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For the acupuncture study, n = 15, x-bar = 8.2267, s = 1.6722, df = 14, and a 95% confidence level gives t(0.025,14) = 2.14. What is the resulting confidence interval?
A(6.30, 10.15)
B(8.20, 9.15)
C(5.55, 10.90)
D(7.30, 9.15)
Answer & Solution
Correct answer: D. (7.30, 9.15)
1. EBM = t(s/sqrt(n)) = (2.14)(1.6722/sqrt(15)) ≈ (2.14)(0.4318) ≈ 0.924.
2. Lower bound: 8.2267 - 0.924 ≈ 7.30.
3. Upper bound: 8.2267 + 0.924 ≈ 9.15.
4. Option B applies the error bound to only the upper side of x-bar, so it is not a valid 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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