lesson6 - Sampling methods and the Central Limit Theorem

lesson6 - Sampling methods and the Central Limit Theorem -...

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Unformatted text preview: Ka-fu Wong 2007 ECON1003: Analysis of Economic Data Lesson6-1 Lesson 6: Sampling Methods and the Sampling Methods and the Central Limit Theorem Central Limit Theorem Ka-fu Wong 2007 ECON1003: Analysis of Economic Data Lesson6-2 Outline Point estimate Why sample the population? Probability sampling Choice of sampling method: Sampling straws Sampling distribution of the sample means Probability histograms and empirical histograms Central Limit Theorem Normal approximation to Binomial Ka-fu Wong 2007 ECON1003: Analysis of Economic Data Lesson6-3 Making statements about a population by examining sample results Sample Population Inferential Statistics Inference Population parameters (unknown, but can be estimated from sample evidence) Sample statistics (known) Ka-fu Wong 2007 ECON1003: Analysis of Economic Data Lesson6-4 Inferential Statistics Inferential Statistics Estimation Hypothesis Testing Ka-fu Wong 2007 ECON1003: Analysis of Economic Data Lesson6-5 Point Estimates Examples of point estimates are the sample mean , the sample standard deviation , the sample variance , the sample proportion . A point estimate is one value ( a single point ) that is used to estimate a population parameter. Ka-fu Wong 2007 ECON1003: Analysis of Economic Data Lesson6-6 Estimating the percentage of Earth covered by water Experiments: Paint a dot on your thumb. Catch the globe and tell me whether the dot on your thumb lands on water. Estimate the percentage of Earth covered by water by the average of all trials. Idea: If we draw many observations with replacement, the sample average will approach the population proportion. Code water as 1 and land as 0, the sample average will be an estimate of the proportion will be the percentage of Earth covered by water. Truth: Water covers 71% of the Earth's surface. e.g., http://pao.cnmoc.navy.mil/educate/neptune/trivia/earth.htm Ka-fu Wong 2007 ECON1003: Analysis of Economic Data Lesson6-7 Why Sample the Population? The physical impossibility of checking all items in the population. The cost of studying all the items in a population. The sample results are usually adequate. Contacting the whole population would often be time- consuming. The destructive nature of certain tests. Ka-fu Wong 2007 ECON1003: Analysis of Economic Data Lesson6-8 Probability Sampling A probability sample is a sample selected such that each item or person in the population being studied has a known likelihood of being included in the sample....
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lesson6 - Sampling methods and the Central Limit Theorem -...

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