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 β -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 β -where t* is our CRITICAL VALUE
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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 β 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 = = = β 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 
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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 (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 β -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 0  if: * ˆ t t j - <
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4.2 Two Sided Tests
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Econ 399 Chapter4b - -Before we construct a rule for...

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