Margin of Error|sample size and E

8.3 Margin of Error

由该公式可知：

To improve the precision of the estimate, we need to decrease the margin of error, E. Because the sample size, n, occurs in the denominator of the formula for E, we can decrease E by increasing the sample size.

可以通过减小Z或增大n的方式，减小E，以此增加 precision of the estimate

所以，在已知E和置信度的前提下，为了获得最好的precision of the estimate，可以采用公式倒推：

根据E与置信区间的关系，可以写出置信区间：

The simpler method might have yielded a somewhat wider confidence interval because the sample size is rounded up. Hence, this simpler method gives, at worst, a slightly conservative estimate, so is acceptable in practice.

对于population标准差不可知的情况：

The formula for finding the required sample size, Formula 8.1, involves the population standard deviation, σ, which is usually unknown. In such cases, we can take a preliminary large sample, say, of size 30 or more, and use the sample standard deviation, s, in place of σ in Formula 8.1

所以，最理想的状态是：

Ideally, we want both a high confidence level and a small margin of error. Accomplishing these specifications generally takes a large sample size.