Chapter 13
Experiments and QuasiExperiments
±
Solutions to Exercises
1.
For students in kindergarten, the estimated small class treatment effect relative to being in a regular
class is an increase of 13.90 points on the test with a standard error 2.45. The 95% confidence
interval is 13.90
±
1.96
×
2.45
=
[9.098, 18.702].
For students in grade 1, the estimated small class treatment effect relative to being in a regular class is
an increase of 29.78 points on the test with a standard error 2.83. The 95% confidence interval is
29.78
±
1.96
×
2.83
=
[24.233, 35.327].
For students in grade 2, the estimated small class treatment effect relative to being in a regular class is
an increase of 19.39 points on the test with a standard error 2.71. The 95% confidence interval is
19.39
±
1.96
×
2.71
=
[14.078, 24.702].
For students in grade 3, the estimated small class treatment effect relative to being in a regular class is
an increase of 15.59 points on the test with a standard error 2.40. The 95% confidence interval is
15.59
±
1.96
×
2.40
=
[10.886, 20.294].
2.
(a) On average, a student in class A (the “small class”) is expected to score higher than a student in class
B (the “regular class”) by 15.89 points with a standard error 2.16. The 95% confidence interval for
the predicted difference in average test scores is 15.89
±
1.96
×
2.16
=
[11.656, 20.124].
(b) On average, a student in class A taught by a teacher with 5 years of experience is expected to score
lower than a student in class B taught by a teacher with 10 years of experience by 0.66
×
5
=
3.3
points. The standard error for the score difference is 0.17
×
5
=
0.85. The 95% confidence interval
for the predicted lower score for students in classroom A is 3.3
±
1.96
×
0.85
=
[1.634, 4.966].
(c) The expected difference in average test scores in 15.89
+
0.66
×
(
−
5)
=
12.59. Because of random
assignment, the estimators of the small class effect and the teacher experience effect are
uncorreleated. Thus, the standard error for the difference in average test scores is
1
2
222
[2.16
( 5)
0.17 ]
2.3212.
+− ×
=
The 95% confidence interval for the predicted difference in
average test scores in classrooms A and B is 12.59
±
1.96
×
2.3212
=
[8.0404, 17.140].
(d) The intercept is not included in the regression to avoid the perfect multicollinearity problem that
exists among the intercept and school indicator variables.
3.
(a) The estimated average treatment effect is
TreatmentGroup
Control
XX
−
=
1241
−
1201
=
40 points.
(b) There would be nonrandom assignment if men (or women) had different probabilities of being
assigned to the treatment and control groups. Let
p
Men
denote the probability that a male is
assigned to the treatment group. Random assignment means
p
Men
=
0.5. Testing this null
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 Spring '09
 Smith
 Normal Distribution, Regression Analysis, class a, treatment effect, β1 Xit

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