Sampling Error|Sampling mean|population mean

7.1 Sampling Error; the Need for Sampling Distributions

样本均值的三种表达：

Sampling distribution of the sample mean 

Distribution of the variable x¯ 

Distribution of all possible sample means of a given sample size

用样本估计总体是有难度的，即使样本数非常少（population为1000samples为50）Introducing the sampling distribution of the sample mean with an example that is both realistic and concrete is diffificult because even for moderately large populations the number of possible samples is enormous, thus prohibiting an actual listing of the possibilities：

重复多次抽样：For example, the number of possible samples of size 50 from a population of size 10,000 is approximately equal to 3 × 10^135, a 3 followed by 135 zeros.

Example：population：10；sample：2；

Population：

群体均值：

Sample：

 

In fact, only 1 of the 10 samples has a mean of 80 inches, the eighth sample in Table 7.2. The chances are, therefore, only 1/10 , or 10%, that x¯ will equal μ; some sampling error is likely.

只有3/10的样本error保证在1inch之间

如果sample size=4，则：

There is an 80% chance that the mean height of the four players selected will be within 1 inch of the population mean

测试不同sample size 计算sample mean 如下：

sampling error tends to be smaller for large samples than for small samples.

所以：