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Sampling Distributions Central Limit Theorem PSY 2801: Summer 2010 Sampling Distributions Jeff Jones University of Minnesota Jeff Jones Ch 8 Sampling Distributions Central Limit Theorem Sampling Distributions A Sampling Distribution is a distribution of a statistic . If we take one person from a distribution of heights, they most likely will not be equal to the population average height; if we take a finite sample of people from a distribution, their average will probably not equal the population average either. Jeff Jones Ch 8 Sampling Distributions Central Limit Theorem Sampling Dist of the Mean We will focus on the sampling distribution of ¯ x , as that is the most common sampling distribution. Staying with our height example, suppose we wanted to find out the mean height of American men 1 American men is our well-defined population of interest 2 μ of height is our parameter of interest Parameter of Interest : The parameter you’re attempting to make conclusions about for your population. Jeff Jones Ch 8 Notes Notes Notes
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Sampling Distributions Central Limit Theorem Sampling Dist of the Mean So, to get an idea of mean male height from the population, we take a random sample of 9 American men, measure them on height, and take their mean. But there’s a difference between a statistic and a parameter (we only have a statistic), so we decide to take another random sample of 9 American men, measure them on height, and take their mean. Jeff Jones Ch 8 Sampling Distributions Central Limit Theorem Sampling Dist of the Mean Since there’s a discrepancy between our first sample mean and our second sample mean, we decide to take another sample to settle the score. Random Sample of 9 American men Calculate Height Take Mean But each sample mean is a little different than every other sample mean why is this happening? Jeff Jones Ch 8 Sampling Distributions Central Limit Theorem Sampling Dist of the Mean Standard Error : The standard deviation of a sampling distribution If we took a regular distribution, we would have a range of values for people; with a sampling distribution we would have a range of values for means. It is what we would expect to obtain for a statistic! If we are trying to estimate a parameter, we would say that the variation of means is due to sampling error . Sampling error is very important it is what we are trying to estimate in order to make conclusions about parameters for the rest of the semester. Jeff Jones Ch 8 Notes Notes Notes
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Sampling Distributions Central Limit Theorem Sampling Distributions These are the steps to obtaining a sampling distribution: 1 Pick a population of interest, a statistic, and a sample size ( N ) 2 Randomly sample N observations from the population of interest 3 Calculate the statistic on those N observations 4 Throw everybody back into the pool 5 Repeat steps 2-4 an infinite number of times 6 Plot the means, calculate statistics on the means An important point to note is that a sampling distribution is
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