Statistical hypothesis testing (AS Unit 2: Applied Mathematics A) — WJEC A-Level Mathematics
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Statistical hypothesis testing (AS Unit 2: Applied Mathematics A) explained
Hypothesis testing provides a formal decision framework for evaluating claims about a population parameter.
Read the full explanation
The null hypothesis H₀ states the default baseline (e.g. p = p₀), while the alternative hypothesis H₁ expresses what is suspected: one-tailed if directional (p < p₀ or p > p₀), two-tailed if non-directional (p ≠ p₀). The test statistic X is the observed count. The significance level α is the threshold probability for rejecting H₀ when true. The critical region is the set of test statistic values leading to rejection of H₀, bounded by critical values; its complement is the acceptance region. The p-value is the probability of observing a result at least as extreme as the test statistic under H₀.
Your focus
- Formulate null and alternative hypotheses using correct mathematical parameter notation.
- Distinguish between critical regions, acceptance regions, critical values, and significance levels.
- Explain how p-values and critical regions provide equivalent criteria for evaluating hypotheses.
Statistical hypothesis testing (AS Unit 2: Applied Mathematics A) exam tips
Marking Points
- defining the null and alternative hypotheses using the population parameter p
- defining the critical region as the set of test statistic outcomes leading to the rejection of H₀
- explaining the role of the significance level and p-value in deciding whether to reject H₀
Examiner Tips
- 💡Always state hypotheses using the parameter symbol p (e.g. H₀: p = 0.3, H₁: p > 0.3), never sample values.
- 💡In a two-tailed test at significance level α, remember that each tail receives an error probability of α/2.
Common Mistakes
- writing hypotheses using the sample proportion or sample statistic rather than the population parameter p
- confusing the significance level α with the calculated p-value or the critical value itself