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A quality-control specialist samples 12 servings of soda, finding x-bar = 13.30 and s = 1.55, so df = 11. For a 95% confidence level, t(0.025,11) ≈ 2.201. What is the resulting confidence interval for the true mean amount served?
A(11.30, 15.30)
B(13.30, 14.29)
C(10.85, 15.75)
D(12.32, 14.29)
Answer & Solution
Correct answer: D. (12.32, 14.29)
1. EBM = t(s/sqrt(n)) = (2.201)(1.55/sqrt(12)) ≈ (2.201)(0.4475) ≈ 0.985.
2. Lower bound: 13.30 - 0.985 ≈ 12.32.
3. Upper bound: 13.30 + 0.985 ≈ 14.29.
4. Option B only applies the error bound to the upper side of x-bar, leaving the lower bound unchanged, which does not match a two-sided interval.
_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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