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Section 7.4 Sampling Distributions 7.4 / 1 Review of Statistical Terms Population is the set of all measurements or counts (either existing or conceptual) under consideration Sample is a subset of measurements from a population Parameter is a numerical descriptive measure of a population Statistic is a numerical descriptive measure of a sample We use a statistic to make inferences about a population parameter. 7.4 / 2 Some Common Statistics and Corresponding Parameters It is important to notice that for a given population, a specified parameter is a fixed quantity. On the other hand, the value of a statistic might vary depending on which sample has been selected. 7.4 / 3 Principal Types of Inferences Estimation: estimate the value of a population parameter Testing: formulate a decision about the value of a population parameter Regression: Make predictions or forecasts about the value of a statistical variable To evaluate the reliability of our inferences, we will need to know the probability distribution for the statistics we are using, Such a probability distribution is called a sampling distribution. 7.4 / 4 Sampling Distribution • Is a probability distribution for the sample statistic • based on all possible random samples of the same size from the same population 7.4 / 5 Example of a Sampling Distribution • Select samples with two elements each (in sequence with replacement) from the set • {1, 2, 3, 4, 5, 6}. 7.4 / 6 Constructing a Sampling Distribution of the Mean for Samples of Size n = 2 List all samples (with 2 items in each) and compute the mean of each sample. sample: mean: sample: mean {1,1} {1,2} {1,3} {1,4} {1,5} 1.0 1.5 2.0 2.5 3.0 {1,6} {2,1} {2,2} … … 3.5 1.5 2 ... … How many different samples are there? 36 7 Sampling Distribution of the Mean x p 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 1/36 2/36 3/36 4/36 5/36 6/36 5/36 4/36 3/36 2/36 1/36 7.4 / 8 GUIDED EXERCISE 9 PAGE,284 7.4 / 9