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

Quizplus · Accepted Answer

When a sampled population is normally distributed, or whenever the conditions of the Central Limit Theorem are fulfilled, the sample mean is an unbiased estimator of the population mean, because the mean of the sampling distribution of the sample mean equals the population mean. This means that, on average, the sample mean will be an accurate estimate of the population mean. However, this does not necessarily mean that the sample mean is a consistent or efficient estimator of the population mean.

Whenever a Sampled Population Is Normally Distributed, or Whenever the Conditions