Step 1 :Define the null and alternative hypotheses as follows: \(H_{0}: p= 0.54\) versus \(H_{1}: p \neq 0.54\)
Step 2 :Given that in a recent survey, 282 out of 800 parents felt it was a serious problem. We can use this to calculate the sample proportion.
Step 3 :The test statistic for a hypothesis test for a proportion is calculated as follows: \(z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}\) where \(\hat{p}\) is the sample proportion, \(p_0\) is the proportion under the null hypothesis, and \(n\) is the sample size.
Step 4 :Substitute the given 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 :The P-value is then found by looking up the test statistic in the standard normal distribution. The P-value is approximately 0.000.
Step 6 :This is less than the significance level of 0.1, so we reject the null hypothesis. This means 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 different than it was twenty years ago.
Step 7 :Final Answer: The test statistic is \(\boxed{-10.64}\) and the P-value is \(\boxed{0.000}\).