The efficacy of a new drug was tested as follows. Fifty patients were given the drug, and another fifty patients were given a placebo. A week later, the numbers of patients whose symptoms had gone entirely, improved, stayed the same and got worse were recorded, as summarised in the following table.

\begin{tabular}{|c|c|c|} \hline & Drug & Placebo \ \hline symptoms gone & 14 & 6 \ improved & 21 & 19 \ same & 10 & 10 \ worse & 5 & 15 \ \hline \end{tabular}

Conduct a $5 \%$ significance level test of the null hypothesis that the medicine and placebo have the same effect, against the alternative that their effects differ.

[Hint: You may find some of the following values relevant:

\begin{tabular}{|c|cccccc|} \hline Distribution & $\chi_{1}^{2}$ & $\chi_{2}^{2}$ & $\chi_{3}^{2}$ & $\chi_{4}^{2}$ & $\chi_{6}^{2}$ & $\chi_{8}^{2}$ \ \hline 95 th percentile & $3.84$ & $5.99$ & $7.81$ & $9.48$ & $12.59$ & $15.51$ \ \hline \end{tabular}