Constructing a confidence interval btwn two groups

Question

A survey is conducted of whether or not flu vaccinations should be mandatory. 141 out of 210 randomly polled civilians under the age of 30 were in agreement that flu vaccines should be mandatory. Meanwhile 111 out of 190 randomly selected residents aged 30 and above were in favour of flu vaccinations being mandatory. Constructing a 90% Confidence Interval for the difference in proportion (of support) between the 2 age groups

Answer 1

x-bar = 141/210 - 111/190 = .08722

s = √(141*(210-141)/210^3 + 111*(190-111)/190^3) = .04826

z₉₅, appropriate for a 90% confidence interval, is 1.64485

Then, the confidence interval is (.08722 - 1.64485 * .04826, .08722 + 1.64485 * .04826) =

(.00784, .16660)