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Subject:  Statistics

95% confidence interval — x̄ = 50, s = 8, n = 40

Build a 95% confidence interval around a sample mean.

Answer 95% CI = (47.5208, 52.4792)

Solution

  1. Given x̄ = 50, s = 8, n = 40, level = 95%
  2. Critical value z* = 1.96
  3. Standard error SE = s / √n = 8 / √40 = 1.26491
  4. Margin of error E = z*·SE = 1.96·1.26491 = 2.47923
  5. Interval x̄ ± E = (47.5208, 52.4792)

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