Twenty years ago, $48 \%$ 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 307 of 900 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 $n p_{0}\left(1-p_{0}\right)=224.6> 10$, the sample size is less than $\quad \hat{\top} 5 \%$ of the population size, and the sample (can be reasonably assumed to be random, $\hat{\sim}$ the requirements for testing the hypothesis (are satisfied.
(Round to one decimal place as needed.)
What are the null and alternative hypotheses?
$\mathrm{H}_{0}: p=.48$ versus $\mathrm{H}_{1}: p \neq .48$
(Type integers or decimals. Do not round.)
Find the test statistic.
\[
z_{0}=\square \text { (Round to two decimal places as needed.) }
\]

Step 1 ：Define the null and alternative hypotheses. 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 (0.48), and the alternative hypothesis is that the proportion has changed. So, \(H_{0}: p=0.48\) versus \(H_{1}: p \neq 0.48\).

Step 2 ：Calculate the sample proportion, \(\hat{p}\), which is the number of successes (parents who feel it is a serious problem) divided by the sample size. In this case, \(\hat{p} = \frac{307}{900} = 0.3411\).

Step 3 ：Calculate the test statistic using the formula: \(z = \frac{\hat{p} - p_{0}}{\sqrt{\frac{p_{0}(1-p_{0})}{n}}}\), where \(p_{0}\) is the hypothesized population proportion and \(n\) is the sample size. In this case, \(p_{0} = 0.48\) and \(n = 900\).

Step 4 ：Substitute the values into the formula to get the test statistic: \(z = \frac{0.3411 - 0.48}{\sqrt{\frac{0.48(1-0.48)}{900}}} = -8.34\).

Step 5 ：The test statistic is approximately -8.34. This value is quite far from 0, which suggests that the observed 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 the hypothesized proportion of 0.48.

Step 6 ：Final Answer: The test statistic is \(\boxed{-8.34}\).