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A study of 20 newborns' cord blood finds x-bar = 127.45 targeted chemicals with s = 25.965, df = 19. For a 90% confidence level, t(0.05,19) = 1.729. What is the resulting confidence interval?
A(117.41, 137.49)
B(101.49, 153.41)
C(127.45, 137.49)
D(90.00, 165.00)
Answer & Solution
Correct answer: A. (117.41, 137.49)
1. EBM = t(s/sqrt(n)) = (1.729)(25.965/sqrt(20)) ≈ (1.729)(5.807) ≈ 10.04.
2. Lower bound: 127.45 - 10.04 ≈ 117.41.
3. Upper bound: 127.45 + 10.04 ≈ 137.49.
4. Option C only applies the error bound above x-bar, so the interval it produces is not correctly centered.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.2 A Single Population Mean using the Student t Distribution_
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