Subject:  Statistics

Z-test for a proportion: p̂ = 0.58, n = 200

Test a sample proportion against p₀ = 0.5 with a two-tailed z-test.

Answer z = 2.26274, p = 0.0236515, reject H₀

Solution

  1. Given p̂ = 0.58, n = 200, p₀ = 0.5, α = 0.05
  2. Standard error SE = √(p₀(1 − p₀)/n) = √(0.5·0.5/200) = 0.0353553
  3. Test statistic z = (p̂ − p₀)/SE = 2.26274
  4. Critical value Two-tailed critical z at α/2 = 0.025: ±1.95996
  5. p-value 0.0236515
  6. Conclusion p < α — reject H₀: p = 0.5 at α = 0.05.

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