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In A Poll Of 1000, 72 Are Against Bond Measures. What Is The Margin Of Error For The 95% Confidence Level(Z*=2.576)
Sample Answer
To calculate the margin of error for the 95% confidence level, we can use the formula:
Margin of Error = Z * (sqrt(p * (1 – p) / n))
Where:
Z* is the z-score corresponding to the desired confidence level (95% in this case), which is 2.576.
p is the proportion of respondents who are against the bond measures, which is 72/1000 = 0.072.
n is the sample size, which is 1000.
Plugging in the values:
Margin of Error = 2.576 * (sqrt(0.072 * (1 – 0.072) / 1000))
Calculating this expression:
Margin of Error = 2.576 * (sqrt(0.072 * 0.928 / 1000))
Margin of Error = 2.576 * (sqrt(0.067296 / 1000))
Margin of Error = 2.576 * (sqrt(0.000067296))
Margin of Error ≈ 2.576 * 0.008206
Margin of Error ≈ 0.0211
Therefore, the margin of error for the 95% confidence level is approximately 0.0211 or 2.11%.
