Question 3 - A-Level Maths

Exam Board	Edexcel
Module	S3 (Statistics 3)
Year	2008
Session	June
Topic	Hypothesis test of Spearman’s rank correlation coefficien

The product moment correlation coefficient is denoted by \(r\) and Spearman's rank correlation coefficient is denoted by \(r _ { s }\).
1. Sketch separate scatter diagrams, with five points on each diagram, to show
  1. \(r = 1\),
  2. \(r _ { s } = - 1\) but \(r > - 1\).
Two judges rank seven collie dogs in a competition. The collie dogs are labelled \(A\) to \(G\) and the rankings are as follows
Rank 1 2 3 4 5 6 7
Judge 1 \(A\) \(C\) \(D\) \(B\) \(E\) \(F\) \(G\)
Judge 2 \(A\) \(B\) \(D\) \(C\) \(E\) \(G\) \(F\)
1. Calculate Spearman's rank correlation coefficient for these data.
2. Stating your hypotheses clearly, test, at the \(5 \%\) level of significance, whether or not the judges are generally in agreement.