Which of the following statements is true about the sampling distribution of the sample proportion ?
A) The mean of the sampling distribution will equal the population proportion p.
B) An increase in the sample size n will result in a decrease in the standard error of .
C) The sampling distribution will be approximately normal, provided that np ≥ 5 and n(1-p) ≥ 5.
D) All of the above are true.

Question

Which of the following statements is true about the sampling distribution of the sample proportion  ?
A) The mean of the sampling distribution will equal the population proportion p. 
B) An increase in the sample size n will result in a decrease in the standard error of . 
C) The sampling distribution will be approximately normal, provided that np ≥ 5 and n(1-p) ≥ 5. 
D) All of the above are true.

Quizplus · Accepted Answer

A) The mean of the sampling distribution of the sample proportion will equal the population proportion p, regardless of the sample size. This is a fundamental property of the sampling distribution of the sample proportion.
B) An increase in the sample size n will result in a decrease in the standard error of the sample proportion. This is because the standard error is inversely proportional to the square root of the sample size.
C) The sampling distribution of the sample proportion will be approximately normal, provided that np ≥ 5 and n(1-p) ≥ 5. This is the condition for the normal approximation to the binomial distribution, which is the distribution of the sample proportion. If this condition is met, then the sampling distribution will be approximately normal with mean p and standard deviation sqrt(p(1-p)/n).

Which of the Following Statements Is True About the Sampling