Whenever a sampled population is normally distributed or whenever the conditions of the Central Limit Theorem are fulfilled, the sample mean :
A) is a consistent estimator of the population mean μ because the mean of the sampling distribution of the sample mean equals μ.
B) is an efficient estimator of the population mean μ because the mean of the sampling distribution of the sample mean equals μ.
C) is an unbiased estimator of the population mean μ because the mean of the sampling distribution of the sample mean equals μ.
D) is a biased estimator of the population mean μ because the mean of the sampling distribution of the sample proportion equals p.

Question

Whenever a sampled population is normally distributed or whenever the conditions of the Central Limit Theorem are fulfilled, the sample mean  :
A) is a consistent estimator of the population mean μ because the mean of the sampling distribution of the sample mean equals μ. 
B) is an efficient estimator of the population mean μ because the mean of the sampling distribution of the sample mean equals μ. 
C) is an unbiased estimator of the population mean μ because the mean of the sampling distribution of the sample mean equals μ. 
D) is a biased estimator of the population mean μ because the mean of the sampling distribution of the sample proportion equals p.

Quizplus · Accepted Answer

When the conditions are met, the sample mean is an unbiased estimator of the population mean, meaning that it is centered around the true population mean with no systematic over or underestimation. This is because the mean of the sampling distribution of the sample mean is equal to the population mean. However, the sample mean may not necessarily be consistent or efficient.

Whenever a Sampled Population Is Normally Distributed or Whenever the Conditions