There are two sorts of statistical hypotheses.

Null hypothesis. The null hypothesis, denoted by H0, is typically the hypothesis that sample observations result purely from chance.

Alternative hypothesis. The choice hypothesis, denoted by H1 or Ha, is that the hypothesis that sample observations are influenced by some non-random cause.

For example, suppose we wanted to work out whether a coin was fair and balanced. A null hypothesis could be that half the flips would end in Heads and half, in Tails. the choice hypothesis could be that the amount of Heads and Tails would be very different. Symbolically, these hypotheses would be expressed as

H0: p = 0.5

Ha: p 0.5

Suppose we flipped the coin 50 times, leading to 40 Heads and 10 Tails. Given this result, we might be inclined to reject the null hypothesis. That is, we might conclude that the coin was probably not fair and balanced.