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4. In an estimated simple regression model, based on 102 observations, the estimated slope parameter (b2) is 1.1 and the estimated standard error is 0.291. Test the hypothesis that the slope is zero, against the alternative that it is not, at the 1% level of significance. Be sure to do all parts of the hypothesis test. (1 mark)T Test the hypothesis that the slope is zero, against the alternative that it is positive at the 1% level of significance. Be sure to do all parts of the hypothesis test. (1 mark)T Test the hypothesis that the slope is positive, against the alternative that it is negative at the 5% level of significance. Be sure to do all parts of the hypothesis test. (1 mark) a. b. c. d. Calculate the 99% interval estimate of the slope parameter. (1 mark) Is a narrower confidence interval for a parameter desirable? Briefly explain why (1-2 sentences is sufficient). (1 mark) e.

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Book (10) b2 Sb2 102 100 0.291 df n-2 b2/ Sb2 3.78 Test Statistic, t 3.78 9 Critical Value, t crit (2 tailed 2.63 10 Decision Criteria - Reject Ho if t<-t crit or t>+t crit Since t >t crit we Reject Ho and conclude slope is not equal to 0 12 13 14 15 Critical Value, t crit (right tailed)2.36 16 3.78 Decision Criteria - Reiect Ho if t+t crit Since t> t crit we Reject Ho and conclude slope is positive 17 18 19 20 21 3.78 2.36 Critical Value, t crit (left tailed) Decision Criteria - Reject Ho ift <-t crit Since t>tcrit we Fail to Reject Ho and conclude slope is equal to 0 23 24 25 d)99% c.. is 26 27 281 29 t (100, 0.01) 2.63 Lower limit Upper limit 0.33 1.87 Confidence Interval Estimate of the Slope: 31 32 35 36 37 38 39 40 41

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