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 $n p_{0}\left(1-p_{0}\right)=\square \nabla 10$, the sample size is the requirements for testing the hypothesis satisfied (Round to one decimal place as needed.)

Step 1 ：We are given a problem where 20 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. We are asked to determine if parents feel differently today than they did twenty years ago using the \(\alpha=0.1\) level of significance.

Step 2 ：We start by stating our null hypothesis (\(H_0\)) and alternative hypothesis (\(H_1\)). The null hypothesis is that the proportion has not changed, i.e., the proportion is still 54%. The alternative hypothesis is that the proportion has changed, i.e., the proportion is not 54%.

Step 3 ：We are given that the sample size (n) is 800 and the number of successes (x) is 282. We are also given that the level of significance (\(\alpha\)) is 0.1. The hypothesized population proportion (\(p_0\)) is 0.54.

Step 4 ：We calculate the sample proportion (p) as \(\frac{x}{n} = \frac{282}{800} = 0.3525\).

Step 5 ：We calculate the test statistic (Z) using the formula: \(Z = \frac{p - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}\). Substituting the given values, we get \(Z = -10.64\).

Step 6 ：We calculate the p-value using the standard normal distribution. The p-value is approximately 0.0.

Step 7 ：If the null hypothesis were true (i.e., the proportion of parents who feel it is a serious problem that high school students are not being taught enough math and science is still 54%), the probability of observing a sample proportion as extreme as 0.3525 is essentially zero.

Step 8 ：Since the p-value is less than the level of significance (0.1), we reject the null hypothesis. This suggests that the proportion of parents who feel it is a serious problem that high school students are not being taught enough math and science has changed from 20 years ago.

Step 9 ：\(\boxed{\text{Final Answer: Yes, parents feel differently today than they did twenty years ago. The proportion of parents who feel it is a serious problem that high school students are not being taught enough math and science has significantly decreased from 54%.}}\)