A2 October 2021 Q1

EdexcelCurrent spec7 marksIncludes hypothesis testingCorrelation

1. 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.

Student	History mark	Geography mark	History rank	Geography rank
\(A\)	76	58	1	3
\(B\)	70	60	2	2
\(C\)	64	57	\(s\)	\(t\)
\(D\)	64	63	\(s\)	1
\(E\)	64	57	\(s\)	\(t\)
\(F\)	59	50	6	7
\(G\)	55	52	7	6

(a) Write down the value of \(s\) and the value of \(t\) (2)

The full product moment correlation coefficient (pmcc) formula is used with the ranks to calculate the Spearman’s rank correlation coefficient instead of \(r_s = 1 - \dfrac{6\Sigma d^2}{n(n^2 - 1)}\) and the value obtained is 0.7106 to 4 significant figures.

(b) Explain why the full pmcc formula is used to carry out the calculation. (1)

(c) 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. (4)

Scheme	Marks	AO
\(s = 4\)	B1	1.1b
\(t = 4.5\)	B1	1.1b
	(2)

Scheme	Marks	AO
Because there are tied ranks.	B1	2.4
	(1)

Mark scheme (c)

Scheme	Marks	AO
\(\mathrm{H}_0 : \rho_s = 0 \qquad \mathrm{H}_1 : \rho_s \gt 0\)	B1	2.5
CV = 0.7143	B1	1.1b
\(r_s = 0.7106\) does not lie in the critical region.	M1	2.1
There is insufficient evidence to suggest that the higher the rank in the History test, the higher the rank in the Geography test (oe).	A1	2.2b
	(4)
	(7 marks)

Notes

B1: Both hypotheses correct with correct notation (must use \(\rho_s\) or \(\rho\))

B1: Correct critical value 0.7143 or better

M1: Drawing a correct inference using their CV and 0.7106

A1: Drawing a correct inference (condone “marks” instead of ranks) in context using their CV and 0.7106