Answer
Yes, there is significant evidence to conclude that the percentage of employed adults who feel basic mathematical skills are critical or very important to their job has increased.
Work Step by Step
$H_0:~p=0.56$ versus $H_1:~p\gt0.56$
$np_0(1-p_0)=480\times0.56(1-0.56)=118.272\gt10$
$p̂ =\frac{x}{n}=\frac{297}{480}=0.61875$
$z_0=\frac{p̂ -p_0}{\sqrt {\frac{p_0(1-p_0)}{n}}}=\frac{0.61875-0.56}{\sqrt {\frac{0.56(1-0.56)}{480}}}=2.59$
Using the classical method:
$z_α=z_{0.05}$
If the area of the standard normal curve to the right of $z_{0.05}$ is 0.05, then the area of the standard normal curve to the left of $z_{0.05}$ is $1−0.05=0.95$
According to Table V, there are 2 z-scores which give the closest value to 0.95: 1.64 and 1.65. So, let's find the mean of these z-scores: $\frac{1.64+1.65}{2}=1.645$
Since $z_0\gt z_α$, we reject the null hypothesis.
