Which of the following best describes the form of the sampling distribution of the sample proportion?
A) When standardized, it is exactly the standard normal distribution.
B) When standardized, it is the t distribution.
C) It is approximately normal as long as n 30.
D) It is approximately normal as long as np 5 and n(1 - p) 5.

Question

Which of the following best describes the form of the sampling distribution of the sample proportion?
A) When standardized, it is exactly the standard normal distribution. 
B) When standardized, it is the t distribution. 
C) It is approximately normal as long as n 30. 
D) It is approximately normal as long as np 5 and n(1 - p) 5.

Quizplus · Accepted Answer

The sampling distribution of the sample proportion is approximately normal when the sample size is large enough, but since we don't know the population standard deviation, we cannot use the standard normal distribution for it. Moreover, since we are dealing with proportions, the t distribution is not appropriate either. Therefore, the only valid option is to use the approximate normality condition based on the sample size and the sample proportion, which is given by np ≥ 5 and n(1-p) ≥ 5. Option D correctly captures this condition.

Which of the Following Best Describes the Form of the Sampling