1
MASTER’S COMPREHENSIVE EXAMINATION
Part II Applied (90 minutes) April 7, 2012
Instructions: Attempt any three out of the following four questions
on both pages.
Mention which three you would like to have graded
. Open book and open notes.
1)
A researcher wants to compare two methods (M1 vs M2) to teach math.
The researcher
picks a random sample of 8 students, and assigns at random 4 students to learn under M1,
and the other 4 students under M2.
At the end of the term, the researcher picks at random 3
algebra problems, and 3 geometry problems.
All 8 students are given the same 6 problems.
The response variable Y is the number of minutes to solve the problem.
In what follows, let M denote Method, S denote Subject, P denote Problem, and T denote Type
of math(algebra vs geometry).
a)
Write out the ANOVA table just showing Sources of Variability and degrees of Freedom.
and indicate which SV are fixed effects and which are random.
b)
To test for Method effect, what MS terms go in numerator and what MS terms go in
denominator.
2)
Scientists are studying
the sizes of radio-electric disturbances known as “ka-chings” that occur on
Mars and Pluto.
They have obtained 15 measures of ka-chings from Pluto and 10 measures from
Mars.
Since Mars is closer to Earth, ka-chings of any size on Mars can be detected.
However,
because Pluto is much further away from Earth, only ka-chings that are larger than 3 units can be
measured.
Table of the 15 ordered Ka-ching measures from Mars and 10 ordered measures from Pluto
Mars
0.1
0.3
0.5
0.7
1
20
200
600
800
10,000
100,000
250,000
500,000
2,000,000
5,000,000
Pluto
5
50
55
1,200
2,000
5,000
25,000
40,000
1,000,000
10,000,000
A.
It is believed that the median size of a Ka-ching on Mars is 6 units.
Statistical test if the data
dispute this belief with a Type-1 error of 0.05.
B.
Perform the best test within the limits of the available data
of whether the central tendency of
the size of a Ka-ching is the same for Pluto as for Mars.
Remember, that because Pluto is much
further away from Earth, only Ka-chings that are larger than 3 units can be measured on Pluto.
Again use a type-1 error of 0.05.