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,, because the mean of the sampling distribution of the sample mean, equals
B) is an efficient estimator of the population mean,, because the mean of the sampling distribution of the sample mean equals
C) is an unbiased estimator of the population mean,, because the mean of the sampling distribution of the sample mean equals
D) is a biased estimator of the population mean,, because the mean of the sampling distribution of the sample proportion equals p
E) 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, the sample mean,  :
A) is a consistent estimator of the population mean,, because the mean of the sampling distribution of the sample mean, equals 
B) is an efficient estimator of the population mean,, because the mean of the sampling distribution of the sample mean equals 
C) is an unbiased estimator of the population mean,, because the mean of the sampling distribution of the sample mean equals 
D) is a biased estimator of the population mean,, because the mean of the sampling distribution of the sample proportion equals p 
E) 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 the conditions for the central limit theorem are met, the sample mean is an unbiased estimator of the population mean. This is because the mean of the sampling distribution of the sample mean is equal to the population mean. Therefore, choice C is the best answer.

Whenever a Sampled Population Is Normally Distributed or Whenever the Conditions