Asked by cool boy
A survey was taken of 850 people in a neighborhood, and the results were that 230 people were planning on voting for a particular candidate. Determine the margin of error for a 99% confidence interval of population proportion of people in a neighborhood who were planning on voting for this candidate. Round it to the nearest hundredth and interpret its meaning in context.(2 points)
The margin of error=
. With 99% confidence, the population proportion of people in a neighborhood who are planning on voting for a particular candidate falls between
and
.
The margin of error=
. With 99% confidence, the population proportion of people in a neighborhood who are planning on voting for a particular candidate falls between
and
.
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Answered by
GPT-5 mini
p̂ = 230/850 = 0.27059. z* (99%) ≈ 2.576.
SE = sqrt[p̂(1−p̂)/n] = sqrt[(0.27059)(0.72941)/850] ≈ 0.01524.
Margin of error = z*·SE ≈ 2.576·0.01524 ≈ 0.0393 ≈ 0.04.
With 99% confidence, the population proportion falls between 0.27059 ± 0.04, i.e. about 0.23 and 0.31.
Interpretation: We are 99% confident that between 23% and 31% of neighborhood residents plan to vote for this candidate (margin of error ≈ ±4 percentage points).
SE = sqrt[p̂(1−p̂)/n] = sqrt[(0.27059)(0.72941)/850] ≈ 0.01524.
Margin of error = z*·SE ≈ 2.576·0.01524 ≈ 0.0393 ≈ 0.04.
With 99% confidence, the population proportion falls between 0.27059 ± 0.04, i.e. about 0.23 and 0.31.
Interpretation: We are 99% confident that between 23% and 31% of neighborhood residents plan to vote for this candidate (margin of error ≈ ±4 percentage points).
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