Hypothesis Testing for the Binomial Distribution

This lesson covers hypothesis testing using the binomial distribution as required by the Edexcel A-Level Mathematics specification (9MA0), Paper 3 Section A -- Statistics. You need to set up null and alternative hypotheses, calculate p-values, find critical regions, and draw conclusions in context.

---

What is a Hypothesis Test?

A hypothesis test determines whether there is enough evidence in a sample to reject a claim about a population parameter.

The five-step framework

1. State the hypotheses (H0 and H1).
2. State the significance level (alpha).
3. Calculate the test statistic or p-value.
4. Compare with the critical value or alpha.
5. Draw a conclusion in context.

---

Null and Alternative Hypotheses

• H0: p = p0 (the null -- assumed true unless evidence says otherwise)
• H1: p < p0 (one-tailed, lower)
• H1: p > p0 (one-tailed, upper)
• H1: p ≠ p0 (two-tailed)

Exam Tip: H0 always contains "=". H1 contains <, > or ≠. Always state both clearly.

---

Significance Level