Suppose You Want to Estimate the Difference Between Two Population $0.03$

Multiple Choice

Suppose you want to estimate the difference between two population proportions correct to within $0.03$ with probability $0.90$ . If prior information suggests that $\mathrm { p } _ { 1 } \approx 0.4$ and $\mathrm { p } _ { 2 } \approx 0.8$ , and you want to select independent random samples of equal size from the populations, how large should the sample sizes be?

A) $n _ { 1 } = n _ { 2 } = 1708$
B) $\mathrm { n } _ { 1 } = \mathrm { n } _ { 2 } = 963$
C) $\mathrm { n } _ { 1 } = \mathrm { n } _ { 2 } = 1925$
D) $\mathrm { n } _ { 1 } = \mathrm { n } _ { 2 } = 1203$