Math 227
–
Elementary Statistics: A Brief Version, 5/e Bluman
Ch 7.1 pg. 364 #11, 13, 15, 17, 19, 21, 23, 25
11.
Reading Scores
: A sample of the reading scores of 35 fifth-graders has a mean of 82. The
standard deviation of the sample is 15.
Note:
All values we calculated were rounded.
a) Find the best point estimate of the mean.
X
Is the best point estimate for
, therefore, the best point estimate of the population
mean is
82
b)
Find the 95% confidence interval of the mean reading scores of all the fifth-graders.
n=35,
Confidence interval (C.I.) = 0.95,
82,
15
x
s
/2
0.05
0.05
0.025
2
2
1
0.025
0.975
(
)
1.96
Z
/2
/2
[
]
[
]
s
s
X
Z
X
Z
n
n
15
15
82
[1.96
]
82
[1.96
]
35
35
77
87
c)
Find the 99% confidence interval of the mean reading scores of all fifth graders.
/2
0.99
(
)
0.495
2
Z
To find
go to table E and look for area = .4950, the corresponding
z
value for this
area is 2.58.
/2
/2
[
]
[
]
X
Z
X
Z
n
n
82
[2.58 (2.5355)]
82
[2.58 (2.5355)]
/2
Z
/2
2.58
Z
0.95
/2
1.96
Z
0.025
0.975
0.95

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