9.31.
Righttail test.
Given:
μ
0
= $47.50 (the claim)
n
= 64
xbar = $51.00
s
= $12.00
Significance level: Use
α
= 0.05
a.
Mean quarterly water bill is at most $47.50 as claimed (for the
nationwide average) or it is higher (as suggested by the sample).
So
this is a righttailed test.
H
0
:
μ
≤
47.50
H
a
:
> 47.50
This is a righttailed test.
b.
333
.
2
=
64
00
.
12
50
.
47
00
.
51
=
=
0


n
s
x
t
μ
Degrees of freedom
df
=
n
– 1 = 63
Using
t
table: Search the row
df
= 63 for a value of 2.333 or close.
Reading across the row for
df
= 63, the
t
value 2.333 is between 1.998
and 2.387.
Reading up the column from 1.998 to the header, the area
= 0.025.
Reading up from 2.387 to the header, the area = 0.01.
As a result, using
t
table, the area in upper tail is between 0.025 and
0.01.
Therefore, the
p
value is between 0.025 and 0.01.
Exact
p
value corresponding to
t
= 2.333 is
p
= 0.0114 (by Excel, for
one tail; 0.01 < 0.0114 < 0.025).
With a
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 Spring '08
 SINGER
 Statistics, Statistical hypothesis testing, $12.00, $47.50, $51.00

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