Editing One- and two-tailed tests (section)

== Coin flipping example ==
{{main|Checking whether a coin is fair}}
In coin flipping, the [[null hypothesis]] is a sequence of [[Bernoulli trial]]s with probability 0.5, yielding a random variable ''X'' which is 1 for heads and 0 for tails, and a common test statistic is the [[sample mean]] (of the number of heads) <math>\bar X.</math> If testing for whether the coin is biased towards heads, a one-tailed test would be used – only large numbers of heads would be significant. In that case a data set of five heads (HHHHH), with sample mean of 1, has a <math>1/32 = 0.03125 \approx 0.03</math> chance of occurring, (5 consecutive flips with 2 outcomes - ((1/2)^5 =1/32). This would have <math>p \approx 0.03</math> and would be significant (rejecting the null hypothesis) if the test was analyzed at a significance level of <math>\alpha = 0.05</math> (the significance level corresponding to the cutoff bound). However, if testing for whether the coin is biased towards heads or tails, a two-tailed test would be used, and a data set of five heads (sample mean 1) is as extreme as a data set of five tails (sample mean 0). As a result, the ''p''-value would be <math>2/32 = 0.0625 \approx 0.06</math> and this would not be significant (not rejecting the null hypothesis) if the test was analyzed at a significance level of <math>\alpha = 0.05</math>.