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guide to hypothesis testing

# guide to hypothesis testing - ECON 351 A Guide to...

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ECON 351* -- A Guide to Hypothesis Testing M.G. Abbott A Guide to Hypothesis Testing in Linear Regression Models Tests of One Coefficient Restriction: One Restriction on One Coefficient H 0 specifies only one equality restriction on one coefficient . Two-Tail Tests of One Restriction on One Coefficient Example: H 0 : β j = b j versus H 1 : β j b j where b j is a specified constant. Use: either a two-tail t-test or an F-test . Test Statistics: Ö t se t N k j j j j ( \$ ) \$ \$ ( \$ ) ~ [ ] β β β β = sample value = ) ˆ ( e ˆ s b ˆ ) ˆ ( j j j j 0 β β = β t . Ö ( ) F Var F N k j j j j ( \$ ) \$ \$ ( \$ ) ~ [ , β β β β = 2 1 ] sample value = ( ) ) ˆ ( r a ˆ V b ˆ ) ˆ ( j 2 j j j 0 β β = β F . Note: [ ] or t F j j ( \$ ) ( \$ ) β β 2 = ) ˆ ( F ) ˆ ( t j j β = β and [ ] ] k N , 1 [ F ] k N [ t 2 2 / = α α . Decision Rules: Reject H 0 if ] k N [ t t 2 / 0 > α or two-tail p-value for ( ) α < > = 0 0 t t Pr t ; or p-value for ] k N , 1 [ F F 0 > α α < > = ) F F Pr( F 0 0 . Retain H 0 if ] k N [ t t 2 / 0 α or two-tail p-value for ( ) α > = 0 0 t t Pr t ; or p-value for ] k N , 1 [ F F 0 α α > = ) F F Pr( F 0 0 . ECON 351*: Guide to Hypothesis Testing Page 1 of 5 351guide.doc

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ECON 351* -- A Guide to Hypothesis Testing M.G. Abbott One-Tail Tests of One Restriction on One Coefficient Examples: H 0 : β j = b j (or β j b j ) versus H 1 : β j < b j a left-tail test H 0 : β j = b j (or β j b j ) versus H 1 : β j > b j a right-tail test Use: a one-tail t-test .
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