ENMA 420/520 Statistical Processes Spring 2007. Michael F. Cochrane, Ph.D. Dept. of Engineering Management Old Dominion University. Class Eight Readings & Problems. Continuing assignment from last week! Reading assignment M & S Chapter 7 Sections 7.1 – 7.7; 7.9, 7.11 Recommended problems
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ENMA 420/520Statistical ProcessesSpring 2007
Michael F. Cochrane, Ph.D.
Dept. of Engineering Management
Old Dominion University
Class EightReadings & Problems
What are the cases
in which the sampling
Now want to estimate 2y
What is the
Recall from Section 6.11
Which variables are random variables?
Here is conceptual approach to be taken:
- sample n observations
- calculate s02 from sample
- substitute for X02 in terms of s02 and y2 in the following
p(X2(1-/2) X02 X2(/2) ) = 1 -
- the above range provides the (1-)100% CI for y2
Where do we get these?
Notes: - the parent distribution y is assumed normal
- the CI is not necessarily symmetric about s2
This is pdf of s2,
a scaled X2
s^2 = y2
This area is 0.05
What are the critical values on the pdf?
How do you interpret the above confidence interval?
Your sample variance was 0.00009604, do you see that the
CI is not symmetric about your sample statistic?
This is the width of the CI,
the actual CI will depend on your sample.
This is THE pdf of s2,
a scaled X2 distribution.
For n=10, it exists and is
s^2 = y2
This is s^2 which
you do not know,
but you wish you did.
This area is 0.05,
how often will your sample s2
fall in this range?
What keeps you from
determining it exactly?
The F distribution
is a “standard”
Which are the
Take note of
Also a function of cost of sampling!
Small sample half-width for pop. mean
Recall our polling example… H is the “margin of error”