Use simulation to decide whether data are consistent with a proposed model.
Compare simulation evidence using a stated tail and alpha
Problem
A two-sided simulation has \(230\) of \(500\) statistics at least as extreme as observed, with \(α~=~0.05\). Compute the empirical \(p\)-value, compare it with \(α\), and state the model decision and typicality interpretation.
Big Picture
What this problem is really about
Use the supplied at-least-as-extreme count exactly according to the predeclared tail rule; do not double a count that already represents a two-sided definition. Divide that count by all simulations to obtain the empirical p-value, then compare it with the stated alpha using the exact rejection inequality. The resulting decision describes evidence against the model, not proof that the model is true or false.
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