Statistics 252 – Homework #2 Solutions – Summer 2011
STAT 252 Homework 2 Solutions (30 marks) – Due Monday, July 18 at 10 pm
1.
(3 marks)
A psychology student, interested in the migratory eating habits of human
organisms during the lunch hour upon the university campus, sections “Quad” into six
sections. Over the course of two
full
weeks, the student measured the organism concentration
for
each day
in each section.
Set up the null and alternative hypotheses to test for any
difference between the average concentrations of humans among the sections. What is the
distribution of the test statistic under the null hypothesis?
Define
:
μ
i
= average concentration of humans from
i
th
section,
i
= 1, …, 6
Given
:
I
= 6,
N
= 6 × 14 = 84.
H
0
: All sections have the same average concentration.
Æ
All means are equal (OneMean model:
μ
1
=
μ
2
=
μ
3
=
μ
4
=
μ
5
=
μ
6
Æ
μ
)
H
A
: Not all sections have the same average concentration.
Æ
Not all means are equal (SixMean model:
μ
1
,
μ
2
,
μ
3
,
μ
4
,
μ
5
,
μ
6
)
1
)
(
)
(
)
(
0
~
−
−
−
=
I
I
N
f
df
r
df
f
df
F
F
F
(since the test is a OneFactor ANOVA
F
test)
Thus, the distribution of the test statistic under
H
0
is
5
78
F
.
2.
(3 marks)
Consider a situation where there are nine sections of Statistics 252. There are three
instructors and each instructor teaches three sections. Each section has 50 students enrolled.
Define the null and alternative hypotheses for the test to determine if any instructor has
different marks between their own sections. What is the distribution of the test statistic under
the null hypothesis?
Define
:
μ
i
= average mark from
i
th
section,
i
= 1, …, 9
Also, let the instructors be instructor A, B, and C.
Let
μ
1
,
μ
2
, and
μ
3
be the means for the three sections for instructor A.
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 Summer '11
 PaulCartledge
 Statistics, Null hypothesis, Statistical hypothesis testing

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