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
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
behind this?Getting Confidence Interval for y2:Conceptually Same Approach
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?The (1- )100% CI for y2: Working Through the Math
Notes: - the parent distribution y is assumed normal
- the CI is not necessarily symmetric about s2
a scaled X2
s^2 = y2
This area is 0.05
What are the critical values on the pdf?Estimating CI for y2:Example Problem
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?
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?Thinking About the Solutionto Example Problem
What keeps you from
determining it exactly?
is a “standard”
Which are the
random variables?Ratio of VarianceTwo Populations
all variablesCI for the Ratio of VariancesFrom Two Populations
Also a function of cost of sampling!
Recall our polling example… H is the “margin of error”