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Date	May 2014	Marks available	2	Reference code	14M.1.sl.TZ1.4
Level	SL only	Paper	1	Time zone	TZ1
Command term	Deduce	Question number	4	Adapted from	N/A

Question

A study was carried out to determine whether the country chosen by students for their university studies was influenced by a person’s gender. A random sample was taken. The results are shown in the following table.

A ${\chi ^2}$ test was performed at the 1% significance level.

The critical value for this test is 9.210.

State the null hypothesis.

[1]

a.

Write down the number of degrees of freedom.

[1]

b.

Write down

(i) the ${\chi ^2}$ statistic;

(ii) the associated p-value.

[2]

c.

State, giving a reason, whether the null hypothesis should be accepted.

[2]

d.

Markscheme

Country chosen and gender are independent. (A1) (C1)

Notes: Accept there is no association between country chosen and gender.

Do not accept “not related” or “not correlated” or “influenced”.

[1 mark]

a.

2 (A1) (C1)

[1 mark]

b.

(i) 9.17 (9.16988…) (A1)

Notes: Accept 9.169.

(ii) 0.0102 (0.0102043…) (A1) (C2)

Notes: Award (A1) for 0.010, but (A0) for 0.01.

[2 marks]

c.

Since $0.0102 > 0.01$ , we accept the null hypothesis. (R1)(A1)(ft)

OR

Since $9.17 < 9.210$ , we accept the null hypothesis. (R1)(A1)(ft) (C2)

Notes: To award (R1) there should be value(s) given in part (c). If a value is given in (c), we do not need it explicitly stated again in (d).

It is sufficient to state a correct comparison.

e.g. $p{\text{-value}} > {\text{significance level}}$ OR $\chi _{{\text{calc}}}^2 < {\text{critical value}}$

Do not award (R0)(A1). Follow through from part (c).

[2 marks]

d.

Examiners report

[N/A]

a.

[N/A]

b.

[N/A]

c.

[N/A]

d.

Syllabus sections

Topic 4 - Statistical applications » 4.4 » The

χ^{2}

${\chi ^2}$ test for independence: formulation of null and alternative hypotheses; significance levels; contingency tables; expected frequencies; degrees of freedom;

p

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