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. can be reasonably assumed to be random, the requirements for testing the hypothesis are satisfied. (Round to one decimal place as needed.) What are the null and alternative hypotheses? $\mathrm{H}_{0}: \mathrm{p}=0.54$ versus $\mathrm{H}_{1}: \mathrm{p} \neq 0.54$ (Type integers or decimals. Do not round.) Find the test statistic. $z_{0}=\square$ (Round to two decimal places as needed.)

Step 1 ：The null hypothesis is 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 the same as it was twenty years ago (54%). The alternative hypothesis is that the proportion has changed. So, \(H_{0}: p=0.54\) versus \(H_{1}: p \neq 0.54\)

Step 2 ：To find the test statistic, we will use the formula for the z-score of a proportion: \[z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}\] where \(\hat{p}\) is the sample proportion, \(p_0\) is the hypothesized population proportion, and \(n\) is the sample size.

Step 3 ：In this case, \(\hat{p} = \frac{282}{800} = 0.3525\), \(p_0 = 0.54\), and \(n = 800\).

Step 4 ：Substitute these 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 ：Final Answer: The test statistic is \(z_{0} = \boxed{-10.64}\)