Section 7.1 Student Learning Objectives
In this section we integrate the concept of data that is extracted from a sample with the concept of a random variable. The new element that connects between these two concepts is the notion of sampling distribution. The data we observe results from the specific sample that was selected. The sampling distribution, in a similar way to random variables, corresponds to all samples that could have been selected. (Or, stated in a different tense, to the sample that will be selected prior to the selection itself.) Summaries of the distribution of the data, such as the sample mean and the sample standard deviation, become random variables when considered in the context of the sampling distribution. In this section we investigate the sampling distribution of such data summaries. In particular, it is demonstrated that (for large samples) the sampling distribution of the sample average may be approximated by the Normal distribution. The mathematical theorem that proves this approximation is called the Central Limit Theory. By the end of this chapter, the student should be able to:
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Comprehend the notion of sampling distribution and simulate the sampling distribution of the sample average.
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Relate the expectation and standard deviation of a measurement to the expectation and standard deviation of the sample average.
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Apply the Central Limit Theorem to the sample averages.
