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Say you flip a coin 10 times and observe only one head. What would be the null hypothesis and p-value for testing whether the coin is fair or not?

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The null hypothesis is that the coin is fair, and the alternative hypothesis is that the coin is biased. The p-value is the probability of observing the results obtained given that the null hypothesis is true, in this case, the coin is fair.

In total for 10 flips of a coin, there are 2^10 = 1024 possible outcomes and in only 10 of them are there 9 tails and one head.

Hence, the exact probability of the given result is the p-value, which is 10/1024 = 0.0098. Therefore, with a significance level set, for example, at 0.05, we can reject the null hypothesis.

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