AS June 2022 Q1

EdexcelAS paperCurrent spec7 marksIncludes hypothesis testingCorrelation

1. Abena and Meghan are both given the same list of 10 films.

Each of them ranks the 10 films from most favourite to least favourite.

For the differences, \(d\), between their ranks for these 10 films, \(\sum d^2 = 84\)

(a) Calculate Spearman’s rank correlation coefficient between Abena’s ranks and Meghan’s ranks. (1)

A test is carried out at the 5% level of significance to see if there is agreement between their ranks for the films.

The hypotheses for the test are

\[\mathrm{H}_0 : \rho_\mathrm{S} = 0 \qquad \mathrm{H}_1 : \rho_\mathrm{S} \gt 0\]

(b)

(i) Find the critical region for the test.

(ii) State the conclusion of the test. (2)

An 11th film is added to the list. Abena and Meghan both agree that this film is their least favourite.

A new test is carried out at the 5% level of significance using the same hypotheses.

Scheme	Marks	AO
\(\left[r_s = 1 - \dfrac{6 \times 84}{10(10^2 - 1)}\right]\) \(= 0.4909\ldots\) awrt 0.491	B1	1.1b
	(1)

Mark scheme (b)

Scheme	Marks	AO
(i) \((1 \gt)\, r_s \gt 0.5636\)	B1	1.1b
(ii) (0.491 is not in the critical region) There is insufficient evidence of agreement between their film ranks.	B1ft	2.2b
	(2)

Notes

(i) B1: Correct critical region with 0.5636 or better. Condone use of \(\rho\) instead of \(r_s\)

(ii) B1ft: Correct ft contextualised conclusion (must include film or ranks) based on their (a) and their CR Allow ft on their CV if a CR is not stated

Mark scheme (c)

Scheme	Marks	AO
new \(r_s = 1 - \dfrac{6 \times 84}{11(11^2 - 1)}\)	M1	1.1b
\(= 0.61818\ldots\) awrt 0.618	A1	1.1b
new critical value is 0.5364	B1	1.1b
There is now sufficient evidence of agreement between their film ranks.	A1	2.2b
	(4)
	(7 marks)

Notes

M1: Use of formula with same \(\sum d^2\) and 11

A1: awrt 0.618 (allow \(\dfrac{34}{55}\))

B1: 0.5364 or better

A1: fully correct solution with awrt 0.618 and contextualised conclusion (must include film or ranks)