Extra Exercises: Chapters 1–3
Statistics 301
Professor Wardrop
Section 2.3
1. Consider a balanced study with eight subjects,
identified as A, B, C, D, E, G, H, and J. In the
actual study,
•
A, B, C and D are assigned to the first
treatment, and
•
There are exactly four successes, and they
are obtained by A, B, C, and H.
This information is needed for parts (a)–(c) be
low.
(a) Compute the observed value of the test
statistic.
(b) Assume that the Skeptic is correct. Deter
mine the observed value of the test statistic
for the assignment that places A, D, E, and
G on the first treatment, and the remaining
subjects on the second treatment.
(c) We have obtained the sampling distribu
tion of the test statistic on the assumption
that the Skeptic is correct. It also is possi
ble to obtain a sampling distribution of the
test statistic if the Skeptic is wrong
pro
vided
we specify
exactly
how the Skep
tic is in error.
Assume that the Skeptic
is incorrect about subjects C, D, H, and
J, but correct about subjects A, B, E, and
G. This means that for subjects C, D, H,
and J, his/her/its response will change if
the treatment changes.
For the assignment that puts A, D, E, and
H on the first treatment, and the other sub
jects on the second treatment, determine
the response for each of the eight subjects.
2. Consider a unbalanced study with nine subjects,
identified as A, B, C, D, E, G, H, J, and K. In the
actual study,
•
A, B, C, D, and E are assigned to the first
treatment, and
•
There are exactly five successes, and they
are obtained by B, C, E, H, and J.
This information is needed for parts (a)–(c) be
low.
3. An unbalanced yields the data below.
Treatment
S
F
Total
1
a
b
10
2
c
d
5
Total
10
5
15
On the assumption the Skeptic is correct, list all
possible values of the test statistic.
4. A comparative study yields the following data.
Treatment
S
F
Total
1
a
b
5
2
c
d
4
Total
6
3
9
On the assumption the Skeptic is correct, deter
mine all possible values of the test statistic.
1
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Section 2.5
5. Below is the sampling distribution of the test
statistic for Fisher’s test for a comparative study.
x
P
(
X
=
x
)
P
(
X
≤
x
)
P
(
X
≥
x
)
−
0
.
405
0
.
0003
0
.
0003
1
.
0000
−
0
.
340
0
.
0019
0
.
0022
0
.
9997
−
0
.
275
0
.
0104
0
.
0126
0
.
9978
−
0
.
210
0
.
0378
0
.
0504
0
.
9874
−
0
.
145
0
.
0973
0
.
1477
0
.
9496
−
0
.
080
0
.
1782
0
.
3259
0
.
8523
−
0
.
015
0
.
2335
0
.
5594
0
.
6741
0
.
050
0
.
2172
0
.
7766
0
.
4406
0
.
115
0
.
1410
0
.
9176
0
.
2234
0
.
180
0
.
0620
0
.
9796
0
.
0824
0
.
245
0
.
0174
0
.
9970
0
.
0204
0
.
310
0
.
0028
0
.
9998
0
.
0030
0
.
375
0
.
0002
1
.
0000
0
.
0002
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 Fall '08
 ProfessorWardrop
 Statistics, Normal Distribution, Statistical hypothesis testing, Statistical significance

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