Statistical hypothesis testing (A2 Unit 4: Applied Mathematics B) — WJEC A-Level Mathematics
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Statistical hypothesis testing (A2 Unit 4: Applied Mathematics B) explained
The Product Moment Correlation Coefficient (PMCC) r measures the strength and direction of linear association between bivariate normal variables, bounded by −1 ≤ r ≤ 1.
Read the full explanation
To test whether an observed sample correlation r indicates a genuine linear association in the population, candidates formulate hypotheses about the population correlation coefficient ρ: H₀: ρ = 0 against H₁: ρ > 0, ρ < 0, or ρ ≠ 0. Candidates compare the sample r against tabulated critical values for sample size n at significance level α, or compare the provided p-value against α. If |r| exceeds the critical value (or p < α), H₀ is rejected in favour of significant linear correlation.
Your focus
- Formulate null and alternative hypotheses for correlation tests using population parameter ρ.
- Evaluate sample correlation coefficients against critical values or p-values at given significance levels.
- Interpret test outcomes in practical context, avoiding claims of causal determination.
Statistical hypothesis testing (A2 Unit 4: Applied Mathematics B) exam tips
Marking Points
- stating hypotheses in terms of the population correlation coefficient ρ: H₀: ρ = 0 and H₁: ρ > 0, ρ < 0, or ρ ≠ 0
- looking up or quoting the correct critical value for sample size n at the specified significance level
- comparing sample r to the critical value (or p-value to α) and stating a clear statistical decision
- writing a non-dogmatic conclusion in context regarding the linear correlation between the two variables
Examiner Tips
- 💡Always write the Greek letter ρ (rho) for hypotheses: H₀: ρ = 0, H₁: ρ ≠ 0 (or > 0 or < 0).
- 💡For two-tailed tests at significance level α, use the column for α/2 in one-tail tables or look up the two-tail column.
Common Mistakes
- stating hypotheses in terms of sample correlation r (e.g. H₀: r = 0) rather than population parameter ρ
- concluding that rejecting H₀ proves a causal relationship exists between the two variables