| Exam Board | OCR MEI |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2010 |
| Session | June |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Hypothesis test for positive correlation |
| Difficulty | Standard +0.3 This is a straightforward application of Spearman's rank correlation coefficient with standard hypothesis testing. The question involves routine ranking of data, applying the formula, comparing to critical values from tables, and basic interpretation. The scatter diagram discussion requires minimal insight. While it's a multi-part question, each step follows a standard procedure taught in S2 with no novel problem-solving required, making it slightly easier than average. |
| Spec | 5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank |
| Contestant | A | B | C | D | E | F | G | H |
| \(x\) | 6 | 17 | 9 | 20 | 13 | 15 | 11 | 14 |
| \(y\) | 6 | 13 | 10 | 11 | 9 | 7 | 12 | 15 |
1 Two celebrities judge a talent contest. Each celebrity gives a score out of 20 to each of a random sample of 8 contestants. The scores, $x$ and $y$, given by the celebrities to each contestant are shown below.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | c | }
\hline
Contestant & A & B & C & D & E & F & G & H \\
\hline
$x$ & 6 & 17 & 9 & 20 & 13 & 15 & 11 & 14 \\
\hline
$y$ & 6 & 13 & 10 & 11 & 9 & 7 & 12 & 15 \\
\hline
\end{tabular}
\end{center}
(i) Calculate the value of Spearman's rank correlation coefficient.\\
(ii) Carry out a hypothesis test at the $5 \%$ significance level to determine whether there is positive association between the scores allocated by the two celebrities.\\
(iii) State the distributional assumption required for a test based on the product moment correlation coefficient. Sketch a scatter diagram of the scores above, and discuss whether it appears that the assumption is likely to be valid.
\hfill \mbox{\textit{OCR MEI S2 2010 Q1 [16]}}