A2 June 2024 Q3

EdexcelCurrent spec6 marksIncludes hypothesis testingChi-Squared Tests

3. Tisam took a survey of students’ favourite colours. The results are summarised in the table below.

		Colour
		Red	Blue	Green	Yellow	Black	Total
Year group	1–5	34	15	14	22	3	88
	6–9	23	32	12	9	8	84
	10–12	5	28	19	8	8	68
	Total	62	75	45	39	19	240

Tisam carries out a suitable test to see if there is any association between favourite colour and year group.

(a) Write down the hypotheses for a suitable test. (1)

For her table, Tisam only needs to check one cell to show that none of the expected frequencies are less than 5

(b)

(i) Identify this cell, giving your reason.

(ii) Calculate the expected frequency for this cell. (2)

The test statistic for Tisam’s test is 38.449

(c) Using a 1% level of significance, complete the test.
You should state your critical value and conclusion clearly. (3)

Mark scheme (a)

Scheme	Marks	AO
\(\mathrm{H}_0\): There is no association between the colour chosen and year group (allow use of “independence” instead of association) \(\mathrm{H}_1\): There is some association between colour and year group	B1	2.5
	(1)

Notes

B1 for both hypotheses in context. Must mention colour and year group at least once

NB: condone use of related/correlated/linked etc if recovered with independent/associated

Mark scheme (b)

Scheme	Marks	AO
(i) Need lowest row total and column total so “Black” and “10-12”	B1	2.2a
(ii) With expected frequency \(\dfrac{68 \times 19}{240} = 5.3833\ldots\)	B1	1.1b
	(2)

Notes

(i) B1 for a choosing “Black” and “10-12” with some correct reasoning mentioning row and column totals (allow clear equivalent, e.g. ‘lowest total frequencies’)

(ii) B1 for a correct expression or awrt 5.38

Mark scheme (c)

Scheme	Marks	AO
\(\upsilon = (5 - 1) \times (3 - 1) = \underline{\mathbf{8}}\)	B1	3.4
cv of \(\chi_8^2(1\%) = \underline{\mathbf{20.090}}\)	B1ft	1.1b
(significant) evidence of an association between colour chosen and year group	B1ft	2.2b
	(3)
	(6 marks)

Notes

1^st B1 for a correct calculation or answer of 8. May be implied by sight of cv of 20.09

2^nd B1ft for 20.090 (accept 20.09) or a correct ft 1% cv using their df and correct to 2 d.p.

3^rd B1ft for a correct conclusion in context (ft their cv)
E.g. “students in different years (tend to) have different favourite colours”
Do not allow contradictory statements. Condone ‘related/relationship’ in part (c)
NB: We ignore their hypotheses when marking (c)