Two random samples are taken, one from among UVA students and the other from among UNC students. Both groups are asked if academics are their top priority. A summary of the sample sizes and proportions of each group answering ``yes'' are given below:

$$\begin{array}{lll} \mbox{UVA (Pop. 1)}: & n_1 = 84, & \hat{p}_1 = 0.728 \\ \mbox{UNC (Pop. 2)}: & n_2 = 92, & \hat{p}_2 = 0.668 \\ \end{array}$$

Find a 97.8% confidence interval for the difference $p_1 - p_2$ of the population proportions.

Confidence interval =