Question

In 1994 52% of parents with children in high school felt that it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 256 of 800 parents with children in high school felt the same way. Do parents feel differently than they did in 1994? Use the α = 0.05 level of significance.

Answer 1

To determine if parents feel differently than they did in 1994, a hypothesis test for proportions can be conducted. With a sample of 256 out of 800 parents expressing concern about the lack of math and science education, the observed proportion is 0.32. Using a significance level
`(\( \alpha \)) of 0.05`, a hypothesis test was performed. The p-value was found to be less than 0.05, suggesting that there is significant evidence to conclude that the proportion of parents concerned has changed since 1994.

Step-by-step explanation:

The null hypothesis
`(\(H_0\))` assumes that there is no change, stating that the proportion of parents concerned is still 52%, as in 1994. The alternative hypothesis
`(\(H_1\))` posits that there is a change. A z-test for proportions was applied, using the formula
`\(z = \frac{\hat{p} - p_0}{\sqrt{(p_0(1-p_0))/(n)}}\), where \(\hat{p}\)` is the observed proportion,
`\(p_0\)` is the assumed proportion under the null hypothesis, and \(n\) is the sample size.

In this case,
`\(H_0: p = 0.52\)` (the proportion is the same as in 1994) and \
`(H_1: p \\eq 0.52\)` (the proportion has changed). The calculated z-value was then compared to critical values or used to find the p-value. If the p-value is less than the significance level
`(\( \alpha \))`, the null hypothesis is rejected, indicating that parents' feelings have changed since 1994.

In summary, the statistical analysis provides evidence to suggest a significant change in parents' concerns about the insufficient teaching of math and science in high schools compared to 1994.