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Tests for the Difference of Two Proportions

AP Statistics· difficulty 3/5

Sample 1: 60 of 150 successes. Sample 2: 70 of 200 successes. Test H₀: p₁ = p₂.

Pooled p̂ = (60+70)/(150+200) = 130/350 ≈ 0.371 SE = sqrt(p̂(1−p̂)(1/n₁+1/n₂)) z = (p̂₁ − p̂₂)/SE

What is the pooled proportion p̂?

  • A

    0.371

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  • B

    0.375

  • C

    0.400

  • D

    0.350

Explanation

Pooled p̂ = (x₁ + x₂)/(n₁ + n₂) = 130/350 ≈ 0.371.

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