Twenty years ago, $54 \%$ of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 282 of 800 parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. Do parents feel differently today than they did twenty years ago? Use the $\alpha=0.1$ level of significance.
What are the null and alternative hypotheses?
\[
\mathrm{H}_{0}: p=\$ 0.54 \text { versus } \mathrm{H}_{1}: \mathrm{p} \quad \neq 0.54
\]
(Type integers or decimals. Do not round.)
Find the test statistic.
\[
z_{0}=-10.64 \text { (Round to two decimal places as needed.) }
\]
Find the P-value.
\[
\text { P-value }=\square \text { (Round to three decimal places as needed.) }
\]

Step 1 ：Define the null and alternative hypotheses as follows: \(H_{0}: p= 0.54\) versus \(H_{1}: p \neq 0.54\)

Step 2 ：Given that in a recent survey, 282 out of 800 parents felt it was a serious problem. We can use this to calculate the sample proportion.

Step 3 ：The test statistic for a hypothesis test for a proportion is calculated as follows: \(z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}\) where \(\hat{p}\) is the sample proportion, \(p_0\) is the proportion under the null hypothesis, and \(n\) is the sample size.

Step 4 ：Substitute the given values into the formula to get the test statistic: \(z = \frac{0.3525 - 0.54}{\sqrt{\frac{0.54(1-0.54)}{800}}} = -10.64\)

Step 5 ：The P-value is then found by looking up the test statistic in the standard normal distribution. The P-value is approximately 0.000.

Step 6 ：This is less than the significance level of 0.1, so we reject the null hypothesis. This means that the proportion of parents who feel it is a serious problem that high school students are not being taught enough math and science is different than it was twenty years ago.

Step 7 ：Final Answer: The test statistic is \(\boxed{-10.64}\) and the P-value is \(\boxed{0.000}\).