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A market research firm surveys 500 adult residents and finds 421 own cell phones, so p' = 0.842 and q' = 0.158. For a 95% confidence level, z(0.025) = 1.96 gives EBP ≈ 0.032. What is the resulting confidence interval for the true proportion?
A(0.700, 0.984)
B(0.842, 0.874)
C(0.158, 0.842)
D(0.810, 0.874)
Answer & Solution
Correct answer: D. (0.810, 0.874)
1. EBP = z*sqrt(p'q'/n) = 1.96*sqrt((0.842)(0.158)/500) ≈ 1.96*0.01631 ≈ 0.032.
2. Lower bound: 0.842 - 0.032 = 0.810.
3. Upper bound: 0.842 + 0.032 = 0.874.
4. Option B applies the error bound only above p', so its lower bound is wrong.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.3 A Population Proportion_
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