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test2ans-3u03-2011w - ECON 3U03 Test 2 Instructor Shintaro...

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ECON 3U03: Test 2 Instructor: Shintaro Yamaguchi March 8, 2011 1. Chapter 3 (a) 0.898/2.123=0.423 (5 marks) No partial credit. (b) The test statistic is 0.321/0.123=2.610 (4 marks). This follows t -distribution with DF = 36 (2 marks). Draw the same graph as Figure 3.7 on p. 67 (4 marks). The test statistic must be used in the graph. No other partial credit. (c) The test statistic is (0.321-0.5)/0.123=-1.455 (4 marks). The critical value is t . 10 , 36 = - t . 90 , 36 = - 1 . 306 (4 marks). Because the test statistic falls in the rejection region, the null hypothesis is rejected (1 mark) and the alternative hypothesis is accepted (1 mark). No other partial credit. (d) The critical value is t . 995 , 36 = 2 . 719 (4 marks). The confidence interval is [0.321-2.719*0.123, 0.321+2.719*0.123]=[- 0.013, 0.655] (6 marks). Up to 6 marks are awarded when a wrong critical value is used. No other partial credit. 2. Chapters 4 and 5. (a) SST = ( 38 - 1 ) * Var ( y ) = 37 * 2 . 54 = 93 . 98 (4 marks). Notice that ˆ σ = p SSE / ( 38 - 3 ) . Thus, SSE = 0 . 752 2 * ( 38 - 3 ) = 19 . 792 (4 marks). R 2 = 1 - SSE / SST = 0 . 789 (2 mark). 2 marks are deducted if the answer says SST = 38 * Var ( y ) , because this is a biased estimator.
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