sol+API-202A+Assignment+1+S09 - API-202 Spring 2009...

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1 API-202 Spring 2009 Assignment #1: Review of Statistics and Intro to Stata Suggested Solutions The purpose of this exercise is to help you review some key concepts from API-201 and to become familiar with Stata. The assignment has 2 parts: Part I does not require Stata, while Part II does. We have provided a Stata tutorial which will enable you to practice the commands you will need in order to complete this assignment. The Stata tutorial is posted on the course page, together with this assignment. PART I – REVIEW OF STATISTICAL CONCEPTS FROM API-201 In this part of the assignment, we examine math test scores for a sample of California school districts. The appendix to this assignment, which reviews some of the relevant material from API-201, including formulas, may be helpful. Basic summary statistics for math test scores (math_scr) and the number of computers per student (comp_stu), by district, are reported below. sum math_scr comp_stu Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- math_scr | 420 653.3426 18.7542 605.4 709.5 comp_stu | 420 .1359266 .0649558 0 .4208333 1. Using this table and your knowledge of API-201, report the following statistics. a) Mean math test score ( X ) = 653.34 (read directly from data table) b) Variance of math test score ( 2 X S ) = (SD) 2 = (18.75) 2 = 351.72 (standard deviation taken from data table) c) Variance of mean math test score ( 2 X S ) = 2 X S = 351.72 = 0.84 N 420 d) Standard error of mean test score ( X S ) = 2 X S = 0.84 = 0.92 N 2. Estimate a 95% confidence interval for the mean math test score in this sample. To construct a 95% confidence interval for the sample mean ( X) calculate: X ± 1.96 * SE(X) Substituting from above: 653.34 ± 1.96(0.92) or [653.34 – 1.96(0.92), 653.34 + 1.96(0.92)] 653.34 ± 1.8 = [651.54, 655.14]
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2 3. Some education analysts have speculated that access to computers can increase math achievement. Let’s compare the average math test scores of computer-intensive districts (defined as having a computer per student ratio above the median) with the rest of the districts. Computer-intensive districts Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- math_scr | 210 657.81 18.91115 605.4 709.5 _______________________________________________________________________________ All other districts Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- math_scr | 210 648.8752 17.53241 612.5 703.6 3. Assuming independent random samples, indicate the value of: a) Mean difference in test scores between high-spending districts and low-spending ones Simply subtract the differences in means between the two types of districts. Mean for computer intensive districts (X
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This note was uploaded on 04/12/2009 for the course HKS API202A taught by Professor Levy during the Spring '09 term at Harvard.

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sol+API-202A+Assignment+1+S09 - API-202 Spring 2009...

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