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A survey of 200 households finds that in 120 of them, the woman makes the majority of purchasing decisions, so p' = 0.60 and q' = 0.40. For a 95% confidence level, z(0.025)=1.96. What is the resulting confidence interval?
A(0.4000, 0.8000)
B(0.6000, 0.6679)
C(0.5321, 0.6679)
D(0.3200, 0.6000)
Answer & Solution
Correct answer: C. (0.5321, 0.6679)
1. EBP = 1.96*sqrt((0.60)(0.40)/200) ≈ 1.96*0.03464 ≈ 0.0679.
2. Lower bound: 0.60 - 0.0679 ≈ 0.5321.
3. Upper bound: 0.60 + 0.0679 ≈ 0.6679.
4. Option B only shifts p' upward instead of subtracting the error bound to get the correct lower bound.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.3 A Population Proportion_
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