Justifying a Claim Based on a Confidence Interval for a Population Proportion

AP Statistics· difficulty 3/5

A 95% CI for p is (0.45, 0.55). Test H₀: p = 0.50 vs Hₐ: p ≠ 0.50.

0.45 0.50 0.55

Using α = 0.05, what is the conclusion?

  • A

    Reject H₀ since 0.50 is in the CI.

  • B

    Fail to reject H₀ since 0.50 is in the CI.

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  • C

    Cannot tell without the test statistic.

  • D

    Reject H₀ since the CI doesn't include 0.

Explanation

Since 0.50 lies in the 95% CI, the value is plausible; fail to reject H₀ at α = 0.05.

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