Which of the following statements is false regarding the Central Limit Theorem (CLT) of the sample proportion ?
A) CLT indicates that the mean of the sampling distribution ofwill be equal to the population proportion p.
B) CLT indicates that the sampling distribution ofcan be approximated by a normal distribution if np 5 and nq 5.
C) CLT is applied regardless of the sample size n and the population proportion p.
D) CLT is applied to non-normal populations.
E) CLT indicates that the mean of the sampling distribution ofwill be equal to the population proportion p and CLT indicates that the sampling distribution ofcan be approximated by a normal distribution if np 5 and nq 5.

Question

Which of the following statements is false regarding the Central Limit Theorem (CLT) of the sample proportion  ?
A) CLT indicates that the mean of the sampling distribution ofwill be equal to the population proportion p. 
B) CLT indicates that the sampling distribution ofcan be approximated by a normal distribution if np > 5 and nq > 5. 
C) CLT is applied regardless of the sample size n and the population proportion p. 
D) CLT is applied to non-normal populations. 
E) CLT indicates that the mean of the sampling distribution ofwill be equal to the population proportion p and CLT indicates that the sampling distribution ofcan be approximated by a normal distribution if np > 5 and nq > 5.

Quizplus · Accepted Answer

The statement "CLT is applied regardless of the sample size n and the population proportion p" is false. CLT has certain assumptions that need to be met, including a large enough sample size (n>30) and when the population is normal or the sample size is sufficiently large. Additionally, the statement "CLT indicates that the mean of the sampling distribution of will be equal to the population proportion p and CLT indicates that the sampling distribution of can be approximated by a normal distribution if np > 5 and nq > 5" is redundant, as both these statements are true and are not contradictory.

Which of the Following Statements Is False Regarding the Central