Two samples are taken with the following num]jers of successes and sample sizes \[ \begin{array}{l} r_{1}=35 r_{2}=33 \\ n_{1}=86 n_{2}=67 \end{array} \] Find a 93\% confidence interval, round answers to the nearest thousandth.

Step 1 ：Calculate the proportions for each sample: \(p_1 = \frac{r_1}{n_1} = \frac{35}{86} = 0.407\), \(p_2 = \frac{r_2}{n_2} = \frac{33}{67} = 0.493\)

Step 2 ：Find the difference in proportions: \(p_{diff} = p_1 - p_2 = 0.407 - 0.493 = -0.086\)

Step 3 ：Calculate the standard error: \(SE = \sqrt{\frac{p_1(1-p_1)}{n_1} + \frac{p_2(1-p_2)}{n_2}} = 0.081\)

Step 4 ：Find the z-score for a 93% confidence interval: \(z = 1.812\)

Step 5 ：Calculate the margin of error: \(ME = z \times SE = 1.812 \times 0.081 = 0.146\)

Step 6 ：Find the confidence interval: \(CI = (p_{diff} - ME, p_{diff} + ME) = (-0.232, 0.061)\)

Step 7 ：\(\boxed{(-0.232, 0.061)}\)