In a survey of 930 students in a school, $92 \%$ reported having pets at home. What is the margin of error? Use the formula $\frac{ \pm \frac{1}{\sqrt{n}}}{}$ where n is the population.
Answer (2)
Substitute the given value of n = 930 into the margin of error formula: ± n 1 .
Calculate the square root of 930: 930 ≈ 30.4959 .
Divide 1 by the square root of 930: 30.4959 1 ≈ 0.03279 .
State the margin of error: ± 0.03279 .
Explanation
Understand the problem and provided data We are given a survey of 930 students, and we want to find the margin of error using the formula ± n 1 , where n is the number of students surveyed.
Substitute the value of n into the formula We are given that n = 930 . We will substitute this value into the formula.
Calculate the square root of n The margin of error is calculated as follows: ± 930 1 We need to find the square root of 930.
Calculate the margin of error The square root of 930 is approximately 30.4959. Now we divide 1 by this value: 30.4959 1 ≈ 0.03279 So, the margin of error is approximately ± 0.03279 .
State the final answer Therefore, the margin of error is ± 0.03279 .
Examples
In political polling, the margin of error indicates how much the results of a survey might differ from the true population value. For example, if a poll finds that 52% of voters support a candidate with a margin of error of ± 3% , the true support level could realistically be anywhere between 49% and 55%. This helps to understand the reliability of the survey results and make informed decisions based on the data.
The margin of error for the survey of 930 students is approximately ± 0.03279 . This reflects the amount that survey results might vary from the true percentage of students who have pets. It indicates a variation of about 3.279%.
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