Back to Decide if a model is consistent with data — Problem 1 · Task Set 13

Exercises: Decide if a Model Is Consistent with Data Using Simulation

Work through each section in order. A "model" is an assumed chance mechanism (for example, "this coin lands heads with probability 0.5"). To decide if data is consistent with a model, assume the model is true, simulate the data-generating process many times, build the simulated distribution, and see how often the model produces a result as extreme as the one observed. Remember: a surprising result is EVIDENCE to question a model, never proof the model is false; and an ordinary result never proves a model true.

Grade 10·22 problems·~35 min·Common Core Math - HS Statistics and Probability·group·hss-ic-a-2

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Fluency Practice

Apply the simulation framework: device, trial, statistic, repetitions, and reading distributions.

A model says a spinning coin lands heads with probability $0.5$ . Rank these results from LEAST surprising to MOST surprising under this model: getting 3 tails in a row, 5 tails in a row, 10 tails in a row.

3 tails (least), then 5 tails, then 10 tails (most surprising).

10 tails (least), then 5 tails, then 3 tails (most surprising).

All three are equally surprising, since each is possible.

5 tails (least), then 3 tails, then 10 tails (most surprising).