Leave lesson

Statistics · Hypothesis testing

Chapter 1 · 3

The idea

Two-tailed tests

Carrying out a two-tailed binomial test (H1 : p ≠ p0), where a change in either direction counts as evidence. Splitting the significance level α into two tails of α/2, finding both critical regions and the actual significance level (the sum of the two tail probabilities), the equivalent p-value method (compare the observed tail with α/2, or 2× the tail with α), and writing a full conclusion in context.

A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.

In this lesson — start anywhere

Statistics · Hypothesis testing

Two-tailed tests

Carrying out a two-tailed binomial test (H1 : p ≠ p0), where a change in either direction counts as evidence. Splitting the significance level α into two tails of α/2, finding both critical regions and the actual significance level (the sum of the two tail probabilities), the equivalent p-value method (compare the observed tail with α/2, or 2× the tail with α), and writing a full conclusion in context.

Why it works

Splitting the significance level

A sack of beads used to be 14%14\% red — after heavy use, has that changed? Not "risen", not "fallen": changed, either way. A two-tailed test asks exactly this, with no direction specified, so H1:p≠p0H_1 : p \ne p_0. Evidence can come from the result being unusually high or low, so the significance level α\alpha is split between the two tails — α2\tfrac{\alpha}{2} in each. A 5%5\% two-tailed test therefore uses 2.5%2.5\% at each end.

Keep reading — free

The rest of the explanation, plus 2 worked examples you step through move by move.

Start free

Takes a minute — no card.