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STAT 3120 Statistical Methods I

STAT 3120 Statistical Methods I. Lecture 6 The Central Limit Theorem. STAT3120 - Central Limit Theorem. Before we get into a discussion of the Central Limit Theorem, lets take a minute to talk about the differences between Descriptive and Inferential statistics:.

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STAT 3120 Statistical Methods I

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  1. STAT 3120Statistical Methods I Lecture 6 The Central Limit Theorem

  2. STAT3120 - Central Limit Theorem Before we get into a discussion of the Central Limit Theorem, lets take a minute to talk about the differences between Descriptive and Inferential statistics: Analysis of a SAMPLE of data – population is unavailable because of time, cost, access, etc. Results are NEVER 100% accurate. Analysis of ALL available data of interest. Results are ALWAYS 100% accurate. Descriptive Statistics • Descriptions of central tendency and variation; • Visualizations through tables and graphics. Inferential Statistics • Drawing an inference onto a population through Confidence Intervals, Hypothesis Testing, Statistical Models, etc.

  3. STAT3120 - Central Limit Theorem When we draw a sample (>30) because we cannot access the entire population, the descriptive measures of the sample (specifically the mean) will not equal the descriptive statistics for the population. Sample statistics will follow a distribution – which is normal. This concept forms the basis for the Central Limit Theorem – which forms the basis for why statistics “works”. Take a look at this applet: http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/index.html

  4. STAT3120 - Central Limit Theorem Important concepts to remember about the Central Limit Theorem: • The distribution of sample means will, as the number of samples increases approach a normal distribution; • The mean of all sample means approximates the population mean; • The std of all sample means is the std of the population/the SQRT of the sample size; • If the population is NOT normally distributed, sample sizes must be greater than 30 to assume normality; • If the population IS normally distributed, samples can be of any size to assume normality (although greater than 30 is always preferred). • The CLT DOES NOT provide that any individual sample will be normally distributed.

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