Confidence Interval for a Proportion (3 of 3)

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Summary of Computations

  1. Compute p
  2. Estimate σp by

  3. Find z for the level of confidence desired with a z table.

  4. Lower limit = p - (z) (Estimated σp) - 0.5/N

  5. Upper limit = p + (z) (Estimated σp) + 0.5/N

  6. Lower limit ≤ π ≤ Upper limit

Assumptions
  1. Observations are sampled randomly and independently.

  2. The adequacy of the normal approximation depends on the sample size (N) and π. Although there are no hard and fast rules, the following is a guide to needed sample size:

    If π is between 0.4 and 0.6 then an N of 10 is adequate. If π is as low as 0.2 or as high as 0.8 then N should be at least 25. For π as low as 0.1 or as high as 0.9, N should be at least 30.

    A more conservative rule of thumb that is often recommended is that Nπ and N(1 - π) should both be at least 10.

Click here for an interactive demonstration of the normal approximation to the binomial to explore the validity of these rules of thumb.


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