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.
Because $n p_{0}\left(1-p_{0}\right)=\square \square 10$, the sample size is less than $5 \%$ of the population size, and the sample the requirements for testing the hypothesis are not satisfied. (Round to one decimal place as needed.)

Step 1 ：Given that the sample size is 800 parents, of which 282 feel it is a serious problem that high school students are not being taught enough math and science. The hypothesized proportion from twenty years ago is 54% and the significance level is 0.1.

Step 2 ：First, calculate the sample proportion, which is \(\hat{p} = \frac{x}{n} = \frac{282}{800} = 0.3525\).

Step 3 ：Next, calculate the test statistic using the formula \(Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}\). Substituting the given values, we get \(Z = \frac{0.3525 - 0.54}{\sqrt{\frac{0.54(1 - 0.54)}{800}}} = -10.64\).

Step 4 ：Then, find the critical value for a two-tailed test with significance level 0.1, which is approximately 1.645.

Step 5 ：Since the test statistic is less than the critical value, we reject the null hypothesis.

Step 6 ：\(\boxed{\text{Final Answer: Yes, parents feel differently today than they did twenty years ago. The proportion of parents who feel it is a serious problem that high school students are not being taught enough math and science is significantly different from 54%.}}\)