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Date May 2014 Marks available 1 Reference code 14M.1.sl.TZ1.4
Level SL only Paper 1 Time zone TZ1
Command term Write down 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 \({\chi ^2}\) test for independence: formulation of null and alternative hypotheses; significance levels; contingency tables; expected frequencies; degrees of freedom; \(p\)-values.
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