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C
HAPTER
9
E
STIMATION
AND
CONFIDENCE
I
NTERVALS
1.
51.314 and 58.686, found by
55
2.58(10/ 49)
.
2.
38.911 and 41.089, found by
40 1.96(5/ 81)
.
3.
a.
1.581, found by
5/ 10
X
σ
=
b.
The population is normally distributed and the population variance is known.
c.
16.901 and 23.099, found by 20
±
3.099
4.
1.44
5.
a.
$20.
It is our best estimate of the population mean.
b.
$18.60 and $21.40, found by
$20 1.96($5/ 49)
.
about 95 percent of the intervals
similarly constructed will include the population mean.
6.
a.
$18.775 and $21.225, found by
$20 1.96($5/ 64)
.
b.
The confidence interval is based on the standard error computed by
/
s
n
.
As
n
, the
sample size, increases (in this case from 49 to 64) the standard error decreases and the
confidence interval becomes smaller.
7.
a.
8.60 gallons
b.
7.83 and 9.37, found by
8.60
2.58(2.30/ 60)
.
c.
If 100 such intervals were determined, the population mean would be included in about
99 intervals.
8.
5.29 and 6.81 errors found by
6.05 1.96(2.44/ 40)
.
9.
a.
2.201
b.
1.729
c.
3.499
10.
a.
2.145
b.
2.500
c.
1.796
11.
a.
The population mean is unknown, but the best estimate is 20, the sample mean.
b.
Use the
t
distribution as the standard deviation is unknown and the sample size is small.
However, assume the population is normally distributed.
c.
2.093
d.
Between 19.06 and 20.94, found by
2
20
2.093
20
.
e.
Neither value is reasonable because they are not inside the interval.
Chapter 9
81
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View Full Document12.
a.
The population mean is unknown, but the best estimate is 60, the sample mean.
b.
Use the
t
distribution as the standard deviation is unknown and the sample size is small.
However, assume the population is normally distributed.
c.
1.753
d.
Between 51.235 and 68.765, found by
20
60 1.753
16
.
e.
That value is reasonable because it is inside the interval.
13.
Between 95.39 and 101.81, found by
5.54
98.6 1.833
10
.
14.
Between 30.99 and 39.15, found by
6.02
35.07
2.624
15
.
15.
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 Spring '08
 HALEY

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