Editing Test statistic (section)

==Example==
Suppose the task is to test whether a coin is fair (i.e. has equal probabilities of producing a head or a tail).  If the coin is flipped 100 times and the results are recorded, the raw data can be represented as a sequence of 100 heads and tails.  If there is interest in the [[marginal distribution|marginal]] probability of obtaining a tail, only the number ''T'' out of the 100 flips that produced a tail needs to be recorded. But ''T'' can also be used as a test statistic in one of two ways:
*the exact [[sampling distribution]] of ''T'' under the null hypothesis is the [[binomial distribution]] with parameters 0.5 and 100.
*the value of ''T'' can be compared with its expected value under the null hypothesis of 50, and since the sample size is large, a [[normal distribution]] can be used as an approximation to the sampling distribution either for ''T'' or for the revised test statistic ''T''&minus;50.

Using one of these sampling distributions, it is possible to compute either a [[two-tailed test|one-tailed or two-tailed]] p-value for the null hypothesis that the coin is fair. The test statistic in this case reduces a set of 100 numbers to a single numerical summary that can be used for testing.