AS June 2024 Q1

EdexcelAS paperCurrent spec6 marksIncludes hypothesis testingChi-Squared Tests

1. Sharma believes that each computer game he sells appeals equally to all age ranges.
To investigate this, he takes a random sample of 100 people who play these games and asks them which of the games \(A\), \(B\) or \(C\) they prefer.
The results are summarised in the table below.

Computer game		\(A\)	\(B\)	\(C\)
Age range	\(\lt 20\)	8	15	6
	20 – 30	21	12	9
	\(\gt 30\)	6	10	13

(a) Write down hypotheses for a suitable test to assess Sharma’s belief. (1)

(b) For the test, calculate the expected frequency for

(i) those players aged under 20 who prefer game \(C\)

(ii) those players aged between 20 and 30 who prefer game \(A\) (2)

Sharma correctly calculates the test statistic for this test to be 11.542 (to 3 decimal places).

(d) Using a 5% significance level, and stating your critical value, comment on Sharma’s belief. (2)

Mark scheme (a)

Scheme	Marks	AO
\(\mathrm{H}_0\): There is no association between age range and preferred game \(\mathrm{H}_1\): There is an association between age range and preferred game	B1	1.2
	(1)

Notes

B1 for both hypotheses in context
must mention independence/dependence or no association/association
must mention age and game at least once
Do not allow e.g. ‘\(\mathrm{H}_0\): games sold appeal equally to all age ranges’
Use of ‘correlation’, ‘link’, ‘relationship’, ‘connection’ is B0 but allow for 2^nd B1 in (d)
ignore comments about sales

Mark scheme (b)

Scheme	Marks	AO
(i) \(\dfrac{29 \times 28}{100} = \underline{\mathbf{8.12}}\) (ii) \(\dfrac{42 \times 35}{100} = \underline{\mathbf{14.7}}\)	M1 A1	1.1b 1.1b
	(2)

Scheme

Marks

(i) \(\dfrac{29 \times 28}{100} = \underline{\mathbf{8.12}}\)

(ii) \(\dfrac{42 \times 35}{100} = \underline{\mathbf{14.7}}\)

M1
A1

1.1b
1.1b

(2)

Notes

M1 for one correct expression or correct value.

A1 for both correct values (correct to 1 dp). Accept 8.1

Scheme	Marks	AO
[Since (b)(i) \(\gt 5\) there is no pooling so df \(= (3-1) \times (3-1) =\)] 4	B1	1.1b
	(1)

Mark scheme (d)

Scheme	Marks	AO
\(\chi_4^2(0.05) = \underline{\mathbf{9.488}}\)	B1ft	3.4/ 1.1b
[The test is significant so reject \(\mathrm{H}_0\):] Sharma’s belief is not supported / there is significant evidence of an association between age range and computer game preference.	B1	2.2b
	(2)
	(6 marks)

Notes

1^st B1ft for awrt 9.488 or ft their df for a 5% critical value
may see \(\chi_3^2(0.05) = 7.815\) \(\chi_2^2(0.05) = 5.991\) \(\chi_7^2(0.05) = 14.067\) \(\chi_8^2(0.05) = 15.507\)

2^nd B1 Indep of hypotheses but dep on cv < 11.542
for correct statement in context about Sharma’s belief
condone e.g ‘games sold do not appeal equally to all age ranges’
for a contextual statement must mention age and game
B0 for contradictory statements e.g. “test is not significant so belief is not supported”