Construct the Indicated Confidence Interval for the Difference Between Population $20 - 24,22 \%$

Multiple Choice

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.
-In a random sample of 500 people aged $20 - 24,22 \%$ were smokers. In a random sample of 450 people aged $25 - 29,14 \%$ were smokers. Construct a $95 \%$ confidence interval for the difference between the population proportions $\mathrm { p } _ { 1 } - \mathrm { p } 2$ .

A) $0.025 <$ p $_ { 1 } -$ p $_ { 2 } < 0.135$
B) $0.035 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.125$
C) $0.032 < \mathrm { p } _ { 1 } - \mathrm { p } _ { 2 } < 0.128$
D) $0.048 < p _ { 1 } - p _ { 2 } < 0.112$