A2 June 2025 Q2

EdexcelCurrent spec7 marksIncludes hypothesis testingCorrelation

2. Two lecturers are marking a large batch of students’ essays, to place them in rank order.

A random sample of 9 students is taken and their essays are marked by both lecturers.

The marks awarded are given in the table below.

Student	\(A\)	\(B\)	\(C\)	\(D\)	\(E\)	\(F\)	\(G\)	\(H\)	\(I\)
Lecturer 1	10	16	5	17	12	7	14	11	8
Lecturer 2	17	22	19	24	21	15	23	18	20

(a) Calculate Spearman’s rank correlation coefficient for these data. (4)

(b) Carry out a suitable test to assess whether the lecturers agree about the rank order of the essays. You should use a 5% level of significance and state your hypotheses and critical value clearly. (3)

Mark scheme (a)

Scheme

Marks

Student	\(A\)	\(B\)	\(C\)	\(D\)	\(E\)	\(F\)	\(G\)	\(H\)	\(I\)
Rank 1	6	2	9	1	4	8	3	5	7
Rank 2	8	3	6	1	4	9	2	7	5

1.1b

\(\sum d^2 = 4 + 1 + 9 + 0 + 0 + 1 + 1 + 4 + 4\ \ (= 24)\)

dM1

1.1b

\(r_s = 1 - \dfrac{6 \times \text{“}24\text{”}}{9 \times (9^2 - 1)}\)

1.1b

\(= \dfrac{4}{5}\) or 0.8

1.1b

(4)

Notes

1^st M1: for an attempt to rank marks (at least 5 correct in one row) Allow reverse ranking. May be implied by 24

2^nd dM1: dep on 1^st M1 for attempt at calculating \(d^2\) (does not need to be summed). (Allow 1 error squaring their differences)
May be implied by 24

3^rd M1: indep of first two Ms for using correct formula with their \(12 \lt \sum d^2 \lt 240\)
May be implied by 0.8 o.e.

A1: for 0.8 o.e.

Mark scheme (b)

Scheme	Marks	AO
\(\mathrm{H}_0 : \rho = 0 \qquad \mathrm{H}_1 : \rho \gt 0\)	B1	2.5
cv one tail 5% = 0.6	M1	3.4
(Significant result so there is evidence that) the lecturers agree about the rank order of the essays.	A1	2.2b
	(3)
	(7 marks)

Notes

B1: for both hypotheses correct in terms of \(\rho\) or \(\rho_s\) (condone if it appears as \(p\)). Do not allow hypotheses in words on their own.

M1: for selecting the correct critical value. Allow \(\pm\)
If they scored B0 for 2-tail test allow 0.7

A1: dep on \(0.7 \lt \text{“}0.8\text{”} \lt 1\) for a correct conclusion in context stating agreement (or agree) between lecturers. Do not allow correlation for agreement (not contextual)
Can award this mark independently of hypotheses.
Do NOT award this mark if contradictory statements are seen e.g. not significant so lecturers agree.
If a comparison is made then it must be correct.
Note that M0A1 is not possible