If you run a test and get a p-value of 0.0083, assuming an alpha of 0.05, what can you conclude?

Question

BlackTom AI · Accepted Answer

Because 0.0083 is less than the significance level 0.05, you reject the null hypothesis.

1) Relevant concepts:
- p-value: the probability of obtaining data as extreme as (or more extreme than) the observed data assuming the null hypothesis is true.
- Significance level α: the threshold probability for making a Type I error; common decision rule is: if p ≤ α, reject H0; if p > α, fail to reject H0.
- Rejecting H0 means the observed data provide statistically significant evidence against the null (in favor of the alternative), not an absolute proof.

2) Step-by-step reasoning:
- Given p-value = 0.0083 and α = 0.05.
- Compare p to α: check whether p ≤ α.

3) Calculation / intermediate step:
- 0.0083 < 0.05
- Numerically: 0.0083 = 0.83% and 0.05 = 5%. 0.83% is substantially smaller than 5%.

4) Why the correct answer is correct:
- Because the p-value (0.0083) falls below the pre-specified α (0.05), the result is statistically significant at the 5% level. According to the standard decision rule, this leads to rejecting the null hypothesis. The small p-value indicates that, under the null, observing such extreme data would be unlikely (about 0.83% chance), so the null is not a plausible explanation.

5) Why other possible answers would be incorrect:
- “Fail to reject the null” or “do not reject H0” would be incorrect because those apply only when p > α, which is not the case here.
- “Accept the null” is incorrect because statistical tests do not prove the null true; they only fail to reject it when evidence is insufficient.
- Any statement claiming the null is definitely false would be too strong; the correct phrasing is that we reject H0 at the 5% significance level.

Conclusion: The correct decision is to reject the null hypothesis (Answer A), which matches the provided answer.

If you run a test and get a p-value of 0.0083, assuming an alpha of 0.05, what can you conclude?单项选择题

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