Question 1 - A-Level Maths

Exam Board	Edexcel
Module	S3 (Statistics 3)
Year	2015
Session	June
Topic	Hypothesis test of Spearman’s rank correlation coefficien

The names of the 720 members of a swimming club are listed alphabetically in the club's membership book. The chairman of the swimming club wishes to select a systematic sample of 40 names. The names are numbered from 001 to 720 and a number between 001 and \(w\) is selected at random. The corresponding name and every \(x\) th name thereafter are included in the sample.
1. Find the value of \(w\).
2. Find the value of \(x\).
3. Write down the probability that the sample includes both the first name and the second name in the club's membership book.
4. State one advantage and one disadvantage of systematic sampling in this case.
5. Nine dancers, Adilzhan \(( A )\), Bianca \(( B )\), Chantelle \(( C )\), Lee \(( L )\), Nikki \(( N )\), Ranjit \(( R )\), Sergei \(( S )\), Thuy \(( T )\) and Yana \(( Y )\), perform in a dancing competition.
Two judges rank each dancer according to how well they perform. The table below shows the rankings of each judge starting from the dancer with the strongest performance.
Rank 1 2 3 4 5 6 7 8 9
Judge 1 \(S\) \(N\) \(B\) \(C\) \(T\) \(A\) \(Y\) \(R\) \(L\)
Judge 2 \(S\) \(T\) \(N\) \(B\) \(C\) \(Y\) \(L\) \(A\) \(R\)
Calculate Spearman's rank correlation coefficient for these data.
Stating your hypotheses clearly, test at the \(1 \%\) level of significance, whether or not the two judges are generally in agreement.