| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2024 |
| Session | January |
| Marks | 7 |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Hypothesis test for association |
| Difficulty | Standard +0.3 This is a straightforward application of Spearman's rank correlation coefficient hypothesis test with data already ranked. Students must calculate differences, apply the formula rs = 1 - 6Σd²/[n(n²-1)], and compare to critical values. While it requires careful arithmetic and knowledge of the test procedure, it's a standard textbook exercise with no novel problem-solving or conceptual challenges beyond routine application. |
| Spec | 5.08f Hypothesis test: Spearman rank |
| Runner | A | B | C | D | E | F | G | H |
| First race | 3 | 1 | 5 | 6 | 2 | 8 | 7 | 4 |
| Second race | 4 | 3 | 8 | 7 | 2 | 5 | 6 | 1 |
3.
Eight runners took part in two races. The positions in which the runners finished in the two races are shown in the table.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | c | }
\hline
Runner & A & B & C & D & E & F & G & H \\
\hline
First race & 3 & 1 & 5 & 6 & 2 & 8 & 7 & 4 \\
\hline
Second race & 4 & 3 & 8 & 7 & 2 & 5 & 6 & 1 \\
\hline
\end{tabular}
\end{center}
Test at the $5 \%$ significance level whether those runners who do better in one race tend to do better in the other.\\
\hfill \mbox{\textit{SPS SPS FM Statistics 2024 Q3 [7]}}