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Sample_Midterm_Econ140A_2011Spr

Sample_Midterm_Econ140A_2011Spr - Economics 140A Spring...

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Economics 140A Spring 2011 Professor Startz Sample Midterm Answer all 5 questions. Each question is worth 15 points, although some questions are easier than others. Be sure to show your work for each question. Notice that there is some reference material provided after the questions. You may use a calculator, but no other electronic devices. (No phones or laptops for example.) The exam is closed book. You may be asked to show your student id when turning in the exam. 1. Suppose you have the regression equation and find that we get an estimate ̂ . Assume that all our usual regression assumptions hold. Now suppose you are given a new data set, data set 2, which is identical to the first set of data except that every value of has doubled, with a corresponding change in . Call the new estimator ̂ . a. Would you expect ̂ to be either higher or lower than ̂ ? b. How does the variance of the two estimators compare? c. Assuming that the true value of is , would the probability of rejecting the null hypothesis using a standard t- test be higher or lower in the first regression or in the second? Explain. (This question is a little subtle.) 2. Consider tests on a sample mean. Explain you answer in each case. a. Suppose is rejected in favor of at the significance level. Would you necessarily reject at the significance level? b. Suppose is rejected in favor of at the significance level. Would you necessarily reject at the significance level? c. Assuming is rejected in favor of , will it necessarily be rejected in favor of at the same significance level. d. Suppose is rejected in favor of . If and , what p- value is associated with the sample mean ̅ (You will need to use the Z- score table.) 3. This problem uses the CPS March 2010 dataset. The following command was executed in EViews yielding the regression results below lnwage c fe age log(hrswk) ed ed*ed
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page 2 Dependent Variable: LNWAGE Method: Least Squares Date: 04/20/11 Time: 15:55 Sample (adjusted): 2 135962 Included observations: 95124 after adjustments Variable Coefficient Std. Error t-Statistic Prob.
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