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# 46 - Chapter 3 Exercise Solutions Principles of...

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Chapter 3, Exercise Solutions, Principles of Econometrics, 3e 46 EXERCISE 3.9 (a) We set up the hypotheses H 0 : 2 0 β = versus H 1 : 2 0 β > . The alternative 2 0 β > is chosen because we assume that growth, if it does influence the vote, will do so in a positive way. The test statistic, given H 0 is true, is 2 (29) 2 ~ se( ) b t t b = The rejection region is (0.95,29) 1.699 t t > = . The value of the test statistic is 0.6599 4.0460 0.1631 t = = Since t = 4.0460 > 1.699, we reject the null hypothesis that β 2 = 0 and accept the alternative that 2 0 β > . We conclude that economic growth has a positive effect on the percentage vote. (b) A 95% interval estimate for 2 β from the regression in part (a) is: 2 (0.975,29) 2 se( ) b t b ± = 0.6599 ± 2.045 × 0.1631 = (0.3264, 0.9934) This interval estimate suggests that, with 95% confidence, the true value of 2 β is between 0.3264 and 0.9934. Since 2 β represents the change in percentage vote due to economic growth, we expect that a 1% increase in the growth rate will increase the percentage vote by an amount between 0.3264 to 0.9934 percent.
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