Answer:
a. 28.47% ± 4.37%
Step-by-step explanation:
The sample proportion is ...
p = 121/425 ≈ 0.2847 = 28.47%
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The margin of error depends on the desired level of confidence. For a level of confidence of about 95%, the margin of error is about ...
±2 × √((p(1 -p)/(sample size)) = ±2×√(.2847·.7153/425) ≈ ±0.0438 = ±4.38%
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Comment on the last decimal place
The multiplier shown as 2 in the formula above corresponds to a confidence level of about 95.45%. The multiplier for 95% is 1.95996, and that gives a margin of error of ±4.29%. The multiplier that causes the margin of error value to round to 4.37% will be between 1.96 and 2, and will have a corresponding confidence level between 95% and 95.5%.
We don't know the confidence level or multiplier you are expected to use for this problem. The multiplier is almost certainly greater than 1, which corresponds to a confidence level of about 68%. Hence the appropriate answer choice will be somewhat larger than ±2.19%. A confidence level of 95% is pretty typical.
