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IOE 265 – Fall 07
November 8, 2007
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So far we have used
point estimators
in order to estimate an unknown parameter.
Now we want
to see how reliable the estimator is.
In other words, we want to see how it will change if we
repeat the sampling.
An alternative to reporting a single value for the parameter being estimated is to calculate and
report an entire interval of plausible values – a
confidence interval
(CI).
A confidence level is a
measure of the degree of reliability of the interval.
Population Standard Deviation (σ) known
Open ‘Lab_8_Data.xls’, and look at the first tab (Normal CI), which provides 40 observations of
a variable that is known to be normally distributed with σ = 1:
1.
Press F9 to refresh the random numbers, taking note of how often the confidence interval
of Xbar (the sample average) captures the true mean of the distribution.
Approximately how
often does the true mean fall outside of that interval?
(0.5 point)
2.
Now, using the above result as a guide, write (in your own words) a definition of what
exactly a confidence interval tells us:
(1 point)
3.
If we are unhappy with the width of the confidence interval and would like to reduce it,
what are the 3 things we can do?
(Hint: what are the 3 variables that affect the width of a
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This lab report was uploaded on 04/01/2008 for the course IOE 265 taught by Professor Jin during the Spring '07 term at University of Michigan.
 Spring '07
 Jin

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