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