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Is it true or false that endogenous sample selection will not cause bias in the OLS estimator.
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- Researchers conducted a prospective cohort study to assess the association between dietary supplements and cognitive ability among children. A total of 500 children age 12-17 years who take an omega-3 fatty acid supplement are compared with 500 children age 12-17 years who do not take an omega-3 fatty acid supplement. Researchers follow the children for 2 years. During this time, 300 children who take the supplement earn what is classified as a “high” score on a cognitive test while 200 children who do not take the supplement earn what is classified as a “high” score on the same cognitive test. Show calculations. a) Construct a 2x2 table from the information presented above b) The risk difference is:If SLR 1-3 hold, but SLR 4 is violated, then... OLS estimators are unbiased and inconsistent OLS test statistics suffer from heteroskedasticity OLS estimators are biased and consistent OLS estimators are biased and inconsistentWhy does a confidence interval contain more information than the resultof a single hypothesis test?
- Q1. State the property of an estimator that gives a correct estimate of the population parameter of interest, but only on average. Q2. State the property of ian estimal or thal converges to the populalion paaameter of interest as the sample size goes to infinity. Q3. Why is an efficient estimator a desirable property of the OLS estimator? Q4. Stare the assumption(s)under the classical linearregression model giving rise to a biased standard error of the coefficient estimates when violated.We are interested in analysing the effect of the lockout laws introduced in some areas of the Sydney CBD and nearby surrounds on the number of alcohol-related violent incidents. Suppose we have two samples of data on the number of violent incidents in a number of local areas of the Sydney CBD and nearby surrounds. Pubs, hotels and clubs located in a subset of these areas became subject to the lockout laws when they were introduced in 2014. The first sample is from 2010 before the introduction of the lockout laws, and the second is from 2015 after the introduction of the law. The hypothesis we wish to test is that the introduction of the lockout laws reduces violent incidents in the areas in which the lockout laws were put in place. We use a difference-in-difference model on the pooled data from 2010 and 2015. We find the following results: viol_inc hat = 33.21 (5.29) + 12.43lockout (7.01) – 4.19Yr2015 (2.98) – 3.32 (lockout x Yr2015) (1.85) N = 181, R^2 = 0.128 Where: viol_incis the…Identify the appropriate test to use for the following scenarios: The population of American adults watch 238 minutes of TV per day on average. I believe that providing adults with bicycles will decrease the daily TV-watching. I provide bicycles to 500 American adults and then measure their daily TV watching. The sample watched 204 minutes of TV per day on average. Did the bicycles decrease TV watching? Group of answer choices A)One-Sample T-Test B) Independent Groups T-Test C)Correlated Groups T-Test D) Linear Regression
- The National Association of Colleges (NAC) reported in 2003 that the mean starting salary for collegegraduates majoring in management information systems was $40,915 and for psychology major was$27,454. Suppose the NAC data are based on surveys of size 144 for each major, with a standarddeviation of $10,000 for the management information systems majors and $7000 for the psychologymajors. Construct and interpret a 95% confidence interval for the difference between two means.States (and provinces) that have control over taxation sometimes reduce taxes in an attempt to spur economic growth. Suppose that you are hired by a state to estimate the effect of corporate tax rates on, say, the growth in per capita gross state product (GSP).(i) What kind of data would you need to collect to undertake a statistical analysis?(ii) Is it feasible to do a controlled experiment? What would be required?(iii) Is a correlation analysis between GSP growth and tax rates likely to be convincing? Explain.The score of 8 candidates prior and after training are given below Test the hypothesis whether performance improved after the training at 5% los. Prior 84 48 36 37 54 69 83 96 After 90 58 42 44 62 81 84 86
- Why can we not use first differences when we have independent cross sections in two years (as opposed to panel data)?Mary Arnold wants to use the results of a random sample market survey to seek strong evidence that her brand of breakfast cereal has more than 20% of the total market. Formulate the null and alternative hypotheses, using P as the population proportion.Consider the following TSLS model, where Ability is an endogenous independent variable, while Educand Age are exogenous.Stage 1 : Ability = 0 + 1 Educ + 2 Age + 3 Expr + 4 ParEduc + 5 KWW + VStage 2 : log(Wage) = 0 + 1 Educ + 2 Age + 2 Ability + UIf we use the Sargan test, the rst-stage F test and the Hausman test together to decide whether aTSLS or an OLS would be more appropriate, ll in the following blanks: at the 5% signicance level, the critical value for the Sargan test is blank, and the critical value forthe Hausman test is blank; if we blank (reject or fail to reject) the Sargan test, blank (reject or fail to reject) the rst-stageF test, and blank (reject or fail to reject) the Hausman test, then it is implied that we shall use theTSLS instead of the OLS estimation.