Z-test for a proportion: p̂ = 0.58, n = 200
Test a sample proportion against p₀ = 0.5 with a two-tailed z-test.
Solution
- Given p̂ = 0.58, n = 200, p₀ = 0.5, α = 0.05
- Standard error SE = √(p₀(1 − p₀)/n) = √(0.5·0.5/200) = 0.0353553
- Test statistic z = (p̂ − p₀)/SE = 2.26274
- Critical value Two-tailed critical z at α/2 = 0.025: ±1.95996
- p-value 0.0236515
- Conclusion p < α — reject H₀: p = 0.5 at α = 0.05.
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