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Jaynes
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7 months ago
in Hypothesis Testing: The Basics | 20bits on 20bits
I'm confused about one thing. If the null hypothesis is that the coin is fair and there is insufficient evidence to reject this, but we cannot assert the null hypothesis, doesn't that mean we cannot conclude that the coin is fair?
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Hypothesis testing lets us quantify that variance and see whether or not the observed results fall outside that bounds. If they do we can say with some level of confidence that the coin is biased.
Let's say a coin lands on heads 51% of the time. If we flip a coin 100 times and get 51 heads it's impossible to tell whether that was the natural variance of a fair coin or the bias of a 51% coin.
In reality a "fair coin" means a "fair enough coin." We'd have to flip a coin 10,000 times before we'd be able to detect a 51% bias for heads.