题目
Which of the following statements about sampling and the central limit theorem is least likely correct?
选项
A.The variance of the distribution of sample means is \u03c32\/n.
B.The central limit theorem may be used for large sample sizes for skewed distributions.
C.The mean of the population and the mean of all possible sample means are always equal.
D.The standard deviation of the mean of many observations is more than the standard deviation of a single observation.
答案
D
解析
The central limit theorem holds for any distribution (skewed or not) as long as the sample size is large (i.e., n >30). The mean of the population and the mean of the distribution of all sample means are equal. The standard deviation of the mean of many observations is less than the standard deviation of a single observation.只要样本量较大（即n> 30），则中心极限定理适用于任何分布（偏斜或不偏斜）。 总体均值和所有样本均值的分布均值相等。 许多观测值的平均值的标准偏差小于单个观测值的标准偏差。