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A poll of 1,200 voters finds 65% name the economy as the most significant election issue. For a 90% confidence level, z(0.05)=1.645. What is the resulting confidence interval?
A(0.5500, 0.7500)
B(0.6500, 0.6726)
C(0.3500, 0.6500)
D(0.6274, 0.6726)
Answer & Solution
Correct answer: D. (0.6274, 0.6726)
1. p' = 0.65, q' = 0.35, and n = 1,200.
2. EBP = 1.645*sqrt((0.65)(0.35)/1200) ≈ 1.645*0.01377 ≈ 0.02265.
3. Lower bound: 0.65 - 0.02265 ≈ 0.6274, and upper bound: 0.65 + 0.02265 ≈ 0.6726.
4. Option B only shifts p' upward, giving an incorrect lower bound.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.3 A Population Proportion_
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