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 n1p) ≥ 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 n1­p) ≥ 5.

Quizplus · Accepted Answer

The form of the sampling distribution of the sample proportion is approximately normal as long as np ≥ 5 and n(1­p) ≥ 5. This is known as the rule of thumb for the normal approximation to the binomial distribution. When these conditions are met, the distribution can be approximated by a normal distribution with mean µ = p and standard deviation σ = √(p(1-p)/n), also known as the standard error of the proportion. This allows for the use of normal distribution properties and formulas for inference and hypothesis testing.

Which of the Following Best Describes the Form of the Sampling