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A camp director surveys 20 campers about letters sent home, finding x-bar = 7.9 with a known σ = 2.5. For a 90% confidence level, z(0.05) = 1.645. What is the resulting confidence interval for the population mean?
A(5.40, 10.40)
B(7.90, 8.82)
C(2.50, 7.90)
D(6.98, 8.82)
Answer & Solution
Correct answer: D. (6.98, 8.82)
1. EBM = z(σ/sqrt(n)) = (1.645)(2.5/sqrt(20)) ≈ (1.645)(0.559) ≈ 0.92.
2. Lower bound: 7.9 - 0.92 ≈ 6.98.
3. Upper bound: 7.9 + 0.92 ≈ 8.82.
4. Option B applies the error bound only above x-bar, which does not produce a correctly centered interval.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.1 A Single Population Mean using the Normal Distribution_
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