ecn10-lecture13-v1

ecn10-lecture13-v1 - Economics 10: Introduction to...

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Unformatted text preview: Economics 10: Introduction to Statistical Methods Statistical Inference Overview of Inference Methods for drawing conclusions about a population from sample data are called statistical inference Methods Confidence Intervals- estimating a value of a population parameter Tests of significance- assess evidence for a claim about a population Inference is appropriate when data are produced by either a random sample or a randomized experiment Confidence Intervals Today: Confidence Intervals The confidence interval is a range of values with an associated probability or confidence level C . The probability quantifies the chance that the interval contains the true population parameter. Using a sample to estimate a population parameter Estimate will be somewhat different than the true population parameter by chance (sampling variability). Can we be more informative than somewhat different? Ask: what interval can we say contains X C % of the time? Ex: what interval contains X 95 % of the time? A confidence interval is known Special case: polling conservative bounds is unknown t-distribution When is ? When SRS + Any time the data are drawn from a normally distributed population Linear functions of normally distributed random variables are also normally distributed When SRS + large n Central Limit Theorem ( 29 2 , ~ X X i N X n N X X X 2 , ~ SRS = simple random sample Review: standardizing the normal curve using z N (0,1) z x N (64.5, 2.5) N ( , / n ) Standardized height (no units) z = x - n Here, we work with the sampling distribution, and / n is its standard deviation (spread). Remember that is the standard deviation of the original population. 68-95-99.7% Rule Rule of thumb for areas under a normal 68% of values within 1 s.d. of the mean 95% of values within 2 s.d. of the mean 99.7% of values within 3 sd of the mean Implications for the sample mean 68% of estimates on interval 95% of estimates on interval 99.7% of estimates on interval n X X ( 29 n X X * 2 ( 29 n X X * 3 Graphical representation...
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This note was uploaded on 05/05/2010 for the course ECON 010 taught by Professor Giummo during the Spring '08 term at Dartmouth.

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ecn10-lecture13-v1 - Economics 10: Introduction to...

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