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Six of 25 surveyed statistics students report smoking in the past week. Using the plus-four method, the working values become x=8 and n=29, giving p'=0.276 and q'=0.724. For a 95% confidence level, z(0.025)=1.96 gives EBP ≈ 0.163. What is the resulting confidence interval?
A(0.000, 0.276)
B(0.276, 0.439)
C(0.050, 0.500)
D(0.113, 0.439)
Answer & Solution
Correct answer: D. (0.113, 0.439)
1. Using the plus-four sample, EBP = 1.96*sqrt((0.276)(0.724)/29) ≈ 0.163.
2. Lower bound: 0.276 - 0.163 = 0.113.
3. Upper bound: 0.276 + 0.163 = 0.439.
4. Option B applies the error bound only above p', so its lower bound is incorrect.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.3 A Population Proportion_
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