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Midterm 2 Study Guide General guide for preparing for the midterm: The topics below are the ones that you must know for the exam. However, even if it is not mentioned here anything that we covered in the lecture can be on the exam so make sure you study the slides and your notes thoroughly. Chapter 5. 1) Null and alternative hypotheses Null Hypothesis- (in a statistical test) the hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error. - Statement of the values that the researcher does not expect Ex. If you expect a positive coefficient, then you don’t expect a zero or negative coefficient, and then the null hypothesis is: Ho: B < 0 Alternative Hypothesis- typically a statement of the values that the researcher expects. “Ha” Ex. If you expect a positive coefficient, then the alternative hypothesis is: Ha: B>0 2) One-sided test a. Ex: Ho: B>/equal o, Ha= B<0 i. The above hypotheses are for one-sided test, because the alternative hypothesis have values on only one side of the null hypothesis. 3) Two-sided test a. Ex: Ho: B=0, Ha: B=/=o i. Alterative hypothesis has values on both sides of the null hypothesis. b. Two categories of Two-sided tests: i. Two-sided tests of whether an estimated coefficient is significantly different from zero, and ii. Two-sided test of whether an estimated coefficient is significantly different from a specific nonzero value 4) Type 1 error a. We reject a true null hypothesis i. Sending an innocent defendant to jail 5) Type 2 error a. We do not reject a false null hypothesis i. Freeing a guilty defendant 6) T-test A. economists usually use the t-test to test hypotheses about individual regression slope coefficients. - test accounts for differences in the units of measurement of the variables and in the standard deviations of the estimated coefficients. B. 4 steps for T-test: 1. Set up null and alternative hypotheses. 2. Choose a level of significance and therefore a critical t-value 3. Run the regression and obtain an estimated t-value (or t-score) 4. Apply the decision rule by comparing the calculated t-value with the critical t-value in order to reject the null hypothesis 7) T-statistic A. the t-statistic is the appropriate test to use when the stochastic error term is normally distributed and when the variance of that distribution must be estimated. 8) Critical value A. the value that divides the “acceptance” region from the rejection region when testing a null hypothesis 9) P-values (marginal significance level) A. p-value for a t-score is the probability of observing a t-score that size or larger (in absolute value) if the null hypothesis were true. B. probability, runs from 0 to 1. C. It tells us the lowest significance level at which we could reject the null hypothesis. D. Calculating: Reject Ho is p-valuek < the level of significance and if Beta hatk has the sign implied by Ha. Do not reject null hypothesis otherwise 10) Confidence intervals A. a range of values that will contain the true value of Beta a certain percentage of the time, say 90 to 95% 11) Limitations of the t-test A. Limitations of T-test: ii. Does not test theoretical validity. iii. Does not test “importance” iv. Not intended for test of the entire population 12) F-test Ho=β1=β2=0 Ha= Ho is not true F= [(RSSm-RSS)/M] / [RSS/ (N-K-1)] - Critical value- “M”- numerator # - Constrained Vs. unconstrained equation Chapter 6. 1) Omitted variable: Consequence, detection a. Consequences: i. Biased coefficients ii. E(βhat) =/= β iii. E (βhat)= β + β2 x ∞ (∞= correlation) 1. Error term has omitted variable in it, degrees of bias 2) Irrelevant variable: Consequence, detection a. Consequence: 3) Four important specification criteria 4) Specification searches: Sequential specification search, data mining, sensitivity analysis Chapter 7. 1) Interpretation of the constant term (intercept) 2) Should the constant term be suppressed? 3) What does it mean to be linear in variables? Linear in coefficients? 4) Alternative functional forms: Double-log form, Semilog form, Polynomial form, Inverse form 5) Lagged independent variables 6) Dummy variables: intercept dummy, slope dummy 7) Choosing the right functional form