2010-73.md

course	course_year	question_number	tags	title	year
Statistics	IB	73	IB 2010 Statistics	Paper 2, Section I, E	2010

A washing powder manufacturer wants to determine the effectiveness of a television advertisement. Before the advertisement is shown, a pollster asks 100 randomly chosen people which of the three most popular washing powders, labelled $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$, they prefer. After the advertisement is shown, another 100 randomly chosen people (not the same as before) are asked the same question. The results are summarized below.

\begin{tabular}{c|ccc} & $\mathrm{A}$ & $\mathrm{B}$ & $\mathrm{C}$ \ \hline before & 36 & 47 & 17 \ after & 44 & 33 & 23 \end{tabular}

Derive and carry out an appropriate test at the $5 %$ significance level of the hypothesis that the advertisement has had no effect on people's preferences.

[You may find the following table helpful:

$\left.\begin{array}{c|cccccc} & \chi_{1}^{2} & \chi_{2}^{2} & \chi_{3}^{2} & \chi_{4}^{2} & \chi_{5}^{2} & \chi_{6}^{2} \ \hline 95 \text { percentile } & 3.84 & 5.99 & 7.82 & 9.49 & 11.07 & 12.59\end{array} \cdot\right]$