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Back to Decide if a model is consistent with data — Problem 5 · 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.

Dot plot of simulated makes out of 20 under p = 0.8 across 50 trials; dots cluster near 16, and the observed value 11 is marked with a red dot far in the lower tail.
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The dot plot below is a simulated distribution of the number of makes in 20 free throws under the model p=0.8p = 0.8 (50 simulated sessions). The shooter's actual session, 11 makes out of 20, is marked with the red dot far in the lower tail. Describe where the center of the distribution is, and explain in one sentence whether 11 makes looks typical or surprising under this model.