Startup Review Problems Ed257
D Rogosa
January 2001
1. Complete the Anova Table given below. Also state and carry
out a test of the omnibus null hypothesis with Type I error rate
.10.
SOURCE SS df MS
Between 80 4 **
Within ** * **
Total 480 44

2. Salary disputes and their eventual resolutions often leave both employer
and employees embittered by the entire ordeal. To assess employee reactions
to a recently devised salary and fringe benefits plan, the personnel
department obtained random samples of 15 employees from each of three
divisions: manufacturing, marketing, and research. Each employee sampled
was asked to respond (in confidence) to a series of questions. Several
employees refused to cooperate, as reflected in the unequal sample sizes.
Some data summary is given below.
Manufacturing Marketing Research
Sample Size 12 14 11
Sample mean 25.2 32.6 28.1
Sample Variance 3.6 4.8 5.3
a. Write a model for this data structure
b. Carry out an omnibus test of all three employee groups having equal
population means using a standard oneway analysis of variance procedure.
Use Type 1 error rate .01.

3. I've had more knee operations than you've have had statistics
courses....
From Neter Wasserman Kutner problem 16.12
A rehabililitation center researcher was interested in examining the
relationship between physical fitness prior to surgery of persons
undergoing corrective knee surgery and time required in physical therapy
until sucessful rehabilitation. 24 male subjects ranging in age from 18
to 30 years who had undergone similar corrective knee surgery during the
past year were selected for the study.
In the data file knee.dat in the class HW directory
[note path is /afs/ir.stanford.edu/class/ed257/HW or
/usr/class/ed257/HW ]
c1 contains the number of days required for sucessful completion of
physical therapy and c2 contains an indicator of prior physical fitness
status 1 = below average; 2 = average; 3 = above average.
(So this data set is of the form of a timetomastery study.)
a) obtain mean and variance of time to recovery for each group
b) present a graphical look at the scores for the three groups
by constucting aligned dotplots for the three groups
c) carry out an anova for this oneway classification and test the
omnibus null hypothesis of no differences between the group means
using Type I error rate .05.
d) display residuals from the fit of the anova model for each group.

4. Problem 1 from Review Problems (Jan '96)
Could You Get In? The director of admissions at a small college administered a
newly designed entrance test to 20 students randomly selected from the new
freshman class. The purpose was to study the relation between the entrance test
(in C2) and first year grade point average (GPA in C1). Minitab output given below.
MTB > plot c1 c2
 *
C1  *

 *
3.20+ *
 * *
 * *

 * *
2.40+
 * * *
 * *
 *
 *
1.60+ *
 * *

++++++C2
4.00 4.50 5.00 5.50 6.00 6.50
MTB > regress c1 on 1 c2
The regression equation is
C1 =  1.70 + 0.840 C2
Predictor Coef Stdev
Constant 1.6996 0.7268
C2 0.8399 0.1440
s = 0.4350 Rsq = 65.4%
MTB > regress c2 on 1 c1
The regression equation is
C2 = 3.05 + 0.778 C1
Predictor Coef Stdev
Constant 3.0539 0.3467
C1 0.7785 0.1335
s = 0.4188 Rsq = 65.4%
a. Using the scatterplot, give values for the median and quartiles
of GPA.
b. Use the entrance test to predict GPA. From the leastsquares fit
computed by Minitab, what is the predicted GPA for a student scoring 5.0? What
is the residual from the fit for a student scoring 6.0 on the entrance exam?
c. If the mean of the entrance exam scores is 5.0, what is the mean
GPA?
d. What's the correlation between GPA and the entrance exam?
NOTE the data reside in the class HW directory as admit.dat. Try to
reproduce the simple output above using Minitab.

5.
An experiment was run in which a tumor was induced in a laboratory
animal. The size of the tumor was recorded as
Number of Days Size of Tumor
After Induction (cc)
14 1.15
16 1.90
19 4.75
21 5.45
23 7.53
26 14.5
28 16.7
30 21.0
33 27.1
35 30.3
37 40.5
41 51.4
(You may want to "snip" these data out of this text for the analysis)
Use a polynomial regression model to carry out a test of
the curvilinear fit versus a straight line model? I.e.,
can you detect curvature in these data?

6. The 2x2 table below crossclassifies level of education (rows)
and voting intention (columns). Compute a measure of association
between these two variables and test whether the association is
different from zero.
Will Vote Not Vote
Some HS 1481 132
No HS 1036 173
