Constructing a Confidence Interval for a Population Proportion

AP Statistics· difficulty 2/5

A researcher wants to construct a one-sample z-interval for a proportion.

Conditions 1. Random 2. np̂ ≥ 10, n(1−p̂) ≥ 10 3. n ≤ 10% of population

For the Large Counts condition with n=50 and p̂=0.10, is the condition satisfied?

  • A

    No: n is less than 100.

  • B

    Yes: n exceeds 30.

  • C

    No: np̂ = 5, less than 10.

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  • D

    Yes: both np̂ and n(1−p̂) exceed 10.

Explanation

np̂ = 50·0.10 = 5 < 10. Large Counts condition fails.

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