Standard +0.3 This is a standard textbook application of Spearman's rank correlation coefficient with straightforward ranking (no ties), calculation using the formula, and a one-tailed hypothesis test using tables. It requires methodical execution of a learned procedure rather than problem-solving or insight, making it slightly easier than average.
During a village show, two judges, \(P\) and \(Q\), had to award a mark out of 30 to some flower displays. The marks they awarded to a random sample of 8 displays were as follows:
Display
\(A\)
\(B\)
\(C\)
\(D\)
\(E\)
\(F\)
\(G\)
\(H\)
Judge \(P\)
25
19
21
23
28
17
16
20
Judge \(Q\)
20
9
21
13
17
14
11
15
Calculate Spearman's rank correlation coefficient for the marks awarded by the two judges.
After the show, one competitor complained about the judges. She claimed that there was no positive correlation between their marks.
Stating your hypotheses clearly, test whether or not this sample provides support for the competitor's claim. Use a \(5 \%\) level of significance.
\begin{enumerate}
\item During a village show, two judges, $P$ and $Q$, had to award a mark out of 30 to some flower displays. The marks they awarded to a random sample of 8 displays were as follows:
\end{enumerate}
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | }
\hline
Display & $A$ & $B$ & $C$ & $D$ & $E$ & $F$ & $G$ & $H$ \\
\hline
Judge $P$ & 25 & 19 & 21 & 23 & 28 & 17 & 16 & 20 \\
\hline
Judge $Q$ & 20 & 9 & 21 & 13 & 17 & 14 & 11 & 15 \\
\hline
\end{tabular}
\end{center}
(a) Calculate Spearman's rank correlation coefficient for the marks awarded by the two judges.
After the show, one competitor complained about the judges. She claimed that there was no positive correlation between their marks.\\
(b) Stating your hypotheses clearly, test whether or not this sample provides support for the competitor's claim. Use a $5 \%$ level of significance.
\hfill \mbox{\textit{Edexcel S3 2007 Q1 [10]}}