Based on the central limit theorem,for a given population,the mean of all the sample means ( )of sample size n,and the mean of all (N)population observations (x)are
A)equal to
B)not equal
C)are equal to ( - x)
D)equal to the population mean,µ

Question

Based on the central limit theorem,for a given population,the mean of all the sample means (  )of sample size n,and the mean of all (N)population observations (x)are
A)equal to 
B)not equal 
C)are equal to ( - x) 
D)equal to the population mean,µ

Quizplus · Accepted Answer

According to the central limit theorem, the mean of all sample means approaches the population mean µ as the sample size increases. Therefore, if we take the mean of all the sample means and the mean of all population observations, both will approach the population mean µ. Thus, the best choice is D which states that they are equal to the population mean, µ.

Based on the Central Limit Theorem,for a Given Population,the Mean