1.Which of the following statements about sample statistics is FALSE?

A)   The Z-statistic is used to test normally distributed data with a known variance, whether testing a large or a small sample.

B)   There is no sample statistic for non-normal distributions with unknown variance for either small or large samples.

C)   The t-statistic is used for normally distributed samples with unknown variance. The t-statistic is used for large or small samples.

D)   The Z-statistic is used for nonnormal distributions with known variance, but only for large samples.

2.When sampling from a nonnormal distribution with an known variance, which statistic should be used if the sample size is large and if the sample size is small?

A)                                        t-statistic      t-statistic

B)                                        z-statistic      z-statistic

C)                                        t-statistic      z-statistic

D)                                        z-statistic      Not available

3.When sampling from a population, the most appropriate sample size:

A)   involves a trade-off between the cost of increasing the sample size and the value of increasing the precision of the estimates.

B)   is at least 30.

C)   is the largest sample for which data are available.

D)   minimizes the sampling error and the standard deviation of the sample statistic around its population value.

答案和详解如下：

1.Which of the following statements about sample statistics is FALSE?

A)   The Z-statistic is used to test normally distributed data with a known variance, whether testing a large or a small sample.

B)   There is no sample statistic for non-normal distributions with unknown variance for either small or large samples.

C)   The t-statistic is used for normally distributed samples with unknown variance. The t-statistic is used for large or small samples.

D)   The Z-statistic is used for nonnormal distributions with known variance, but only for large samples.

The correct answer was B)

There is no sample statistic for non-normal distributions with unknown variance for small samples, but the t-statistic is used when the sample size is large.

2.When sampling from a nonnormal distribution with an known variance, which statistic should be used if the sample size is large and if the sample size is small?

Large Sample Size

Small Sample Size

A)                                        t-statistic      t-statistic

B)                                        z-statistic      z-statistic

C)                                        t-statistic      z-statistic

D)                                        z-statistic      Not available

The correct answer was D)

When you are sampling from a:	and the sample size is small, use a:	and the sample size is large, use a:
Normal distribution with a known variance	z-statistic	z-statistic
Normal distribution with an unknown variance	t-statistic	t-statistic*
Nonnormal distribution with a known variance	not available	z-statistic
Nonnormal distribution with an unknown variance	not available	t-statistic*

*The z-statistic is theoretically acceptable here, but use of the t-statistic is more conservative.

3.When sampling from a population, the most appropriate sample size:

A)   involves a trade-off between the cost of increasing the sample size and the value of increasing the precision of the estimates.

B)   is at least 30.

C)   is the largest sample for which data are available.

D)   minimizes the sampling error and the standard deviation of the sample statistic around its population value.

The correct answer was A)

A larger sample reduces the sampling error and the standard deviation of the sample statistic around its population value. However, this does not imply that the sample should be as large as possible, or that the sampling error must be as small as can be achieved. Larger samples might contain observations that come from a different population, in which case they would not necessarily improve the estimates of the population parameters. Cost also increases with the sample size. When the cost of increasing the sample size is greater than the value of the extra precision gained, increasing the sample size is not appropriate.