principles of econometrics Hill chapter 6 question 4 answer

principles of econometrics (Hill) chapter 6 question 4 answer please

Solution

In each case we use a two-tail test with a 5% significance level. The critical values are given by (0.025,60) t = ?2.000 and (0.975,60) t = 2.000 . The rejection region is t < ?2 or t > 2 . (a) The value of the t statistic for testing the null hypothesis 0 2 H : 0 ? = against the alternative 1 2 H : 0 ? ? is 2 2 3 1.5 se( ) 4 b t b = == Since ?< < 2 1.5 2 , we fail to reject H0 and conclude that there is no sample evidence to suggest that ?2 ? 0. (b) For testing H0: ?1 + 2?2 = 5 against the alternative H1: ?1 + 2?2 ? 5, we use the statistic ( ) ( ) 1 2 1 2 2 5 se 2 b b t b b + ? = + For the numerator of the t-value, we have 1 2 b b + ?= +