This is for Econometrics

Suppose you are interested in testing the null hypothesis that "half of the residents are against soda tax." For part (d) - (e), assume that n=200. As a result of the survey, you have already known that i=1100Yi=101200Yi=58 (d) (i) [7 pts.] Can you reject (with 5% size) the null hypothesis if you use p~a as an estimator for p ? Clearly state the theorems you referred to, your steps, and your reasoning. Writing only the equations and your answer will not be given credits. (ii) [3 pts.] Derive 95% confidence interval associated with the estimator pa~. (e) (i) [7 pts.] Can you reject (with 5% size) the null hypothesis if you use pb~ as an estimator for p ? Clearly state the theorems you referred to, your steps, and your reasoning. Writing only the equations and your answer will not be given credits. (ii) [3 pts.] Derive 95% confidence interval associated with the estimator pb~ (f) [5 pts.] Your colleague C (who is notorious for his laziness) suggested that "Why do not we ask the couples? We can finish the survey in half the time!!" Briefly explain why the independence of the sampling may be violated if we follow this suggestion. Suppose you are interested in testing the null hypothesis that "half of the residents are against soda tax." For part (d) - (e), assume that n=200. As a result of the survey, you have already known that i=1100Yi=101200Yi=58 (d) (i) [7 pts.] Can you reject (with 5% size) the null hypothesis if you use p~a as an estimator for p ? Clearly state the theorems you referred to, your steps, and your reasoning. Writing only the equations and your answer will not be given credits. (ii) [3 pts.] Derive 95% confidence interval associated with the estimator pa~. (e) (i) [7 pts.] Can you reject (with 5% size) the null hypothesis if you use pb~ as an estimator for p ? Clearly state the theorems you referred to, your steps, and your reasoning. Writing only the equations and your answer will not be given credits. (ii) [3 pts.] Derive 95% confidence interval associated with the estimator pb~ (f) [5 pts.] Your colleague C (who is notorious for his laziness) suggested that "Why do not we ask the couples? We can finish the survey in half the time!!" Briefly explain why the independence of the sampling may be violated if we follow this suggestion