Answer
$α=0.01$
$z_0\lt z_α$: null hypothesis is not rejected.
There is not enough evidence to conclude that a majority of the district favors the tax increase.
Work Step by Step
Let's recommend the congresswoman to use $α=0.01$ level of significance.
$H_0:~p=0.5$ versus $H_1:~p\gt0.5$
Requirement:
$np_0(1−p_0)=8250\times0.5(1-0.5)=2062.5\gt10$
$p̂ =\frac{x}{n}=\frac{4205}{8250}=0.510$
$z_0=\frac{p̂ -p_0}{\sqrt {\frac{p_0(1-p_0)}{n}}}=\frac{0.510-0.5}{\sqrt {\frac{0.5(1-0.5)}{8250}}}=1.82$
Using the Classical Method:
$z_α=z_{0.01}$
If the area of the standard normal curve to the right of $z_{0.01}$ is 0.01, then the area of the standard normal curve to the left of $z_{0.01}$ is $1−0.01=0.99$
According to Table V, the z-score which gives the closest value to 0.99 is 2.33.
Since $z_0\lt z_α$, we do not reject the null hypothesis.
