Null & Alternative Hypothesis

Concept

Terminology

Null Hypothesis: A precise assumption about how the data was generated.

• Example: The coin is fair (the probability of tossing a head is equal to 0.5).

Alternative Hypothesis: A different view about how the data was generated.

• Example:
  1. The coin is not fair (the probability of tossing a head is not equal to 0.5).
  2. The coin is biased towards heads (the probability of tossing a head is greater then 0.5).
  3. The coin is biased towards tails (the probability of tossing a head is less then 0.5).

note

The null hypothesis must be written with equal sign. A statement with uncertainty, such as 'approximately equal', will not be considered as a null hypothesis.

• Example: "The coin is fair" can be interpreted as the probability of getting a head is 0.5. If the statement is "the coin is almost fair" or "the probability of tossing a head is approximately equal to 0.5", it is no longer a null hypothesis.

Since the alternative hypothesis is different from the null, it can be less than, greater than, or not equal to, but cannot be $\geq$ or $\leq$.