Tests for the Difference of Two Proportions

AP Statistics· difficulty 3/5

Treatment group: 30 successes in 100. Control group: 20 successes in 100. Test H₀: p₁ = p₂ vs Hₐ: p₁ > p₂.

p̂₁ = 0.30, p̂₂ = 0.20 Pooled p̂ = 0.25 SE = sqrt(0.25·0.75·(1/100+1/100)) ≈ 0.0612

What is the test statistic z?

  • A

    1.96

  • B

    1.00

  • C

    1.63

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  • D

    2.31

Explanation

z = (0.30 − 0.20)/0.0612 ≈ 1.63.

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