Unit 10

# Unit 10 - Statistics V3100018.001 UNIT 10 Sampling and...

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Statistics – V3100018.001 UNIT 10 – Sampling and sampling distributions Giuseppe Arbia , Catholic University of the Sacred Hearth, Roma, Italy 1

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STATISTICAL INFERENCE The second part of the course is entirely devoted to introducing statistical inferential procedures
Example: inference on a mean

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http://electoralmap.net/2012/ intrade.php Example: inference on a proportion
Example: inference on the coefficient of variation Coefficient of variation of per-capita income among EU countries

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Example: inference on regression ln y T , i y 0, i ! " # \$ % & = ! 0 + 1 ln y 0, i Growth equation If β <0 then the regions “converge” y t,i = per-capita income at time t , in region i
7 We will distinguish 3 inferential problems 1. Point estimation 2. Confidence intervals 3. Hypothesis testing

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8 1. Point estimation •We approximate one unknown parameter with a SINGLE value. •We want to find the BEST approximation. •E. g. what is the BEST WAY of estimating the population mean ? •We need to specify the criteria to establish what is the BEST WAY
9 2. Confidence intervals •We acknowledge that an estimate might contain an error due to sampling and we attach to the estimate a measure that expresses the degree of confidence we have on the result (expressed as a probability). P ( m ! ! " μ " m + ) = 1 ! " error Probability of error

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10 3. Hypothesis testing •Both inductive and deductive. •We have some a priori idea and we ask the data to confirm or reject this idea. •E. g. We believe that μ=μ 0 and we look at a sample to see how likely is this to be true given the observed sample.