Econ 526 In Class Exercises
1.
Week 2
SAT scores are assumed to be normally distributed with mean=500 and SD=100.
Find the following:

Pr(X>=500)

Pr(X<=400)

Pr(500<X<650)
Econ 526 In Class Exercises
Week 2
2. Data on fifth-grade test scores fore 420 school districts yield a mean test score of
646.2 and a standard deviation of 19.5.
(a)
Construct a 95% Confidence Interval for the mean test score in the population.
(b) When the data area divided into districts with small classes (<20 students per
teacher) and large classes (over 20 students per teacher), we have the following:
Class Size
Average Score
Standard
N
Deviation
Small
657.4
19.4
238
Large
650.0
17.9
182
Is there statistically significant evidence that districts with smaller classes have higher
average test scores? Explain?
Econ 526 In Class Exercises
2.
Week 2
SAT scores are assumed to be normally distributed with mean=500 and SD=100.
Find the following:

æ X - m 500 - 500 ö
Pr(X>=500) Pr ç
³
÷ = Pr(z ³ 0) = .5
è s
100 ø

æ X - m 400 - 500 ö
Pr(X<=400) Pr ç
£
÷ = Pr(z £ -1) = ..1587
è s
100 ø
= 1 - F(1) = 1 - .8413 = .1587

Pr(500<X<650)
A- mö
500 - 500 ö
æ B-m
æ 650 - 500
Pr ç
<X<
= Pr ç
<X<
÷
÷
è s
è 100
s ø
100 ø
= Pr(1.5 < z < 0) = F(1.5) - F(0) = .9332 - .5 = .4332
2. Data on fifth-grade test scores fore 420 school districts yield a mean test score of
646.2 and a standard deviation of 19.5.
(a)
Construct a 95% Confidence Interval for the mean test score in the population.
Data on Sample size n  420, sample average Y
646.2 sample standard
deviation sY  195. The standard error of Y is SE (Y ) 
sY
n

19.5
 09515. The
420
95% confidence interval for the mean test score in the population is
  Y  196SE(Y )  6462  196  09515  (64434 64806)
(b) When the data area divided into districts with small classes (<20 students per
teacher) and large classes (over 20 students per teacher), we have the following:
Class Size
Average Score
Standard
N
Deviation
Small
657.4
19.4
238
Large
650.0
17.9
182
Is there statistically significant evidence that districts with smaller classes have higher
average test scores? Explain?
The data are: sample size for small classes n1  238, sample average Y 1  6574, sample
standard deviation s  194; sample size for large classes n2  182, sample average
1
Y 2  6500, sample standard deviation s2  179. The standard error of Y1  Y2 is
SE (Y1  Y2 ) 
s12 s22
19.42 17.92



 18281. The hypothesis tests for higher
n1 n2
238
182
average scores in smaller classes is
H 0  1  2  0 vs H1  1  2  0
The t-statistic is
t act 
Y 1  Y 2  6574  6500  40479
SE(Y 1  Y 2)
18281