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Stat
201
Exam
3
Spring
2008
Version 3 KEY
Page
1
of
10
1.
In order to estimate the proportion,
p
, of current smokers among all Pennsylvania
residents, suppose a random sample of 900 residents was chosen, and 90 of them were
found to be smokers.
(a)
Compute as necessary and report the value of the
sample
statistic
(i.e., the ‘point
estimate’ of the parameter of interest). Also, give its appropriate symbol.
[2 pts for symbol;
3
pts for value]
.10
900
90
=
“peehat
”
p
ˆ
=
.10
(symbol ) (numerical value)
[2 pts]
[3 pts]
(b)
Construct a 95% confidence interval for the proportion of smokers. [Show work.]
[5 pts]
n
)
p
(1
p
z
p
ˆ
ˆ
ˆ

±
– or –
Using z=2:
900
.10)
.10(1
2
.10

±
2(.01)
.10
±
=
.02
.10
±
=
=
.12)
,
(.08
[some rounding ok]
Using z=1.96:
900
.10)
.10(1
1.96
.10

±
1.96(.01)
.10
±
=
.0196
.10
±
=
=
.12)
,
(.08
[some rounding ok]
(c)
Report the margin of error.
[3 pts]
.02 or .0196
(depending which z was used)
[exercise 1 continues on next page]
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201
Exam
3
Spring
2008
Version 3 KEY
Page
2
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10
(d)
Suppose that, ten years ago, the proportion of smokers among all Pennsylvania
residents was 17%. Based on your confidence interval, is there evidence that the
proportion has changed from ten years ago? Give the best answer, as follows:
[4 pts total]
Choose the appropriate response:
The answer to this part depends on the interval, as follows:
If .17 outside
the interval
“yes” (changed) (this is the intended answer)
If .17 falls in
the interval
“no” (not changed)
(i)
yes, there is evidence the proportion has changed
(ii)
no, there isn’t evidence that the proportion changed
Because [select the appropriate reason]:
(i)
You checked to see if 0
.
10 is in the interval.
(ii)
You checked to see if 90 is in the interval.
(iii)
You checked to see if 1
.
96 is in the interval.
(iv)
You checked to see if 63 is in the interval.
(v)
You checked to see if
.
05 is in the interval.
(vi)
You checked to see if 0
.
07 is in the interval.
(vii)
You checked to see if 0
.
17 is in the interval.
(viii)
You checked to see if the margin of error is in the interval.
(ix)
You checked to see if zero is in the interval.
(x)
There were 90 smokers in the sample.
Stat
201
Exam
3
Spring
2008
Version 3 KEY
Page
3
of
10
2.
Hemoglobin is a protein in red blood cells that carries oxygen from the lungs to the
body tissues. Having too much hemoglobin can be bad.
The hemoglobin level for healthy adults follows a Normal distribution, with mean of 13
grams per unit of blood, and standard deviation
1
1
.
=
σ
grams per unit of blood.
To test whether eating meat is associated with abnormally high hemoglobin, suppose
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This note was uploaded on 02/01/2009 for the course STAT 36201 taught by Professor Gordon during the Fall '08 term at Carnegie Mellon.
 Fall '08
 gordon

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