The p-value denotes the amount of unusual sample values we get from a population. It defines how extreme the test statistics is in the direction of alternative hypothesis. Also it defines the consistancy of a test statistics.

Let α be the significance level, then (1-α) is the confidence level.

Assume α = 5% i.e., 95% (1-α) confidence level

Let H_{0} be the null hypothesis.

If the calculated p-value is less than α i.e., 5%, then H_{0} will be rejected.

i.e., 5% of the time we would reject null hypothesis H_{0} wrongly.

i.e., 5% of the time we erroneously conclude that the coin is unfair.

This leads to 5% Type-I error (fail to accept H_{0} when it is true)

i.e., 95% of the time we accept H_{0} correctly

i.e., 95% of the time we correctly conclude that the coin is indeed fair.

Suppose we get p-value just above 5%, then H_{0} is accepted and observed data is a rare event.

Please read this page for p-values & binomial trials.

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