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At the Ice Chalet, a randomly selected beginning skating class of 80 children has 64 girls and 16 boys, so p' = 0.80 for the proportion of girls. For a 92% confidence level, z(0.04) ≈ 1.751. What is the resulting confidence interval for the true proportion of girls?
A(0.7217, 0.8783)
B(0.6000, 1.0000)
C(0.8000, 0.8783)
D(0.2000, 0.8000)
Answer & Solution
Correct answer: A. (0.7217, 0.8783)
1. p' = 64/80 = 0.80 and q' = 1 - 0.80 = 0.20.
2. EBP = 1.751*sqrt((0.80)(0.20)/80) ≈ 1.751*0.04472 ≈ 0.0783.
3. Lower bound: 0.80 - 0.0783 ≈ 0.7217, and upper bound: 0.80 + 0.0783 ≈ 0.8783.
4. Option C only shifts p' upward instead of subtracting the error bound for the lower side.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.3 A Population Proportion_
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