A controversial bill is being debated in the state legislature. Representative Williams wants to estimate within 2percentage points and with 95% confidence the difference in the proportion of her male and femaleconstituents who favor the bill. What sample size should she obtain?
A) $n _ { 1 } = n _ { 2 } = 4802$
B) $\mathrm { n } _ { 1 } = \mathrm { n } _ { 2 } = 3383$
C) $\mathrm { n } _ { 1 } = \mathrm { n } _ { 2 } = 97$
D) $n _ { 1 } = n _ { 2 } = 2401$ 11.2 Inference about Two Means: Dependent Samples1 Test hypotheses regarding matched-pairs data.

Question

A controversial bill is being debated in the state legislature. Representative Williams wants to estimate within 2percentage points and with 95% confidence the difference in the proportion of her male and femaleconstituents who favor the bill. What sample size should she obtain? 
A) $n _ { 1 } = n _ { 2 } = 4802$
B) $\mathrm { n } _ { 1 } = \mathrm { n } _ { 2 } = 3383$
C) $\mathrm { n } _ { 1 } = \mathrm { n } _ { 2 } = 97$
D) $n _ { 1 } = n _ { 2 } = 2401$ 11.2 Inference about Two Means: Dependent Samples1 Test hypotheses regarding matched-pairs data.

Quizplus · Accepted Answer

To estimate the sample size needed for a proportion with a specific margin of error (E) and confidence level (typically 95% confidence level corresponds to a Z-score of 1.96), the formula is $n = \left( \frac{Z^2 \cdot p \cdot (1-p)}{E^2} \right)$, where $p$ is the estimated proportion (if unknown, 0.5 is used for maximum sample size), and $E$ is the margin of error. Without specific proportions given, assuming $p = 0.5$ for maximum variability, and $E = 0.02$ for a 2 percentage point margin, the calculation for each group (male and female) would be $n = \left( \frac{1.96^2 \cdot 0.5 \cdot (1-0.5)}{0.02^2} \right) = 2401$. However, since the question specifies the difference in proportions, we consider the formula for the difference in two proportions, which effectively doubles the sample size requirement, leading to $n_1 = n_2 = 4802$, making option A correct.

A Controversial Bill Is Being Debated in the State Legislature n1=n2=4802n _ { 1 } = n _ { 2 } = 4802n1​=n2​=4802

A Controversial Bill Is Being Debated in the State Legislature $n _ { 1 } = n _ { 2 } = 4802$