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Date May 2014 Marks available 2 Reference code 14M.1.sl.TZ2.8
Level SL only Paper 1 Time zone TZ2
Command term State Question number 8 Adapted from N/A

Question

A group of 100 students gave the following responses to the question of how they get to school.



 

A \({\chi ^2}\) test for independence was conducted at the \(5\%\) significance level. The null hypothesis was defined as

 

\({{\text{H}}_0}\): Method of getting to school is independent of gender.

Find the expected frequency for the females who use public transport to get to school.

[2]
a.

Find the \({\chi ^2}\) statistic.

[2]
b.

The \({\chi ^2}\) critical value is \(7.815\) at the \(5\%\) significance level.

State whether or not the null hypothesis is accepted. Give a reason for your answer.

[2]
c.

Markscheme

\(\frac{{30}}{{100}} \times \frac{{48}}{{100}} \times 100\)   OR   \(\frac{{30 \times 48}}{{100}}\)     (M1)

 

Note: Award (M1) for correct substitution into correct formula.

 

\( = 14.4{\text{ }}\left( {\frac{{72}}{5}} \right)\)     (A1)     (C2)

[2 marks]

a.

\(13.0{\text{ }}(12.9554…)\)     (A2)     (C2)

 

Note: Award (A1)(A0) for \(12.9\).

 

[2 marks]

b.

the null hypothesis is not accepted     (A1)(ft)

\(\chi _{calc}^2 > \chi _{crit}^2\)   OR   \(13.0 > 7.82\)    (R1)

OR

the null hypothesis is not accepted     (A1)(ft)

p-value \({\text{(0.0047) (0.00473391}} \ldots {\text{)}} < 0.05\)     (R1)     (C2)

 

Notes: Follow through from their answer to part (b).

     Do not award (A1)(ft)(R0).

 

[2 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

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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