| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2018 |
| Session | June |
| Marks | 13 |
| 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 standard textbook hypothesis testing question requiring straightforward application of correlation formulas and critical value comparison. All necessary summary statistics are provided, eliminating computational burden. The multi-part structure guides students through routine steps (calculate r, state hypotheses, compare to critical value, repeat for Spearman's), making it slightly easier than an average A-level question despite being Further Maths content. |
| Spec | 5.08a Pearson correlation: calculate pmcc5.08d Hypothesis test: Pearson correlation5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank |
| Sample | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) |
| \(c\) | 625 | 700 | 650 | 645 | 720 | 600 | 825 | 665 |
| \(a\) | 1.28 | 1.30 | 1.00 | 1.20 | 1.55 | 1.15 | 1.40 | 1.45 |
I appreciate you providing this content, but what you've shared appears to be a data table (numbers: 1, 45, 37.5, 1.5, 54) rather than mark scheme content with marking annotations (M1, A1, B1, etc).
Could you please provide the actual mark scheme text that needs cleaning? I'm ready to convert unicode symbols to LaTeX and format it once you share the content that contains:
- Marking annotations (M1, A1, B1, DM1, etc)
- Solution steps or marking guidance
- Unicode symbols to convert (θ, Σ, ≥, etc)\begin{enumerate}
\item Phil measures the concentration of a radioactive element, $c$, and the amount of dissolved solids, $a$, of 8 random samples of groundwater. His results are shown in the table below.
\end{enumerate}
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | c | }
\hline
Sample & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ & $G$ & $H$ \\
\hline
$c$ & 625 & 700 & 650 & 645 & 720 & 600 & 825 & 665 \\
\hline
$a$ & 1.28 & 1.30 & 1.00 & 1.20 & 1.55 & 1.15 & 1.40 & 1.45 \\
\hline
\end{tabular}
\end{center}
Given that
$$\mathrm { S } _ { c c } = 34787.5 \quad \mathrm {~S} _ { a a } = 0.2172875 \quad \mathrm {~S} _ { c a } = 47.7625$$
(a) calculate, to 3 decimal places, the product moment correlation coefficient between the concentration of the radioactive element and the amount of dissolved solids for these groundwater samples.\\
(b) Use your value of the product moment correlation coefficient to test whether or not there is evidence of a positive correlation between the concentration of this radioactive element and the amount of dissolved solids in groundwater. Use a $5 \%$ significance level. State your hypotheses clearly.\\
(c) Calculate, to 3 decimal places, Spearman's rank correlation coefficient between the concentration of the radioactive element and the amount of dissolved solids.\\
(d) Use your value of Spearman's rank correlation coefficient to test for evidence of a positive correlation between the concentration of the radioactive element and the amount of dissolved solids. Use a $5 \%$ significance level. State your hypotheses clearly.\\
(e) Using your conclusions in part (b) and part (d), comment on the possible relationship between these variables.
\hfill \mbox{\textit{Edexcel S3 2018 Q1 [13]}}