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An accounting firm surveys 100 people and finds a sample mean tax-form time of 23.6 hours, with a known σ = 7.0 hours. For a 95% confidence level, z(0.025) = 1.96. What is the resulting confidence interval?
A(16.60, 30.60)
B(23.60, 24.97)
C(22.23, 24.97)
D(20.00, 27.00)
Answer & Solution
Correct answer: C. (22.23, 24.97)
1. EBM = z(σ/sqrt(n)) = (1.96)(7.0/sqrt(100)) = (1.96)(0.7) ≈ 1.372.
2. Lower bound: 23.6 - 1.372 ≈ 22.23.
3. Upper bound: 23.6 + 1.372 ≈ 24.97 hours.
4. Option B only applies the error bound to the upper side of x-bar, leaving the lower bound unchanged, which is not a valid two-sided 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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