新SAT数学知识点介绍①：Random Sampling & Random Assignment by JianYu

在新SAT数学里，统计这一块进行了比较大的变动，增加了一些同学们不太熟悉的知识点，包括margins of error/confidence interval，random sampling & random assignment 等。1月份考试将近，今天我们来讲讲random sampling & random assignment在SAT数学考试中的考法和应用。

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定义

• 什么是random sampling？ 如果说你从1000人中随机抽取100人来做实验，那就是 random sampling。

• 什么是random assignment？如果你将不同实验方案随机分配给上述那100人中进行实验，那就是random assignment。

应用

那么random sampling和random assignment在统计题目中意味着什么呢？我们来看一个例子：

Hilary recruits residents from her town who have physical exams scheduled in the next month with the local doctor's office. She randomly assigns the volunteers to either a Vitamin D supplement pill or a placebo pill. Participants do not know which pill they are taking. They have their blood pressures measured before the study begins and at the end of the study.

Suppose Hilary finds that the group who took the Vitamin D supplements had a significant decrease in blood pressure, while the placebo group showed no significant change in blood pressure.

这个时候题目一般会问两个问题：

1、根据我们刚刚的实验, 我们是否能够将结论拓展到整个群体「Can the results be generalized to the entire population?」

2、根据我们刚刚的实验，我们是否得出the difference in blood pressures is caused by the Vitamin D「Can conclusions about cause and effct be drawn？」

以上的问题也就是SAT数学关于random sampling & random assignment的考点，各位同学只要会回答上边两个问题，即可应付考试。那么如何去理解呢？同学们需要记住下边两个结论:

• Was the sample of subjects in the study selected at random from the entire population in question? If so, the results can be generalized to the entire population in question. However, check to make sure that the conclusion is referring to the same population as that in the study.

• ** Were the subjects randomly assigned to treatments?** If so, conclusions about cause and effect can be drawn.

简单总结就是：Random Sampling 可推出 the results can be generalized to the entire population；Random Assignment 可推出 结论因果关系成立。

根据我们刚刚的实验，我们样本来自volunteer，并不是随机从总体里选的，那么最后的结论就不能generalize to the entire population。然而我们在做实验的时候，的确符合random assignment，所以最后的结论就能够得出因果关系。

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真题练习

Researchers in Australia carried out an experiment to determine if the color of a coffee mug affects how people rate the flavor intensity of the coffee.

Volunteers were randomly assigned to taste coffee in mugs that differed only by color: some white and some clear. The same type of coffee was used in both mugs. The researchers concluded that the mean flavor intensity rating was significantly higher for those who drank coffee in a white mug than for those who drank coffee in a clear mug. Based on this study which of the following statements is correct?「11月亚太真题」

A) The color of the mug was the cause of the difference in mean intensity rating for these volunteers, and this conclusion can be generalized to all coffee drinkers.

B) The color of the mug was the cause of the difference in mean intensity rating for these volunteers, but it is not reasonable to generalize this conclusion to all coffee drinkers.

C) It is not reasonable to conclude that the color of the mug was the cause of the difference in mean intensity rating for these volunteers.

D) It is not possible to draw any conclusions from this experiment because volunteers were used.

解析

同学们应对这样的题目，一定要结合考点来解答，这样才能得到一个准确无误的答案。根据我们刚刚的总结：Random Sampling → the results can be generalized to the entire population；Random Assignment → 结论因果关系成立。

题中使用的sample是volunteers，这并不是一个随机抽取的样本，所以结论不能generalize to the entire population。同时这个实验的确是random assignment，所以结论中的因果关系是成立的。因此，答案选B。

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总结

虽然Random Sampling & Random Assignment这两个知识点看起来很生涩，有的同学不太熟悉，但SAT数学在这两个知识点上考的变化并不大，就是围绕上文的两个考点来出题。事实上我们只需要紧扣上文中提到的两个考点和对应的结论，即可应付考试。祝同学们都能够取得数学800，加油！

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