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Lecture 16:
CHAPTER 6: HYPOTHESIS TESTING
LargeSample Tests for the Difference Between
Two Means (Section 6.5, page 418)
So far, we’ve only been looking at a single mean, it’s now time to
extend our knowledge of hypothesis tests on 2 means.
Specifically,
two means which come from large sample sizes.
Our formulas start
to change, as well as our hypothesis.
We now investigate examples
in which we wish to determine whether the means of two populations
are equal.
As an example to set up a hypothesis:
Suppose that a production manager for a manufacturer of industrial
machinery is concerned that ball bearings produced in environments
with low ambient temperatures may have smaller diameters than
those produced under higher temperatures.
Set up the hypothesis:
To investigate this concern, she samples 120 ball bearings that were
manufactured early in the morning, before the shop was fully heated,
and finds their mean diameter to be 5.068 mm and their standard
deviation to be 0.011 mm.
She independently samples 65 ball
bearings manufactured during the afternoon and finds their mean
diameter to be 5.072 mm and their standard deviation to be 0.007
mm.
Can she conclude that ball bearings manufactured in the
morning have smaller diameters, on average, than ball bearings
manufactured in the afternoon?
2
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 Winter '11
 Paula

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