for Midterm, Fall 2008
Statistics 301, Professor Wardrop
1. Sarah performs a CRD with a dichotomous re-
sponse. She obtains the sampling distribution of
the test statistic for Fisher’s test for her data; it
is given below.
x
P
(
X
=
x
)
P
(
X
≤
x
)
P
(
X
≥
x
)
−
0
.
6667
0
.
0001
0
.
0001
1
.
0000
−
0
.
5278
0
.
0024
0
.
0025
0
.
9999
−
0
.
3889
0
.
0242
0
.
0267
0
.
9975
−
0
.
2500
0
.
1104
0
.
1371
0
.
9733
−
0
.
1111
0
.
2588
0
.
3959
0
.
8629
0
.
0278
0
.
3220
0
.
7179
0
.
6041
0
.
1667
0
.
2094
0
.
9273
0
.
2821
0
.
3056
0
.
0652
0
.
9925
0
.
0727
0
.
4444
0
.
0075
1
.
0000
0
.
0075
(a) Find the P-value for the first alternative
(
p
1
> p
2
) if
x
= 0
.
1667
.
(b) Find the P-value for the second alternative
(
p
1
< p
2
) if
x
=
−
0
.
2500
.
(c) Find the P-value for the third alternative
(
p
1
n
=
p
2
) if
x
=
−
0
.
1111
.
(d) Determine
both
the P-value and
x
that sat-
isfy the following condition: The data are
statistically significant but not highly sta-
tistically significant for the second alter-
native (
p
1
< p
2
).
(e) Determine all combinations of P-values
and
x
’s that satisfy the following condi-
tion: The data are statistically significant
but not highly statistically significant for
the third alternative (
p
1
n
=
p
2
).
(f) Suppose that you want to draw the proba-
bility histogram of this sampling distribu-
tion. How tall is the rectangle centered at
x
= 0
.
0278
.
2. A comparative study, with two treatments, di-
chotomous response and randomization is per-
formed. The study is not balanced.
The observed value of the test statistic,
x
, is
a positive number. The exact P-values for all
three alternatives are obtained and are below.
0.3329, 0.6211 and 0.8234.
Match each P-value with its alternative.
Alternative
>
<
n
=
3. A comparative study, with two treatments, di-
chotomous response and randomization is per-
formed. The study is balanced.
The observed value of the test statistic,
x
, is
a negative number. The exact P-values for all
three alternatives are obtained. The three exact
P-values are below along with three other num-
bers. Also note that for the actual value of
x
,
P
(
X
=
x
) = 0
.
1257
.
0.0863, 0.1215, 0.4336, 0.6921,
0.8672 and 0.9507,
Identify the three P-value and match each with
its alternative.
Alternative
>
<
n
=
4. Consider an unbalanced study with ten subjects,
identified as A, B, C, D, E, G, H, J, K and L. In
the actual study,
•
Subjects A, B, C and D are assigned to the
first treatment, and the other subjects are
assigned to the second treatment.
•
There are exactly four successes, obtained
by A, E, G and L.
This information is needed for parts (a)–(c) be-
low.
(a) Compute the observed value of the test
statistic.
1