Additional Hypothesis Test Problems
Page 1 of 1
The CEO of a company believes that more than 80 percent of the company's customers are “very satisfied”. To
test his belief, the CEO surveys 100 customers, of which 87 say they are “very satisfied”. Based on these results,
can we conclude that more than 80 percent of the customers are very satisfied? Assume a significance level of
0.05.
1.
H
o
:
p
= 0.80
2.
H
a
:
p
> 0.80
3.
87
.
0
100
87
ˆ
=
=
p
4.
Mean and standard deviation of the sampling distribution of
p
ˆ :
p
= 0.8 and
04
.
0
100
16
.
0
100
)
20
.
0
)(
80
.
0
(
)
1
(
.
.
=
=
=
−
=
n
p
p
dev
std
5.
8
.
1
75
.
1
04
.
0
07
.
0
04
.
0
80
.
0
87
.
0
.
.
ˆ
≈
=
=
−
=
−
=
−
dev
std
p
p
score
z
z
–
score
of 1.8 is the 96.41
th
percentile.
6.
Pvalue = probability we would obtain a
87
.
0
ˆ
=
p
or greater if
p
= 0.80
= proportion of the data that is greater than
87
.
0
ˆ
=
p
= 1 – 0.9641 = 0.0359
7.
Pvalue (0.0359) <
α
(0.05), so Reject H
o
: There is sufficient evidence at the 0.05 level of significance
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This note was uploaded on 06/13/2011 for the course STAT 110 taught by Professor Johnson during the Spring '07 term at South Carolina.
 Spring '07
 JOHNSON

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