A-Level Maths: O1-03 [Hypothesis Testing: One-Tail or Two-Tail Test?]

When performing a hypothesis test, it is crucial to identify if it's a one-tail or a two-tail test. This distinction is primarily inferred from the null and alternative hypotheses, especially the alternative hypothesis.

In a binomial hypothesis test, the null hypothesis (H0) states that the probability of an event happening is as expected, for instance, p = 0.6. A one-tail alternative hypothesis (H1) suggests the probability has either decreased (p < 0.6) or increased (p > 0.6).

If the alternative hypothesis suggests the probability is simply 'different to' or 'not equal to' 0.6 (p ≠ 0.6), it indicates a two-tailed test. This means we are looking for deviations in both directions (higher or lower).

In a two-tailed test, the significance level (e.g., 10%) is split across both tails. For example, a 10% significance level would be divided into 5% for the lower end and 5% for the upper end, unlike one-tail tests where the entire significance level is in one tail.

To explain the alternative hypothesis, look for keywords like 'less than', 'greater than', 'different to', or 'not equal to' to determine if it's a one-tailed or two-tailed test.