A test has \(p\text{-}\text{value}\) \(0.01\) and significance level \(0.05\), with rejection defined by \(p-\text{value}~<~\text{alpha}\). Compare the values, make the model decision, and interpret what the result does and does not establish.

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Because 0.01 is below 0.05, do not reject the model. The data are statistically consistent under the model.

Because 0.01 is below 0.05, reject the model or null under the rule; the data are statistically inconsistent or unusual under the model.

Compare with 0.005 instead of alpha: because 0.01 is above 0.005, do not reject the model.

Because 0.01 is below 0.05, reject the model. This proves that the model is false in every context.

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Curriculum context

Course: Math III
Standard: S-IC.2
Category: Statistics and Probability
Domain: Making Inferences and Justifying Conclusions
Objective: Use simulation to decide whether data are consistent with a proposed model.
Problem type: Make a simulation decision with explicit alpha