Concluding a Test

The study must decide how much evidence is enough

• The on-time study chose a significance level 显著性水平 $\alpha=0.05$ before testing. Its planned lower-sided p-value is about 0.0478.
• The threshold is a decision rule, not the probability that this particular conclusion is wrong.

Apply the preselected rule

• Reject 拒绝 $H_0$ when the p-value is at most $\alpha$. Here $0.0478\le0.05$, so reject the 90% null claim for the planned lower-sided test.
• If the preselected threshold had been 0.01, these data would not reject. Do not raise the threshold after seeing the result.

State the conclusion about the population

• The checked test gives evidence that the on-time proportion for orders in the specified population is below 0.90.
• Distinguish the population claim from the observed sample: 85% was observed, but the test does not prove that the true population rate is exactly 85%.

A non-rejection leaves uncertainty

• With p-value 0.12 and $\alpha=0.05$, fail to reject 不拒绝 the null. The study has insufficient evidence for its stated alternative at this threshold.
• Fail to reject does not mean the null is proved or that the rate meets the promise. Limited precision or low power can hide a real difference.

Evidence need not imply a useful effect

• A very large sample can detect a small departure. Whether the departure matters depends on its size, uncertainty and consequences.
• A test decision does not establish causation in an observational survey. Report the study design and avoid making a stronger causal claim.

Report the whole reasoning chain

• State the hypotheses, check conditions, calculate the statistic and p-value, compare with the preselected level, then conclude in context.
• For a non-rejection, report insufficient evidence rather than accepting the null as fact. Keep the alternative and study population explicit.

Write from rejecting at the 0.05 level

• The p-value is 0.01.
• The significance level was set at 0.05 before the data. The lesson p-value 0.0022 is another test.