A2 June 2024 Q2

EdexcelCurrent spec7 marksIncludes hypothesis testingCorrelation

2. An estate agent asks customers to rank 7 features of a house, \(A\), \(B\), \(C\), \(D\), \(E\), \(F\) and \(G\), in order of importance. The responses for two randomly selected customers are in the table below.

Rank	1	2	3	4	5	6	7
Customer 1	\(A\)	\(E\)	\(C\)	\(F\)	\(G\)	\(B\)	\(D\)
Customer 2	\(E\)	\(F\)	\(C\)	\(G\)	\(A\)	\(D\)	\(B\)

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

(b) Stating your hypotheses and critical value clearly, test at the 5% level of significance, whether or not the two customers are generally in agreement. (3)

Mark scheme (a)

Scheme

Marks

Rank	\(A\)	\(B\)	\(C\)	\(D\)	\(E\)	\(F\)	\(G\)
Customer 1	1	6	3	7	2	4	5
Customer 2	5	7	3	6	1	2	4

2.1

\(\sum d^2 = 16 + 1 + 1 + 1 + 4 + 1\ [= 24]\)

1.1b

\(r_s = 1 - \dfrac{6 \times 24}{7(7^2 - 1)}\)

dM1

1.1b

\(= 0.57142\ldots\) awrt 0.571

1.1b

(4)

Notes

M1: For pairing up the ranks (at least 4 pairs correct) may be implied by a later calculation or awrt 0.571

M1: For an attempt at \(\sum d^2\) condoning slips. Implied by 24 or awrt 0.571 (If \(\sum d^2\) is not correct then look for attempts at the differences proceeding to a value for \(\sum d^2\))

dM1: Dependent on the previous method mark for use of their \(\sum d^2\) in a correct formula (which must be less than 112) Does not need to be evaluated. Implied by awrt 0.571

A1: awrt 0.571 correct answer with no incorrect working seen scores full marks Accept \(\dfrac{4}{7}\)

Mark scheme (b)

Scheme	Marks	AO
\(\mathrm{H}_0 : \rho_s = 0 \qquad \mathrm{H}_1 : \rho_s \gt 0\)	B1	2.5
5% critical value (\(\pm\)) 0.7143	B1	1.1a
Insufficient evidence to reject H₀. There is no evidence to suggest the customers are in agreement	B1	2.2b
	(3)
	(7 marks)

Notes

B1: For both hypotheses in terms of \(\rho\) or \(\rho_s\) (do not allow \(r\) or \(r_s\))

B1: Correct CV of (\(\pm\)) 0.7143 or better

B1: Correct conclusion in context based on their cv and their \(r_s\) such that \(|r_s| \lt |\text{CV}|\) suggesting there is insufficient evidence to suggest the customers are (generally) in agreement oe / no evidence to suggest a positive correlation between the rankings (of features) by the customers oe. Condone conclusions such as e.g. sufficient evidence to suggest the customers are not in agreement
A comparison statement such as “not sig” is not needed but if seen must be correct. Do NOT award this mark if contradictory comments or working is seen e.g. “reject H₀” or comparison of their 0.571 with 0.05 or e.g. \(0.571 \gt 0.7143\) (corrected from the printed mark scheme: “their 0.517” should read “their 0.571”)

SC: B0(for 2-tail) B1(for CV \(\pm 0.7587\)) and B1 correct conclusion in context based on their cv and their \(r_s\) such that \(|r_s| \lt |\text{CV}|\) (as in main scheme)