What can we conclude?

Answer: Convincing evidence pA pB (since 0 is not in the CI). Both endpoints positive and 0 excluded, so we have evidence pA pB.

What does the interval suggest about the difference in proportions?

Answer: Since 0 is in the interval, no convincing evidence of a difference. A two-sample CI for the difference that contains 0 means we cannot conclude the proportions differ.

AP Statistics · Topic 6.9

Justifying a Claim About the Difference of Two Proportions Practice

Part of Inference for Categorical Data: Proportions.(UNC-4.D)

Practice questions

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Sample questions

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Sample 1difficulty 3/5
$A 95% CI for p_A - p_B is (0.05, 0.20).$
$What can we conclude?$
- A
  $p_A and p_B differ by exactly 0.125.$
- B
  $No difference between groups.$
- C
  $Convincing evidence p_A < p_B.$
- D
  $Convincing evidence p_A > p_B (since 0 is not in the CI).$
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Why
$Both endpoints positive and 0 excluded, so we have evidence p_A > p_B.$
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Sample 2difficulty 3/5
$A 95% CI for p_A - p_B is (-0.02, 0.10).$
$What does the interval suggest about the difference in proportions?$
- A
  $There is convincing evidence p_A < p_B.$
- B
  $The proportions must be equal.$
- C
  $Since 0 is in the interval, no convincing evidence of a difference.$
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- D
  $There is convincing evidence p_A > p_B.$
Why
$A two-sample CI for the difference that contains 0 means we cannot conclude the proportions differ.$
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