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139
Lecture 14:
CHAPTER 6: HYPOTHESIS TESTING
Example:
Consider the population of weights (in kg) of all newborn
babies in Canada for a particular year. In this case, the
Population
Mean
is the average weight of all newborns in the population.
An
investigator may want to use a simple random sample of these
weights to determine if there is sufficient evidence to answer
questions like:
Is
> 3.2 kg?
or Is
< 3.2 kg?
or Is
3.2 kg?
Example:
Consider the population of all lakes in Nova Scotia.
A
biologist may be interested in the following
population proportion
:
= the proportion of all lakes in Nova Scotia that are seriously
affected by acid rain.
He/she may want to use a simple random
sample of lakes from this population to determine if there is sufficient
evidence to answer questions like:
Is
>.7?
or, Is
<.7?
or, Is
.7?
When drawing conclusions about a population using information from
a sample it is important to realize that one can NEVER be absolutely
certain the conclusion is correct.
This is because a sample, though it
may be “representative” of the population, only contains part of all the
information contained in the population.
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LargeSample Tests for a Population Mean
(Section 6.1, page 391)
A
statistical hypothesis
, or just
hypothesis
, is a claim or assertion
either about one or more population or process characteristics
(parameters).
Examples:
1) Parameter:
= proportion of email messages from hotmail that
are undeliverable
Hypothesis:
2) Parameters:
1
= true average lifetime for a particular namebrand
tire (miles)
2
= true average lifetime for a less expensive store
brand tire
Hypothesis:
Example:
A certain type of automobile engine emits a mean of 100
mg of oxides of nitrogen
x
NO
per second at 100 horsepower.
A
modification to the engine design has been proposed that may
reduce
x
NO
emissions.
The new design will be put into production if it
can be demonstrated that its mean emission rate is less than 100
mg/s.
A sample of 50 modified engines are built and tested.
The
sample mean
x
NO
emission is 92 mg/s, and the sample standard
deviation is 21 mg/s.
The question, therefore, is this:
Is it plausible that this sample, with
its mean of 92, could have come from a populations whose mean is
100 or more?
This is the sort of question that hypothesis tests are designed to
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This note was uploaded on 06/20/2011 for the course STAT 2800 taught by Professor Paula during the Winter '11 term at UOIT.
 Winter '11
 Paula

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