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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