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s_m8_handouts - Rev F07 STA 2023 Module 8 The Sampling...

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Rev. F07 http://faculty.valenciacc.edu/ashaw/ 1 Rev.F08 1 STA 2023 Module 8 The Sampling Distribution of the Sample Mean Rev.F08 2 Module Objectives 1. Define sampling error and explain the need for sampling distributions . 2. Find the mean and standard deviation of the variable, given the mean and standard deviation of the population and the sample size. 3. State and apply the central limit theorem . 4. Determine the sampling distribution of the sample mean when the variable under consideration is normally distributed . 5. Determine the sampling distribution of the sample mean when the sample size is relatively large. http://faculty. valenciacc . edu/ashaw/ Click link to download other modules. Rev.F08 3 Why Sampling? http://faculty. valenciacc . edu/ashaw/ Click link to download other modules. We have seen that using a sample to acquire information about a population is often preferable to conducting a census . Generally, sampling is less costly and can be done more quickly than a census ; it is often the practical way to gather information.
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Rev. F07 http://faculty.valenciacc.edu/ashaw/ 2 Rev.F08 4 What is Sampling Error? http://faculty. valenciacc . edu/ashaw/ Click link to download other modules. However, because a sample provides data for only a portion of an entire population , we cannot expect the sample to yield perfectly accurate information about the population. Thus, we should anticipate that a certain amount of error - called sampling error - will result simply because we are sampling. Rev.F08 5 What is a Sampling Distribution? http://faculty. valenciacc . edu/ashaw/ Click link to download other modules. The distribution of all possible observations of the statistic for samples of a given size is called the sampling distribution of the statistic. For example, the sampling distribution of the sample mean is the distribution of all possible sample means for samples of a given size. In this module, we will concentrate on the sampling distribution of the sample mean . Rev.F08 6 Sampling Distribution of the Sample Mean http://faculty. valenciacc . edu/ashaw/ Click link to download other modules. What does it mean? The sampling distribution of the sample mean is the distribution of all possible sample means for samples of a given size.
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Rev. F07 http://faculty.valenciacc.edu/ashaw/ 3 Rev.F08 7 Example: Sample Means for Samples of Size 2 http://faculty. valenciacc . edu/ashaw/ Click link to download other modules. Rev.F08 8 Dotplot for the Sampling Distribution http://faculty. valenciacc . edu/ashaw/ Click link to download other modules. This is a dotplot for the sampling distribution of the sample mean for samples of size 2 in the previous example. The dotplot shows that 3 out of 10 samples have means within 1 inch of the population mean of 80 inches. Rev.F08 9 Dotplot for the Sampling Distribution of the Sample Mean http://faculty. valenciacc . edu/ashaw/ Click link to download other modules.
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