Answer: There is no evidence, at the \(10\%\) significance level, of an association between car type and colour.

We test

\[H_0:\text{colour chosen is independent of type of car}.\]

The row totals are

\[130,\quad 100,\quad 70,\]

and the column totals are

\[110,\quad 100,\quad 90.\]

The grand total is \(300\). For each cell,

\[E=\frac{\text{row total}\times\text{column total}}{300}.\]

So the expected frequencies are

\[\begin{array}{c|ccc} & \text{Silver} & \text{Blue} & \text{Red}\ \hline \text{Hatchback} & 47.67 & 43.33 & 39.00\ \text{Saloon} & 36.67 & 33.33 & 30.00\ \text{Estate} & 25.67 & 23.33 & 21.00 \end{array}\]

Now calculate

\[\chi^2=\sum\frac{(O-E)^2}{E}.\]

This gives

\[\chi^2=5.57\quad\text{approximately}.\]

The degrees of freedom are

\[(3-1)(3-1)=4.\]

At the \(10\%\) significance level, the critical value is

\[\chi^2_{4,0.90}=7.779.\]

Since

\[5.57<7.779,\]

we do not reject \(H_0\). Therefore the data do not give evidence of an association between the colour chosen and the type of car.