applied economics 2020 assignment

2. Coming back to this example we had in class: Populations and samples Suppose the population for variable Yi consists of unit 1 2 3 4 5 6 7 8 9 10 4 2 5 5 3 1 2 5 4 5 Population mean: 3.6 Samples: Sample 1 unit 1 2 4 8 Yi 4 2 5 5 Sample avg: 4 Sample 2 unit 2 5 9 Yi 2 3 4 Sample avg: 3 Standard Error (Mean) September 24, 2013 5 / 22 (a) What are the variance and standard deviation of the population mean Yi? (b) What is the standard error of the means of Samples 1 and Sample 2? (c) Suppose now we want to examine if the sample means of Sample 1 and Sample 2 are significant different from each other, what kind of test we shall use?

(d) What is the exact number and what does it tell us about the difference?

3. Suppose we are interested in find out whether increasing the availability of computer for student could help to improve their test scores. We start from two variables: the number of computers per student and test scores for 5th graders, comp stu and testscr.

Download the data set and read it into R. You could use the code in "ps2.R" to read in the dta dataset to R. It contains on 420 California school districts in 1999 on 14 variables. Description on these variables is as the following: ? district: District code. ? school: School name. ? county: County name. ? gr span: Grade span of district. ? tot: Total enrollment. ? teachers: Number of teachers. ? pct: Percent qualifying for (income assistance). ? meal pct: Percent qualifying for free lunch. ? computer: Number of computers. ? Average test scores. ? comp : Number of computers per student. ? : Number of expenditure per student. ? : Student-teacher ratio. ? Average income. ? el pct: Percent of English learners. ? read Average reading score. ? math scr: Average math score. (a) Draw a of test scores versus number of computers per student. Describe in words what you see. (b) Run the following bivariate regression of test scores on number of computers per student. Report the constant and slope coefficient. test = ? + ?comp stui + ei

(c) What is the predicted test scores of a district with number of computer per student as 0.094? What about 0.164? (d) What is the expected test score difference if the number of computer per student increase from 0.09 to 0.10? What about from 0.16 to 0.17? (e) What is the predicted test score of a district with number of computer per student as 10? Do you think this number is meaningful? Why or why not? (Note: There is no "correct" answer for this question, just think based on common sense).

2. Coming back to this example we had dicussed in class: Suppose the population for variable Y; consists of unit 1 2 3 4 5 6 7 8 9 10 4 2 5 5 3 1 2 5 4 5 Population mean: 3.6 Samples: Sample 1 Sample 2 unit 1 2 4 8 unit 2 5 9 Y; 4 2 5 5 Y; 2 3 4 Sample avg: 4 Sample avg: 3 (a) What are the variance and standard deviation of the population mean Y.? (b) What is the standard error of the means of Samples 1 and Sample 2? (c) Suppose now we want to examine if the sample means of Sample 1 and Sample 2 are significant different from each other, what kind of test we shall use? (d) What is the exact statisics number and what does it tell us about the difference?3. Suppose we are interested in nd out whether increasing the availability of computer for student could help to improve their test scores. We start from two variables: the number of computers per student and test scores for 5th graders, compstu and testscr. Download the data set caschool.dta and read it into R. You could use the code in \"ps2.R" to read in the dta dataset to R. It contains observatiosn on 420 California school districts in 1999 on 14 variables. Description on these variables is as the following: 0 district: District code. 0 school: School name. 0 county: County name. 0 gnspan: Grade span of district. 0 enrl_tot: Total enrollment. 0 teachers: Number of teachers. 0 calw_pct: Percent qualifying for CalWorks {income assistance). 0 mtmcht: Percent qualifying for free lunch. 0 computer: Number of computers. 0 testscr: Average test scores. 0 compstu: Number of computers per student. 0 expn_stu: Number of expenditure per student. 0 str: Studentteacher ratio. 0 avginc: Average income. 0 echt: Percent of English learners. o read_scr: Average reading score. 0 math_scr: Average math score. (a) Draw a scatterplot of test scores versus number of computers per student. Describe in words what you see. (b) Run the following bivariate regression of test scores on number of comput ers per student. Report the constant and slope coefcient. test scores,- = a + "remnpstm + e,- (c) What is the predicted test scores of a district with number of computer per student as 0.094? What about 0.164? (d) What is the expected test score difference if the number of computer per student increase from 0.09 to 0.10? What about from 0.16 to 0.17? (e) What is the predicted test score of a district with number of computer per student as 10? Do you think this number is econommically meaningful? Why or why not? (Note: There is no \"correct" answer for this question, just think based on common sense)