Question 1 - A-Level Maths

Exam Board	Edexcel
Module	FS2 (Further Statistics 2)
Year	2021
Session	June
Topic	Hypothesis test of Spearman’s rank correlation coefficien

Anisa is investigating the relationship between marks on a History test and marks on a Geography test. She collects information from 7 students. She wants to calculate the Spearman's rank correlation coefficient for the 7 students so she ranks their performance on each test.

Write down the value of \(s\) and the value of \(t\) The full product moment correlation coefficient (pmcc) formula is used with the ranks to calculate the Spearman's rank correlation coefficient instead of \(r _ { s } = 1 - \frac { 6 \Sigma d ^ { 2 } } { n \left( n ^ { 2 } - 1 \right) }\) and the value obtained is 0.7106 to 4 significant figures.
Explain why the full pmcc formula is used to carry out the calculation.
Stating your hypotheses clearly, test whether or not there is evidence to suggest that the higher a student ranks in the History test, the higher the student ranks in the Geography test. Use a \(5 \%\) level of significance.