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You are told only that a confidence interval is (67.18, 68.82), with no sample mean given. Using the shortcut for working backwards, what are the sample mean and the error bound?
Ax-bar = 68.00, EBM = 0.82
Bx-bar = 67.18, EBM = 1.64
Cx-bar = 68.82, EBM = 0.00
Dx-bar = 68.00, EBM = 1.64
Answer & Solution
Correct answer: A. x-bar = 68.00, EBM = 0.82
1. Without the sample mean, average the two bounds: (67.18 + 68.82)/2 = 68.00.
2. Find the error bound as half the width: (68.82 - 67.18)/2 = 1.64/2 = 0.82.
3. So x-bar = 68.00 and EBM = 0.82, matching the values used to build this same interval earlier.
4. Option D doubles the error bound by using the full width instead of half of it.
_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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