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For a sample of 40 House candidates, x-bar = $568,873 with a known σ = $909,200 to the nearest hundred. At 95% confidence, z(0.025) = 1.96 gives EBM ≈ $281,764. What is the resulting confidence interval?
A($568,873, $850,637)
B($287,109, $850,637)
C($287,109, $568,873)
D($0, $909,200)
Answer & Solution
Correct answer: B. ($287,109, $850,637)
1. Subtract the error bound from x-bar for the lower bound: 568,873 - 281,764 = 287,109.
2. Add the error bound to x-bar for the upper bound: 568,873 + 281,764 = 850,637.
3. The 95% confidence interval for mean individual contributions is ($287,109, $850,637).
4. Options A and C each apply the error bound to only one side of x-bar, so the interval is not centered correctly.
_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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