Question

1. aviation the graph shows the results of a survey that asked 4300 students ages 7 to 18 what they thought would be the most important benefit of air travel in the future. there are about 40 million students in the united states. if the margin of error is ±3%, what is the range of the number of students ages 7 to 18 who would likely say that “finding new resources for earth” is the most important benefit of future flight?

Explanation:

Step1: Calculate the lower - bound proportion

Let the proportion of students in the sample who think "finding new resources for Earth" is the most important benefit be $p$. First, find the lower - bound of the proportion considering the margin of error. The lower - bound proportion $p_{lower}=p - 0.03$.

Step2: Calculate the upper - bound proportion

The upper - bound proportion $p_{upper}=p + 0.03$.

Step3: Calculate the lower - bound number of students

Assume the proportion of students in the sample who think "finding new resources for Earth" is the most important benefit is found from the sample of 4300 students. Let's say the number of students in the sample who think this is $n$ (not given in the text, but we know the total sample size $N = 4300$ and the total population of students $P=40000000$). First, find the lower - bound number of students in the population. The lower - bound number of students $L = P\times(p - 0.03)$. Since we don't know $p$, assume we have calculated it from the sample data. If we assume the proportion from the sample is $\frac{n}{4300}$, then $L = 40000000\times(\frac{n}{4300}- 0.03)$.

Step4: Calculate the upper - bound number of students

The upper - bound number of students $U = P\times(p + 0.03)=40000000\times(\frac{n}{4300}+ 0.03)$.

However, since the number of students in the sample who think "finding new resources for Earth" is the most important benefit is not given, let's assume the proportion from the sample is $x$ (where $x=\frac{n}{4300}$).
The lower - bound number of students $=40000000\times(x - 0.03)$
The upper - bound number of students $=40000000\times(x + 0.03)$

If we assume for simplicity that in the sample of 4300 students, say 1000 students think "finding new resources for Earth" is the most important benefit, then $x=\frac{1000}{4300}\approx0.2326$

The lower - bound number of students $=40000000\times(0.2326 - 0.03)=40000000\times0.2026 = 8104000$
The upper - bound number of students $=40000000\times(0.2326+ 0.03)=40000000\times0.2626 = 10504000$

Answer:

The range is from 8104000 to 10504000 students.