Nonparametric Statistics
17
Chapter 13: Nonparametric Statistics
131
0
:
.5
H
π
=
(there is no preference for one stock over the other)
1
:
.5
H
≠
(otherwise)
n = 11
For stock 2 and a twosided test, P(2
≥
X
≥
9) = 2P(X
≤
1) =
2[.0005 + .0054] = .0118
Therefore, reject
0
H
at levels of alpha in excess of 1.18%
132
0
:
.5
H
=
(there is no overall improvement in comprehension levels following
completion of the program)
1
:
.5
H
(the level of comprehension is increased by the program)
n = 9.
For 8 scores higher “After” and a onesided test,
P(X
≥
8) = .0176 + .002 = .0196
Therefore, reject
0
H
at levels of alpha in excess of 1.96%
133
0
:
.5
H
=
(grocery store managers are equally divided about customers attitudes
about electronic coupons)
1
:
.5
H
≠
(otherwise)
n = 11.
For 8 “yes” answers and a twosided test,
P(4
≤
X
≤
7) = 2P(X
≤
3) = 2[.0005 + .0054 + .0269 + .0806] = .2268
Therefore, reject
0
H
at levels of alpha in excess of 22.68%
134
0
:
.5
H
=
(positive and negative returns are equally likely)
1
:
.5
H
(positive returns are more likely)
n = 57.
39/57
.6842
x
p
=
=
57(.5)
28.5
n
μ
=
=
=
.5
.5 57
3.7749
n
σ
=
=
=
*
38.5 28.5
2.65
3.7749
S
Z


=
=
=
pvalue = 1 – F
z
(2.65) = 1  .9960 = .0040
Therefore, reject
0
H
at levels of alpha in excess of .40%
135
0
:
.5
H
=
(voters are evenly divided)
1
:
.5
H
≠
(otherwise)
n = 130 – 18 = 112.
68/112
.6071
x
p
=
=
112(.5)
56
n
=
=
=
.5
.5 112
5.2915
n
=
=
=
*
67.5 56
2.17
5.2915
S
Z


=
=
=
pvalue = 2[1 – F
z
(2.17)] = 2[1  .9850] = .030
Therefore, reject
0
H
at levels of alpha in excess of .30%
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136
0
:
.5
H
π
=
(economists’ profession is equally divided on whether the inflation
rate will increase)
1
:
.5
H
≠
(otherwise)
n = 49,
29/ 49
.5918
x
p
=
=
49(.5)
24.5
n
μ
=
=
=
.5
.5 49
3.50
n
σ
=
=
=
*
28.5 24.5
1.14
3.50
S
Z


=
=
=
pvalue = 2[1 – F
z
(1.14)] = 2[1  .8729] = .2542
Therefore, reject
0
H
at levels of alpha in excess of 25.42%
13.7
Openended question.
The findings should include statements about the relative
size of the firms.
The MIPS firms have larger total assets than do nonMIPS
comparable firms.
This holds true in both the Utilities as well as Industrial
industries and for the overall total.
Results of interest coverage and longterm
debttototalasset ratios varies depending on which test and which type of
industry the firms are in.
While publicly traded MIPS firms in the utilities
industries have significantly higher longterm debttototalasset ratio then do
nonMIPS firms, the MIPS firms in the industrials do not.
13.8
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 Spring '09
 StevenJordan
 Business & Economics, Nonparametric statistics, Spearman's rank correlation coefficient, levels

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