Answer
There is statistical evidence that the proportion of students that return for their second year is greater than 0.52.
Practically, the increase is not very significant. But, even a small increase is good thing. So, if it is not hard to implement the policies, it should be done.
Work Step by Step
$H_0:~p=0.52$ versus $H_1:~p\gt0.52$
$np_0(1-p_0)=2843\times0.52(1-0.52)=709.6128\gt10$
$p̂ =\frac{x}{n}=\frac{1516}{2843}=0.5332$
$z_0=\frac{p̂ -p_0}{\sqrt {\frac{p_0(1-p_0)}{n}}}=\frac{0.5332-0.52}{\sqrt {\frac{0.52(1-0.52)}{2843}}}=1.41$
Using the classical method:
$z_α=z_{0.1}$
If the area of the standard normal curve to the right of $z_{0.1}$ is 0.1, then the area of the standard normal curve to the left of $z_{0.1}$ is $1−0.1=0.9$
According to Table V, the z-score which gives the closest value to 0.9 is 1.28.
Since $z_0\gt z_α$, we reject the null hypothesis.
