Monty Hall Style Decision

There are three treasure chests on a fragile platform, two are empty and one has treasure. You can only choose one chest to pick up because the platform will collapse. You start to pick up one chest when a parrot lands on another chest and states that one is empty. Should you change your choice to the only other chest?

Asked in the superday online test stage.

Treat repeated, independent versions of this setup as an experiment. Assume the parrot always lands on a different empty chest and always tells the truth.

1. State the null and alternative hypotheses for switching versus staying.
2. Define the primary outcome, guardrails, unit of randomization, and a practical MDE.
3. Calculate the required sample size per arm for 80% power and alpha 0.05.
4. Specify the analysis plan, including allocation, stopping rule, and sample-ratio checks.
5. State the ship or do-not-ship recommendation and explain why.