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

Work through problems with immediate feedback

Warm-Up: Models, Chance, and Distributions

These problems review ideas you already know about chance and distributions.

A fair coin is one that lands heads with probability $0.5$ . You flip a fair coin 5 times and get 5 tails in a row. Which statement is true?

This is an unlikely result, but it is possible and does happen for genuinely fair coins.

This is impossible for a fair coin, so the coin must be rigged.

This proves the coin is biased toward tails.

A fair coin can never produce a streak, so the result cannot occur.