Home › AP Statistics › Statistics › Confidence Intervals › Continuing the exam-score example, σ = 3, n = 36…
Continuing the exam-score example, σ = 3, n = 36, x-bar = 68, and z(0.05) = 1.645 for a 90% confidence level. What is the resulting confidence interval?
A(67.18, 68.82)
B(65.00, 71.00)
C(68.00, 71.65)
D(64.36, 71.65)
Answer & Solution
Correct answer: A. (67.18, 68.82)
1. Compute EBM = z(σ/sqrt(n)) = (1.645)(3/sqrt(36)) = (1.645)(0.5) = 0.8225.
2. Lower bound: 68 - 0.8225 = 67.1775, which rounds to 67.18.
3. Upper bound: 68 + 0.8225 = 68.8225, which rounds to 68.82.
4. Option D doubles the error bound by mistake, giving a needlessly wide interval.
_Source: OpenStax Introductory Statistics (CC BY 4.0), Ch 8 "Confidence Intervals", section 8.1 A Single Population Mean using the Normal Distribution_
Related questions
A campus survey wants to estimate, with 95% confidence and a margin of error no greater thIn a Zogby poll of 48 respondents, nine rated a terrorist attack in their community as likOf 511 southern California homes surveyed for earthquake preparedness, 338 did NOT meet miContinuing the Field Poll example, p' = 0.79 from 400 of 506 surveyed. For a 90% confidencA Field Poll finds that 400 out of 506 surveyed California adults, about 79%, feel educatiAt the Ice Chalet, a randomly selected beginning skating class of 80 children has 64 girlsA poll of 1,200 voters finds 65% name the economy as the most significant election issue. A survey of 200 households finds that in 120 of them, the woman makes the majority of purc