[size=14.000000pt]

希望大侠来帮个忙，也当给各位英雄练个手。感激不尽
[size=14.000000pt]

[size=14.000000pt]Problem set 1
[size=11.000000pt]1. A sample of [size=11.000000pt]n [size=11.000000pt]even observations is [size=11.000000pt]i.i.d [size=11.000000pt]and comes from a [size=11.000000pt]N [size=11.000000pt]～ [size=11.000000pt]([size=11.000000pt]μ, σ[size=8.000000pt]Y[size=8.000000pt]2 [size=11.000000pt])[size=11.000000pt]. Consider
                               
                       
                                                                                                [size=11.000000pt]the estimator [size=11.000000pt]Y[size=11.000000pt] ̃
[size=11.000000pt]Y[size=11.000000pt] ̃ [size=11.000000pt]= [size=8.000000pt]1[size=11.000000pt]([size=8.000000pt]1[size=11.000000pt]Y[size=8.000000pt]1 [size=11.000000pt]+ [size=8.000000pt]3[size=11.000000pt]Y[size=8.000000pt]2 [size=11.000000pt]+ [size=8.000000pt]1[size=11.000000pt]Y[size=8.000000pt]3 [size=11.000000pt]+ [size=8.000000pt]3[size=11.000000pt]Y[size=8.000000pt]4 [size=11.000000pt]+[size=11.000000pt]...[size=11.000000pt]+ [size=8.000000pt]1[size=11.000000pt]Y[size=8.000000pt]n[size=8.000000pt]−[size=8.000000pt]1 [size=11.000000pt]+ [size=8.000000pt]3[size=11.000000pt]Y[size=8.000000pt]n[size=11.000000pt])
                               
                       
                                                                                                                                                                                                                                                                        [size=8.000000pt]n[size=8.000000pt]222222
[size=11.000000pt]show that (a) [size=11.000000pt]Y[size=11.000000pt] ̃ [size=11.000000pt]is an unbiased estimator and (b) [size=11.000000pt]var[size=11.000000pt]([size=11.000000pt]Y[size=11.000000pt] ̃ [size=11.000000pt]) = 1[size=11.000000pt].[size=11.000000pt]25[size=11.000000pt]σ[size=8.000000pt]Y[size=8.000000pt]2 [size=11.000000pt]/n[size=11.000000pt]. Would
                               
                       
                                                                                                [size=11.000000pt]you choose this estimator instead of the sample average [size=11.000000pt]Y[size=11.000000pt] ̄[size=11.000000pt]?
                                        [size=11.000000pt]2. To investigate possible gender discrimination in a 􏰌rm, a sample of 100 menad 64 women with similar job descriptions are selected at random. A summary ofthe resulting monthly salaries in USD is as follows:
                               
                       
                                                                                                                        [size=11.000000pt]Average SalaryMen 3100
                                        [size=11.000000pt]Women 2900
                               
                                                                        [size=11.000000pt]Std Dev n200 100320 64
                               
                       
                                                                                                                                                [size=11.000000pt](i) What do these data suggest about wage di􏰋erences in the 􏰌rm? Do theyrepresent statistically signi􏰌cant evidence that wage of men and women are di􏰋er-ent?
                                        [size=11.000000pt](ii) Do these data suggest that the 􏰌rm is guilty of gender discrimination inits compensation policies? Explain.
                                        [size=11.000000pt]3. The data 􏰌le [size=11.000000pt]C P S [size=11.000000pt]92 [size=11.000000pt]− [size=11.000000pt]08 [size=11.000000pt]contains data on average hourly earnings forfull-time workers, de􏰌ned as workers employed more than 35 hours per week forat least 48 weeks in the previous year. The series in the dataset are:
FEMALE: 1 if female; 0 if male
YEAR: Year
AHE : Average Hourly Earnings
BACHELOR: 1 if worker has a bachelor degree; 0 if worker has a high school degree
                                        [size=11.000000pt]Use these data to answer the following questions:
                                        [size=11.000000pt](a) Compute the sample mean for average hourly earnings (AHE) in 1992 andin 2008. Construct a 95% con􏰌dence interval for the population means of AHE in1992 and 2008 and the change between 1992 and 2008.
                                        [size=11.000000pt](b) In 2008, the value of the Consumer Price Index ( CPI) was 215.2. In 1992,the value of the CPI was 140.3. Repeat (a) but use AHE measured in real USD2008; that is, adjust the 1992 data for the price in􏰍ation that occurred between1992 and 2008.
                               
                       
                                                                                               
                                                                                                [size=11.000000pt](c) If you were interested in the change in workers􏰎 purchasing power from1992 to 2008, would you use the results from (a) or from (b)? Explain.
                                        [size=11.000000pt](d) Use the 2008 data to construct a 95% con􏰌dence interval for the mean ofAHE for high school graduates. Construct a 95% con􏰌dence interval for the meanof AHE for workers with a college degree. Construct a 95% con􏰌dence interval forthe di􏰋erence between the two means.
                                        [size=11.000000pt](e) Did real (in􏰍ation- adjusted) wages of high school graduates increase from1992 to 2008? Did real wages of college graduates increase? Explain using appro-priate estimates and con􏰌dence intervals.
                                        [size=11.000000pt](f) Did the gap between earnings of college and high school graduates increase?Explain, using appropriate estimates, con􏰌dence intervals, and test statistics.
                                        [size=11.000000pt](g) Is there a gender gap for high school graduates in 2008? Is there a gendergap for college graduates in 2008? Are there any notable di􏰋erences between theresults for high school and college graduates?