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ADM2304: One Proportion
Dr. Suren Phansalker
Basic Theory:
(This is Strictly Optional!)
When (n p > 5) and so is (n q > 5),
(1
)
~(
)
,
(
)
p
pq
p
p
pNE
p
p p
nn
μσ
⎛⎞
−
==
=
=
⎜⎟
⎝⎠
/2
1
()
pp
Pz
z
p
αα
α
σ
−
−<
<
=
−
)
{
}
)
)
1
z
p
−−
>
>−
=−
1
z
p
−
>>
−
=
−
() 1
P
p
zp
p
p
σα
+>
>
−
=
−
, or
P
p
p
p
<
+
=
−
This is the CI:
p
p
p
σσ
<
+
This theoretical CI is some times written as:
Theoretical CI:
)
p
p
pz
p pz
n
−
±=
±
Obviously, ‘p’ is to be estimated and is
not
known.
This problem is circumvented by
using the sampleproportion
p
or
.
The CI is thus found by using the following
expression.
ˆ
p
Actual CI:
ˆˆ
)
ˆ
p
p
pz sp pz
n
−
±
1
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View Full Document An Example:
A random sample (Sample1 in C3) of 100 North American Males was taken.
Their
height was measured in inches.
The following data was the result.
Data Display
Sample1 (in c3)
60.5
73.0
67.3
67.3
71.0
65.0
79.2
65.0
72.3
67.6
62.2
75.4
74.9
69.3
61.3
71.4
67.0
67.8
70.1
68.2
67.1
75.7
72.8
71.1
67.8
70.3
74.4
66.7
73.6
66.8
64.2
61.8
71.7
65.1
69.1
69.1
72.0
72.2
69.5
64.7
68.1
64.5
69.8
70.0
76.1
66.8
65.7
69.6
70.1
66.2
75.3
63.3
67.2
75.2
76.6
68.9
72.3
77.1
66.4
69.8
70.7
70.1
74.8
72.7
73.9
62.5
60.3
65.6
66.2
73.7
61.8
61.4
69.0
74.4
67.8
63.2
67.3
67.5
63.0
75.6
72.2
63.0
52.1
63.7
68.8
66.4
71.5
68.0
64.2
76.7
71.6
68.1
74.4
65.3
69.4
70.5
72.4
73.9
64.8
69.4
Any male with a height of 70” or more was considered “Tall”.
Find:
a.
The 95% and 99% CIs for the population proportion of “Tall” people.
b.
Test the hypothesis that the population proportion is not 0.45.
c.
Test the hypothesis that the population proportion is more than 0.30.
d.
Test the hypothesis that the population proportion is less than 0.51.
For ‘b’, ‘c’, and ‘d’ use a Level of Significance (LS) of 5% and 1%.
This problem cannot be done without coding the data.
Coding allows us to make
groups; in this situation two groups: “Short” males less than 70” tall and
“Tall” males 70” or more in height.
It can be done readily as follows.
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This note was uploaded on 01/10/2012 for the course TEFLER 2304 taught by Professor Phansalker during the Winter '11 term at University of Ottawa.
 Winter '11
 Phansalker

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