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Econ 399 Chapter4b

# Econ 399 Chapter4b - -Before we construct a rule for...

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4.2 One Sided Tests -Before we construct a rule for rejecting H 0 , we need to pick an ALTERNATE HYPOTHESIS -an example of a ONE SIDED ALTERNATIVE would be: 0 : j a H -Which technically expands the null hypothesis to 0 : 0 j H -Which means we don’t care about negative values of B j -This can be due to introspection or economic theory

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4.2 One Sided Tests -If we pick an α (level of significance) of 5%, we are willing to reject H 0 when it is true 5% of the time -in order to reject H 0 , we need a “sufficiently large” positive t value -a one sided test with α=0.05 would leave 5% in the right tail with n-k-1 degrees of freedom -our rejection rule becomes reject H 0 if: * ˆ t t j -where t* is our CRITICAL VALUE
4.2 One Sided Example -Take the following regression where we are interested in testing whether Pepsi consumption has a +’ve effect on coolness: 43 N 62 . 0 5 . 0 3 . 0 3 . 4 ˆ 2 21 . 0 25 . 0 1 . 2 R Pepsi Geek ol o C -We therefore have the following hypotheses: 0 : 0 : 2 2 0 a H H

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4.2 One Sided Example -We then construct our test statistic: 38 . 2 21 . 0 5 . 0 ) ˆ ( ˆ 2 2 ˆ 2 se t -With degrees of freedom=43-3=40 and a 1% significance level, from a t table we find that our critical t, t*=2.423 -We therefore do not reject H 0 at a 1% level of significance; Pepsi has no positive effect on coolness at the 1% significance level in our study
4.2 One Sided Tests -From looking at a t table, we see that as the significance level falls, t* increases -We therefore need a bigger test t statistic in order to reject H 0 (the hypothesis that a variable is not significant) -as degrees of freedom increase, the t distribution approximates the normal distribution -after df=120, one can in practice use normal critical values

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4.2 One Sided Tests -The other one-sided test we can conduct is: 0 : j a H -Which technically expands the null hypothesis to 0 : 0 j H -Here we don’t care about positive values of B j -We now reject H if: * ˆ t t j
4.2 Two Sided Tests

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