1.The sample mean is a consistent estimator of the population mean because the:

A)   expected value of the sample mean is equal to the population mean.

B)   sampling distribution of the sample mean has the smallest variance of any other unbiased estimators of the population mean.

C)   sample mean provides a more accurate estimate of the population mean as the sample size increases.

D)   sampling distribution of the sample mean is normal.

2.The sample mean is an unbiased estimator of the population mean because the:

A)   expected value of the sample mean is equal to the population mean.

B)   sampling distribution of the sample mean has the smallest variance of any other unbiased estimators of the population mean.

C)   sample mean provides a more accurate estimate of the population mean as the sample size increases.

D)   sampling distribution of the sample mean is normal.

答案和详解如下：

1.The sample mean is a consistent estimator of the population mean because the:

A)   expected value of the sample mean is equal to the population mean.

B)   sampling distribution of the sample mean has the smallest variance of any other unbiased estimators of the population mean.

C)   sample mean provides a more accurate estimate of the population mean as the sample size increases.

D)   sampling distribution of the sample mean is normal.

The correct answer was C)

A consistent estimator provides a more accurate estimate of the parameter as the sample size increases.

2.The sample mean is an unbiased estimator of the population mean because the:

A)   expected value of the sample mean is equal to the population mean.

B)   sampling distribution of the sample mean has the smallest variance of any other unbiased estimators of the population mean.

C)   sample mean provides a more accurate estimate of the population mean as the sample size increases.

D)   sampling distribution of the sample mean is normal.

The correct answer was A)

An unbiased estimator is one for which the expected value of the estimator is equal to the parameter you are trying to estimate.