| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2026 |
| Session | January |
| Marks | 7 |
| 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 hypothesis test with clear data, standard procedure (rank the data, calculate rs, compare to critical value), and no complications. The only slight elevation above routine is that students must recognize 'high level of agreement' means testing for positive correlation at 1% level, but this is standard exam interpretation. |
| Spec | 2.05g Hypothesis test using Pearson's r |
| Wine | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) |
| Judge I | 86.3 | 87.5 | 87.6 | 88.8 | 89.4 | 89.9 | 90.5 |
| Judge II | 85.3 | 88.1 | 82.7 | 87.7 | 89.0 | 89.4 | 91.5 |
1.
At a wine-tasting competition, two judges give marks out of 100 to 7 wines as follows.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | c | c | }
\hline
Wine & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ & $G$ \\
\hline
Judge I & 86.3 & 87.5 & 87.6 & 88.8 & 89.4 & 89.9 & 90.5 \\
\hline
Judge II & 85.3 & 88.1 & 82.7 & 87.7 & 89.0 & 89.4 & 91.5 \\
\hline
\end{tabular}
\end{center}
A spectator claims that there is a high level of agreement between the rank orders of the marks given by the two judges. Test the spectator's claim at the $1 \%$ significance level.\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM Statistics 2026 Q1 [7]}}