Null and Alternative Hypotheses

A hypothesis test checks whether a sample gives enough evidence to doubt a claim about a population. Before examining any data, state the claim in two competing forms.

Null Hypothesis

The null hypothesis, written H₀, is the default position. It states that there is no change, no difference or no effect. A test starts by assuming H₀ is true and then asks how surprising the data would be under that assumption.

Alternative Hypothesis

The alternative hypothesis, written H₁, is what you suspect or want to show. You accept it only if the data strongly contradict H₀.

Example: A website converts 10% of visitors. A new page design is tested to see if it does better.

• H₀: p = 0.10 (the new design has the same conversion rate)
• H₁: p > 0.10 (the new design converts more visitors)

We choose the direction of H₁ before collecting the data, not after seeing which way the results point.

Possible Outcomes

A test ends in one of two decisions. Either you reject H₀, because the evidence is strong, or you fail to reject H₀, because it is not. Failing to reject does not prove H₀ is true. It only means the sample did not provide enough evidence against it.