What does it mean if data collected refutes a hypothesis?

Question

BlackTom AI · Accepted Answer

Refuting a hypothesis means the collected data contradicts the hypothesis's predictions and provides evidence that the hypothesis may not be true.

1) Relevant knowledge points and concepts
- A hypothesis is a testable prediction. Empirical data is used to evaluate whether observations match that prediction.
- In statistics, "refute" or "reject" a hypothesis means the data are inconsistent with the hypothesis at the chosen level of confidence (e.g., p < 0.05).
- Refutation is not the same as proving absolute falsity; it means evidence points against the hypothesis.

2) Step-by-step reasoning
- Formulate a hypothesis that makes a clear prediction.
- Collect data and compare observations to the prediction.
- If observations systematically conflict with the predicted outcome beyond expected random variation, the hypothesis is refuted (rejected).

3) Example calculation (illustrative)
- Hypothesis: population mean μ = 100.
- Sample: n = 25, sample mean x̄ = 120, known σ = 10.
- Standard error = σ/√n = 10/5 = 2.
- Z = (x̄ − μ) / SE = (120 − 100) / 2 = 20 / 2 = 10.
- A z-score of 10 corresponds to p ≈ 0, so data strongly contradict the hypothesis; we reject (refute) it.

4) Why the correct answer is correct
- Option (a) states that the data provide evidence the hypothesis may not be true, which precisely captures the meaning of "refute": empirical evidence contradicts the hypothesis’s prediction.

5) Why the other options are incorrect
- (b) "Partially true" is vague and does not capture the binary nature of refutation: data either support or contradict predictions; partial truth is not the standard meaning of refute.
- (c) "No data was collected" is irrelevant—refutation requires data.
- (d) "Provides evidence that the hypothesis may be true" is the opposite of refute.

Conclusion: The correct choice is (a). This explanation confirms the provided answer that refuting a hypothesis means the data collected provides evidence the hypothesis may not be true.

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