In a survey of 930 students in a school, 92% reported having pets at home. What is the margin of error? Use the formula ± 1/vn where n is the population
A. ±13.3%
B. ±30.5%
C. ±1.2%
D. ±15.8%
The Correct Answer and Explanation is :
To calculate the margin of error, we are using the formula:
[
\text{Margin of Error} = \pm \frac{1}{\sqrt{n}}
]
where n is the sample size or population. In this case, n = 930 students.
Step 1: Compute the square root of n.
[
\sqrt{930} \approx 30.5
]
Step 2: Now, apply the formula:
[
\text{Margin of Error} = \pm \frac{1}{30.5} \approx \pm 0.0328
]
Step 3: Convert this into a percentage by multiplying by 100:
[
\text{Margin of Error} = \pm 3.28\%
]
Given this result, none of the provided options exactly match ±3.28%. However, since the problem offers choices where rounding may play a role, let’s focus on the key aspects.
Analysis of Answer Choices:
- A. ±13.3% is too high, as our calculation shows the margin of error is much smaller.
- B. ±30.5% is irrelevant as the margin of error would never be this large for a sample size as high as 930.
- C. ±1.2% is too small and underestimates the true margin of error.
- D. ±15.8% is also much too high.
Therefore, while the closest match in magnitude is ±3.28%, none of the choices exactly reflect this. Given the formula and the population size, the calculation reveals that none of the provided answers (A through D) are accurate representations of the correct margin of error.