| Exam Board | Edexcel |
|---|---|
| Module | FS2 AS (Further Statistics 2 AS) |
| Year | 2020 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Pearson’s product-moment correlation coefficient |
| Type | One-tailed test for positive correlation |
| Difficulty | Standard +0.3 This is a straightforward one-tailed hypothesis test for correlation with clear context. Students must state H₀: ρ=0 vs H₁: ρ>0, compare r=0.3892 against the critical value from tables (n=22, α=0.05), and state the critical region. It's a standard textbook exercise requiring only procedural knowledge of hypothesis testing for correlation, slightly above average difficulty due to being Further Maths content but otherwise routine. |
| Spec | 5.08d Hypothesis test: Pearson correlation |
| Answer | Marks | Guidance |
|---|---|---|
| \(H_0: \rho = 0 \quad H_1: \rho > 0\) | B1 | Both hypotheses correct in terms of \(\rho\) |
| 5% one-tail cv for \(r\) is: 0.3598 | M1 | For use of tables to find the cv of 0.3598 |
| Significant result so there is evidence to support the agent's belief | A1 | For a correct conclusion in context mentioning "belief" or description of this |
# Question 1:
$H_0: \rho = 0 \quad H_1: \rho > 0$ | B1 | Both hypotheses correct in terms of $\rho$
5% one-tail cv for $r$ is: 0.3598 | M1 | For use of tables to find the cv of 0.3598
Significant result so there is evidence to support the agent's belief | A1 | For a correct conclusion in context mentioning "belief" or description of this
---\begin{enumerate}
\item An estate agent in Tornep believes that houses further from the railway station are more expensive than those that are closer. She took a random sample of 22 three-bedroom houses in Tornep and calculated the product moment correlation coefficient between the house price and the distance from the station to be 0.3892
\end{enumerate}
Stating your hypotheses clearly, use a $5 \%$ level of significance to test the estate agent's belief. State the critical region used in your test.
\hfill \mbox{\textit{Edexcel FS2 AS 2020 Q1 [3]}}