Statistics 528  Lecture 23
1
Statistics 528  Lecture 23
Prof. Kate Calder
1
Confidence Intervals and Hypothesis Tests
in Minitab
1. Use Minitab to get descriptive statistics and then use formulas.
2. Use Minitab directly to compute confidence intervals and perform
tests:
Stat => Basic Statistics => 1Sample Z
Note:
This function is for computing confidence intervals and hypothesis
tests of
°
, the population mean, assuming the population standard
deviation is known. (Section 6.1 and Section 6.2)
Statistics 528  Lecture 23
Prof. Kate Calder
2
Stat => Basic Statistics => 1Sample Z
•
Variables: enter column of data
•
Sigma: known value of the population standard deviation
•
Test Mean: value of mean under the null hypothesis (H
0
)
Statistics 528  Lecture 23
Prof. Kate Calder
3
Click on
Options
box
Confidence level: level C of confidence interval or level (1
±
) of a
hypothesis test
Alternative: form of alternative hypothesis
•
Not equal => H
0
:
° ²
μ
0
•
Less than => H
0
:
°
<
μ
0
•
Greater than => H
0
:
°
>
μ
0
Note: you need to select
not equal
as the alternative to calculate an equal
tails confidence interval (like the ones we’ve been doing).
Statistics 528  Lecture 23
Prof. Kate Calder
4
tTests
Previously, when making inferences about the population mean,
μ
,
we
were assuming:
1.
Our data (observations) are an SRS of size
n
from the population.
2.
The observations come from a normal distribution with parameters
μ
and
σ
.
3.
The population standard deviation
σ
is known.
Statistics 528  Lecture 23
Prof. Kate Calder
5
To perform statistical inference, we were using the test statistic (one
sample z statistic):
which has a
normal
distribution. This holds approximately for large
samples even if assumption 2 is not satisfied. Why?
CENTRAL LIMIT THEOREM
n
x
z
σ
μ
0

=
Statistics 528  Lecture 23
Prof. Kate Calder
6
Issue:
In a more realistic setting, assumption 3 is not satisfied. That is,
³
is unknown.
In more realistic situations where
³
is unknown, we can use the sample
standard deviation, s, as an estimate of the population standard
deviation,
σ
.
is called the
standard error
of the sample mean.
°
=


=
n
i
i
x
x
n
s
1
2
)
(
1
1
n
s
/
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Statistics 528  Lecture 23
2
Statistics 528  Lecture 23
Prof. Kate Calder
7
When making inferences about the population mean
μ
with
σ
unknown
,
we use the
onesample
t
statistic
:
Note: We are still assuming that assumptions 1 and 2 are satisfied.
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 Winter '09
 Calder
 Normal Distribution, Prof. Kate Calder

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