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- Compute p

- Estimate σ
_{p}by

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

- Lower limit = p - (z) (Estimated σ
_{p}) - 0.5/N

- Upper limit = p + (z) (Estimated σ
_{p}) + 0.5/N

- Lower limit ≤ π ≤ Upper limit

Assumptions

- Observations are sampled randomly and independently.

- 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.

Next section: Difference between proportions