As a general rule, the normal distribution provides a good approximation to the sampling distribution of the sample proportion, , only if which of the following conditions holds?
A) The sample size, n, is greater than 30.
B) The population proportion, p, is greater than 0.50.
C) The underlying population has a small standard deviation and n is large.
D) np and n(1 - p) are both greater than 5.

Question

As a general rule, the normal distribution provides a good approximation to the sampling distribution of the sample proportion,  , only if which of the following conditions holds?
A) The sample size, n, is greater than 30. 
B) The population proportion, p, is greater than 0.50. 
C) The underlying population has a small standard deviation and n is large. 
D) np and n(1 - p) are both greater than 5.

Quizplus · Accepted Answer

The normal distribution approximation for the sampling distribution of the sample proportion holds only if np and n(1 - p) are both greater than 5, regardless of the sample size, population proportion or standard deviation of the population. This is known as the "success-failure" condition, where np and n(1 - p) represent the expected number of successes and failures in the sample, respectively. When these numbers are small, the distribution of the sample proportion becomes skewed and the normal approximation is no longer valid.

As a General Rule, the Normal Distribution Provides a Good