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

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

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.

\(\frac{{30}}{{100}} \times \frac{{48}}{{100}} \times 100\)   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]

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

Note: Award (A1)(A0) for \(12.9\).

[2 marks]

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]