A declared simulation tail contains \(12\) of \(1,000\) trials. Compute the empirical \(p\)-value as a decimal and percent, interpret the count, and state whether the declared count should be doubled.

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Divide by 100 instead of 1000: p = 12/100 = 0.12, or 12%. About 120 in 1000 simulations are counted as extreme.

The p-value is 12/1000 = 0.012, or 1.2%. About 12 in 1000 simulations are at least as extreme; do not double the declared tail count.

Move the decimal one extra place: p = 0.0012, or 0.12%. About 1.2 in 1000 simulations are counted as extreme.

Double the declared tail count: p = 24/1000 = 0.024, or 2.4%. About 24 in 1000 simulations are counted as extreme.

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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: Compute and frame an empirical p-value