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 form of the sampling distribution of the sample proportion is approximately normal if both np and n(1-p) are at least 5. This is known as the "normal approximation to the binomial distribution". Therefore, option D is the best choice. Option A is incorrect as the sampling distribution is not exactly the standard normal distribution, but rather an approximation of it. Option B is incorrect as the t-distribution is used for small sample sizes and unknown population standard deviation, and is not directly related to the sampling distribution of the sample proportion. Option C is incorrect as it does not include the important condition of np and n(1-p) being at least 5.

Which of the Following Best Describes the Form of the Sampling