Statistician Interview Question:

Give example of p-value?

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Suppose that the experimental results show the coin turning up heads 14 times out of 20 total flips
► null hypothesis (H0): fair coin;
► observation O: 14 heads out of 20 flips; and
► p-value of observation O given H0 = Prob(≥ 14 heads or ≥ 14 tails) = 0.115.
The calculated p-value exceeds 0.05, so the observation is consistent with the null hypothesis - that the observed result of 14 heads out of 20 flips can be ascribed to chance alone - as it falls within the range of what would happen 95% of the time were this in fact the case. In our example, we fail to reject the null hypothesis at the 5% level. Although the coin did not fall evenly, the deviation from expected outcome is small enough to be reported as being "not statistically significant at the 5% level".
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