There are 100 patients taking part in a trial of a new surgical procedure for a particular medical condition. Of these, 50 patients are randomly selected to receive the new procedure and the remaining 50 receive the old procedure. Six months later, a doctor assesses whether or not each patient has fully recovered. The results are shown below:

\begin{tabular}{l|c|c} & Fully recovered & Not fully recovered \ \hline Old procedure & 25 & 25 \ \hline New procedure & 31 & 19 \end{tabular}

The doctor is interested in whether there is a difference in full recovery rates for patients receiving the two procedures. Carry out an appropriate $5 \%$ significance level test, stating your hypotheses carefully. [You do not need to derive the test.] What conclusion should be reported to the doctor?

[Hint: Let $\chi_{k}^{2}(\alpha)$ denote the upper $100 \alpha$ percentage point of a $\chi_{k}^{2}$ distribution. Then

$$\left.\chi_{1}^{2}(0.05)=3.84, \chi_{2}^{2}(0.05)=5.99, \chi_{3}^{2}(0.05)=7.82, \chi_{4}^{2}(0.05)=9.49 .\right]$$