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.
Fluency Practice
Apply the simulation framework: device, trial, statistic, repetitions, and reading distributions.
A simulated distribution of "number of heads in 10 flips of a fair coin" was built from 200 trials. The dot plot shows: most trials landed between 3 and 7 heads, the center is at 5, and exactly 2 of the 200 trials produced 9 or more heads. Estimate the fraction of trials that produced 9 or more heads (write as a decimal).