I’ve used this application to illustrate how both bootstrapping and the central limit theorem works in statistics.
MOUNTY HALL FREE
Plus, it gives me another opportunity to use the Statistics 101 simulation giftware, which I love using and recommend! It’s free to use, but they do ask for a donation. I’ll use this problem to highlight various statistical concepts that relate to answering this question. A small sample size won’t reveal that difference with an acceptable degree of confidence. That 16% difference is small enough to be difficult to detect through an experiment. Of course, in reality, the difference is 33% to 66%, but they disagree with that notion. However, it dawned on me that, in the minds of the doubters, we need to establish that the winning percentage is 66% rather than 50%.
You just need a friend and play the game multiple times. My response has been, “test it empirically by playing it yourself!” It’s a simple enough experiment to perform on your own. They’re convinced that you have a 50% chance of winning by switching rather than a 66% chance. Motivations for Writing this Postĭespite the universal acceptance among statisticians, there are stubborn resisters to the solution. To learn about that, read my other post about the Monty Hall Problem. I won’t re-explain the logic behind how the Monty Hall Problem works in this post. Conducting an experiment by playing the game repeatedly myself, record the results, and use a proportions hypothesis test to draw conclusions!.Performing a power and sample size analysis to determine the number of times you need to play the Monty Hall game to get an answer.Assessing sampling distributions to compare the 66% percent hypothesis to another contender.
Using a computer simulation to play the game 10,000 times.
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