with certainty
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