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Twenty years ago, $56 \%$ 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 308 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 $\alpha=0.05$ level of significance.
(Type integers or decimals. Do not round)
Find the test statistic
$\mathrm{z}_{0}=-9.97$ (Round to two decimal places as needed)
Find the P-value
P-value $=0.000$ (Round to three decimal places as needed)
Determine the conclusion for this hypothesis test Choose the correct answer below.
A. Since P-value $< \alpha$, reject the null hypothesis and conclude that there is sufficient evidence that parents feel differently today
B. Since P-value $> \alpha$, reject the null hypothesis and conclude that there is not sufficient evidence that parents feel differently today
C. Since P-value $> \alpha$, do not reject the null hypothesis and conclude that there is not sufficient evidence that parents feel differently today
D. Since P-value $< \alpha$, do not reject the null hypothesis and conclude that there is sufficient evidence that parents feel differently today
Answer
\(\boxed{\text{A. Since P-value < alpha, reject the null hypothesis and conclude that there is sufficient evidence that parents feel differently today}}\)
Step 1 ：Define the null hypothesis as the proportion of parents who feel it is a serious problem is the same as it was twenty years ago (56%), and the alternative hypothesis as the proportion is different.
Step 2 ：In a recent survey, 308 out of 800 parents felt it was a serious problem.
Step 3 ：The test statistic is given as \(z_{0} = -9.97\).
Step 4 ：The P-value is given as 0.000.
Step 5 ：Compare the P-value with the significance level (0.05).
Step 6 ：Since the P-value is less than the significance level, reject the null hypothesis.
Step 7 ：This suggests that there is sufficient evidence that parents feel differently today about the teaching of math and science in high school compared to twenty years ago.
Step 8 ：\(\boxed{\text{A. Since P-value < alpha, reject the null hypothesis and conclude that there is sufficient evidence that parents feel differently today}}\)
