Questions: Twenty years ago, 55% 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 260 of 700 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 α=0.1 level of significance. Find the test statistic. z₀= (Round to two decimal places as needed.) Find the P-value. P-value = (Round to three decimal places as needed.) Determine the conclusion for this hypothesis test. Choose the correct answer.

Twenty years ago, 55% 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 260 of 700 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 α=0.1 level of significance.

Find the test statistic.
z₀= (Round to two decimal places as needed.)

Find the P-value.
P-value = (Round to three decimal places as needed.)

Determine the conclusion for this hypothesis test. Choose the correct answer.

Transcript text: Twenty years ago, $55 \%$ 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 260 of 700 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. Find the test statistic. $z_{0}=$ $\square$ (Round to two decimal places as needed.) Find the P -value. P -value $=$ $\square$ (Round to three decimal places as needed.) Determine the conclusion for this hypothesis test. Choose the correct answer.

Solution

Solution Steps

Step 1: State the Hypotheses

We are testing whether parents feel differently today about the education of high school students in math and science compared to twenty years ago. The hypotheses are defined as follows:

Null Hypothesis ($H_0$): $p = 0.55$ (The proportion of parents who feel it is a serious problem is the same as twenty years ago.)
Alternative Hypothesis ($H_a$): $p \neq 0.55$ (The proportion of parents who feel it is a serious problem is different from twenty years ago.)

Step 2: Calculate the Test Statistic

The test statistic for a proportion is calculated using the formula:

\[ Z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}} \]

Where:

$\hat{p} = \frac{260}{700} \approx 0.3714$ (Sample proportion)
$p_0 = 0.55$ (Hypothesized population proportion)
$n = 700$ (Sample size)

Substituting the values:

\[ Z = \frac{0.3714 - 0.55}{\sqrt{\frac{0.55(1 - 0.55)}{700}}} \approx -9.4967 \]

Thus, the test statistic is:

\[ Z \approx -9.50 \]

Step 3: Calculate the P-value

The P-value associated with the test statistic $Z = -9.50$ is calculated. Given the extreme value of the test statistic, the P-value is:

\[ \text{P-value} = 0.000 \]

Step 4: Make a Decision

We compare the P-value to the significance level $\alpha = 0.1$:

Since $0.000 \leq 0.1$, we reject the null hypothesis.

Step 5: Conclusion

There is sufficient evidence to conclude that parents feel differently today about the education of high school students in math and science compared to twenty years ago.