A sample of 25 observations is taken to estimate a population proportion π.The sampling distribution of sample proportion p is
A)not normal since n

Question

A sample of 25 observations is taken to estimate a population proportion π.The sampling distribution of sample proportion p is
A)not normal since n < 30.
B)approximately normal because p is always normally distributed.
C)approximately normal if nπ ≥ 5 and n(1-π)≥ 5.
D)approximately normal if π approaches 0.50.

Quizplus · Accepted Answer

The sampling distribution of sample proportion p is approximately normal if both conditions are met: nπ ≥ 5 and n(1-π)≥ 5. This means that we need at least 5 successes and 5 failures in our sample. It has nothing to do with the value of π or the sample size being less than 30. Hence, option A is incorrect. Option B is also incorrect as p is not always normally distributed. Option D is also incorrect because the normal approximation only works well when π is not too extreme (close to 0.50 is not a requirement).

A Sample of 25 Observations Is Taken to Estimate a Population