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A tranquilizer's effect on nine patients gives x-bar = 2.51 hours and s = 0.318 hours, so df = 8. For a 95% confidence level, t(0.025,8) ≈ 2.306. What is the resulting confidence interval for the population mean effective time?
A(1.87, 3.15)
B(2.27, 2.76)
C(2.51, 2.76)
D(2.19, 2.83)
Answer & Solution
Correct answer: B. (2.27, 2.76)
1. EBM = t(s/sqrt(n)) = (2.306)(0.318/sqrt(9)) ≈ (2.306)(0.106) ≈ 0.244.
2. Lower bound: 2.51 - 0.244 ≈ 2.27.
3. Upper bound: 2.51 + 0.244 ≈ 2.75, which rounds to 2.76.
4. Option C applies the error bound only above x-bar instead of on both sides of it.
_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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