Chapter 22 Notes Examples
Page 1 of 2
Example
•
We believe that the true proportion of all USC students from South Carolina is greater than 0.71.
H
0
: p = 0.71
H
a
: p > 0.71
•
In a sample of 100 students, 80 are from South Carolina.
80
.
0
100
80
ˆ
=
=
p
02
.
0
≈
−
value
p
•
So, if we took many samples and p = 0.71, we would get results this far or farther from p = 0.71 roughly
2% of the time.
•
We have good evidence against H
0
(and in favor of H
a
).
So, we would reject the null hypothesis and
conclude that the true proportion of USC students from South Carolina is greater than 0.71.
Calculating Pvalues
•
We conduct hypothesis test under the assumption that H
0
is true.
•
If the claim p = 0.71 were true and we tested many random samples of n = 100 students, the sampling
distribution of
p
ˆ would be approximately normal with
mean
= p = 0.71 and
standard deviation
=
0454
.
0
100
)
29
.
0
)(
71
.
0
(
)
1
(
≈
=
−
n
p
p
Calculating Pvalues
•
The alternative hypothesis is onesided (greater than), so the pvalue is the probability of getting an
outcome at least as large as
80
.
0
ˆ
=
p
.
•
Calculate the standard score of
80
.
0
ˆ
=
p
.
2
98
.
1
0454
.
0
71
.
0
80
.
0
.
tan
≈
=
−
=
−
=
−
deviation
dard
s
mean
n
observatio
score
z
•
Table B says that the standard score 2 is the 97.73
th
percentile of a normal distribution.
•
The proportion of data to the left of 2 is 0.9773.
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 Fall '07
 JOHNSON
 Statistics, Normal Distribution, Statistical hypothesis testing, tan dard .deviation

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