| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Marks | 6 |
| 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 application of the PMCC formula using given summary statistics, followed by a standard one-tailed hypothesis test with clear structure. While it requires knowledge of the correlation coefficient formula and hypothesis testing procedure, both parts are routine textbook exercises with no problem-solving insight needed—slightly easier than average due to all computational values being provided. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08d Hypothesis test: Pearson correlation |
| Answer | Marks |
|---|---|
| (a) \(r = \frac{2564.33}{\sqrt{3747.73 \times 2791.33}} = 0.7928\) | M1 A1 |
| (b) \(H_0: \rho = 0\) \(H_1: \rho > 0\) | B1 M1 A1 |
| Answer | Marks | Guidance |
|---|---|---|
| there is evidence that those good at maths are better at visio-spatial | A1 | (6) |
(a) $r = \frac{2564.33}{\sqrt{3747.73 \times 2791.33}} = 0.7928$ | M1 A1 |
(b) $H_0: \rho = 0$ $H_1: \rho > 0$ | B1 M1 A1 |
$n = 15$, 5% level $\therefore$ C.R. is $r > 0.4409$
$0.7928 > 0.4409 \therefore$ significant
there is evidence that those good at maths are better at visio-spatial | A1 | (6)
---2. A Geography teacher is interested in the link between mathematical ability and the ability to visualise three-dimensional situations. He gives a group of 15 students a test and records each student's score, $m$, on the mathematics questions and each student's score, $v$, on the visiospatial questions.
He calculates the following summary statistics:
$$S _ { m m } = 3747.73 , \quad S _ { v v } = 2791.33 , \quad S _ { m v } = 2564.33$$
\begin{enumerate}[label=(\alph*)]
\item Calculate the product moment correlation coefficient for these data.
\item Stating your hypotheses clearly and using a $5 \%$ level of significance test the theory that students who are good at Mathematics tend to have better visio-spatial awareness.\\
(4 marks)
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 Q2 [6]}}