33 - Chapter 3, Exercise Solutions, Principles of...

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Chapter 3, Exercise Solutions, Principles of Econometrics, 3e 33 Exercise 3.1 (continued) (d) Testing 01 :0 H β = against 11 , H β > uses the same t -value as in part (b), t = 1.92. Because it is a one-tailed test, the critical value is chosen such that there is a probability of 0.05 in the right tail. That is, (0.95,38) 1.686 c tt = = . Since t = 1.92 > c t = 1.69, 0 H is rejected, the alternative is accepted, and we conclude that the intercept is positive. In this case p -value = P ( t > 1.92) = 0.0311. We see from Figure xr3.1(b) that having the p -value < 0.05 is equivalent to having t > 1.69. 0.0 0.1 0.2 0.3 0.4 -3 -2 -1 0 1 2 3 T PDF 1.92 c t Rejection Region Figure xr3.1(b) Rejection region and observed t value for Exercise 3.1(d) (e) The term "level of significance" is used to describe the probability of rejecting a true null hypothesis when carrying out a hypothesis test. The term "level of confidence" refers to
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