a politician estimates that 61% of his constituents will vote for him in the coming election. how many…

Explanation:

Step1: Identify the formula for sample - size

The formula for sample size $n$ in estimating a proportion $p$ is $n=\frac{z^{2}\cdot p(1 - p)}{E^{2}}$, where $z$ is the z - score corresponding to the desired confidence level, $p$ is the estimated proportion, and $E$ is the margin of error.

Step2: Determine the values of $z$, $p$, and $E$

For a 95% confidence level, the z - score $z = 1.96$. The estimated proportion $p=0.61$, and the margin of error $E = 0.03$.

Step3: Calculate $p(1 - p)$

$p(1 - p)=0.61\times(1 - 0.61)=0.61\times0.39 = 0.2379$.

Step4: Calculate $n$

$n=\frac{(1.96)^{2}\times0.2379}{(0.03)^{2}}=\frac{3.8416\times0.2379}{0.0009}=\frac{0.91381664}{0.0009}\approx1015.35$. Since we cannot have a fraction of a sample, we round up to the next whole number.

Answer:

1,016