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

A mobile library has 160 books for children on its records. The librarian believes that books with fewer pages are borrowed more often. He takes a random sample of 10 books for children.
1. Explain how the librarian should select this random sample.
  (2)
The librarian ranked the 10 books according to how often they had been borrowed, with 1 for the book borrowed the most and 10 for the book borrowed the least. He also recorded the number of pages in each book. The results are in the table below.
Book \(A\) \(B\) \(C\) \(D\) \(E\) \(F\) \(G\) \(H\) \(I\) \(J\)
Borrowing rank 1 2 3 4 5 6 7 8 9 10
Number of pages 50 212 115 80 301 90 356 283 152 317
Calculate Spearman's rank correlation coefficient for these data.
Test the librarian's belief using a \(5 \%\) level of significance. State your hypotheses clearly.