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A political science student surveys 500 students and finds 300 are registered voters, so p' = 0.600 and q' = 0.400. For a 90% confidence level, z(0.05) = 1.645 gives EBP ≈ 0.036. What is the resulting confidence interval?
A(0.564, 0.636)
B(0.450, 0.750)
C(0.600, 0.636)
D(0.400, 0.600)
Answer & Solution
Correct answer: A. (0.564, 0.636)
1. EBP = z*sqrt(p'q'/n) = 1.645*sqrt((0.60)(0.40)/500) ≈ 1.645*0.0219 ≈ 0.036.
2. Lower bound: 0.600 - 0.036 = 0.564.
3. Upper bound: 0.600 + 0.036 = 0.636.
4. Option C only shifts p' upward, so it does not build a properly centered two-sided interval.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.3 A Population Proportion_
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