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321_09_slides3

# 321_09_slides3 - Week 2 Review of Econ 221 Econ 321...

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Week 2 Review of Econ 221 Econ 321 Introduction to Econometrics Econ 321-Stéphanie Lluis 1 Wooldridge: appendices B & C + chapters 1

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Additional Tools and Issues in Statistical Analysis Hypothesis Testing Confidence Intervals Covariance/Correlation Simple regression Causality Econ 321-Stéphanie Lluis 2
Hypothesis Testing Step 1 State hypotheses What are our beliefs or our predictions? We make what we do not believe our null hypothesis H 0 μ = μ 0 We lay out what we believe as our alternative hypothesis H A : μ < μ 0 or H A : μ > μ 0 or H A : µ ≠ µ 0 Will determine whether one-tail or 2-tail test

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Hypothesis Testing Step 2 What is the statistic of the test ? Are you testing a mean or a relationship between two variables? Sample mean Y or OLS estimator beta hat Under H 0 T= Is the variance of the population 2 known? This will also determine which distribution to use: z (standard normal) or t n-1 student distribution) Compute the value of the statistic (based on the sample info) denoted T when σ is unknown and use S Y standard deviation of Y σ /(n ½ )= standard error
Hypothesis Testing Step 3 Conclude Always in terms of reject or cannot reject H 0 Choose a level of significance Level of significance α = P(Reject H 0 | H 0 true) Find critical values c for 1% or 5% level tests For α =5% and a one-tailed test P(T >c .05 | H 0 )=.05 For α =5% and a two-tailed test P(|T|>c .025 | H 0 )=.05 P(-c 025 < T ≤ c 025 | H 0 ) Uses stat called T here (assumes σ unknown)

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One Tailed Test H A “Greater than” 0 H A “Less than” 0 c α -c α Example based on the t n-1 distribution with n> 120 obs: Reject H 0 at 5% level if Reject H0 at 5% level if t value > 1.645=c 5% t value < -1.645=-c 5% t value Reject H 0 at the α % level And c 1% = 2.326
Two Tailed Test H A “Different from” 0 P(t value -t α /2 )= α /2 -t α /2 t α /2 P(t vaue > t α /2 )= α /2 Reject at α % if t value > t α /2 or t value < -t α /2 P(-c α /2 < T ≤ c α /2 | H0)= α %

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Hypothesis Testing Step 3 Conclude based on the p-value instead of choosing a significance level p-value: what is the largest significance level (probability) at which we reject H 0 In this case, we don’t fix the rejection area at 5% or 1%, we calculate it based on the t value and compare the probability with the 5% or 1% level test
One Tailed Test and p-value H A “Greater than” 0 H A “Less than” 0 P(T > t value )=p t value P(T ≤ -t value )=p -t value Reject H 0 at 10% level if p < 0.10 Reject H0 at 5% level if p < 0.05 Reject H0 at 1% level if p < 0.01

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Two Tailed Test and p-value H A “Different from” 0 P(T ≤ -t value ) -t value P( | T | > t value ) = P(T ≤ -t value ) + P(T> t value ) =2*P(T > t value ) t value P(T > t value )
Example (Holzer, Block, Cheatham and Knott, 1993) (Appendix C, Example C.6) The effects of job training grant on worker productivity Collect info on scrap rates for a sample of 20 manufacturing firms that received job training grants in 1988 (scrap rates are measured as the number of items per 100 produced that are not usable and need to be scrapped)

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321_09_slides3 - Week 2 Review of Econ 221 Econ 321...

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