SAT Math Practice Question #1642 (Medium (630)) | Test Citadel
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SAT Math Difficulty: Medium (630)

Digital SAT Math Practice Question #1642

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A polling institute surveyed a random sample of 400 voters in a city and found a 95% confidence interval with a margin of error of 4.9%. If the institute wishes to cut the margin of error in half to approximately 2.45% while maintaining the same 95% confidence level, how many voters must be surveyed?
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Halve margin of error -> multiply sample size by 2^2 = 4. 400 * 4 = 1,600.

Masterclass Solution & Distractor Trap Analysis

Margin of error is inversely proportional to the square root of the sample size: \(ME \propto \frac{1}{\sqrt{n}}\). To halve the margin of error (divide by 2), the sample size must be multiplied by \(2^2 = 4\). \(400 \times 4 = 1,600\)....

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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