Construct the Indicated Confidence Interval for the Difference Between Population $0.0247 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.0286$

Construct the indicated confidence interval for the difference between population proportions p1 - p2. Assume that the samples are independent and that they have been randomly selected.
-A marketing survey involves product recognition in New York and California. Of 558 New Yorkers surveyed, 193 knew the product while 196 out of 614 Californians knew the product. Construct a 99% confidence interval for the difference between the two population proportions.

A) $0.0247 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.0286$
B) $- 0.0443 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.0976$
C) $- 0.0034 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.0566$
D) $- 0.0177 < p _ { 1 } - p _ { 2 } < 0.1243$