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Young adult male heights have a known standard deviation of 2.5 inches. A researcher wants the sample mean height accurate to within one inch at 93% confidence, so z(0.035) ≈ 1.812. Using n = z^2*σ^2/EBM^2, how many male students must be measured?
A5 students
B217 students
C21 students
D93 students
Answer & Solution
Correct answer: C. 21 students
1. Apply n = z^2*σ^2/EBM^2 with z ≈ 1.812, σ = 2.5, and EBM = 1.
2. n = (1.812)^2 (2.5)^2 / (1)^2 ≈ (3.283)(6.25) ≈ 20.52.
3. Round up to the next whole student, giving n = 21.
4. Option B reuses the sample size from the earlier Foothill College example, which used a different σ and EBM, so it does not apply here.
_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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