# Statistics and Probability Dictionary

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### Alternative Hypothesis

There are two types of statistical hypotheses.

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

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

For example, suppose we wanted to determine whether a coin was fair and balanced. A null hypothesis might be that half the flips would result in Heads and half, in Tails. The alternative hypothesis might be that the number 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, resulting in 40 Heads and 10 Tails. Given this result, we would be inclined to reject the null hypothesis. That is, we would conclude that the coin was probably not fair and balanced.