Hypothesis Testing
In statistics, a
hypothesis
is a statement (a claim)
about a population parameter.
The statement is later
tested by collecting data.
The data either
supports
or
refutes
the statement (claim) made about the
parameter.
The process of collecting data and
determining whether the data supports or refutes the
stated hypothesis is called
hypothesis testing.
We will restrict our attention to
hypothesis testing for a
population mean (µ) using a
z
(in the case where
σ is
known
) or hypothesis testing for a population mean
using a
t
(in the case where
σ is unknown
and we
are using the sample standard deviation
s
as an
estimate for σ).
Examples of hypotheses for a population mean, µ
:
1.The mean highway gas mileage for
2010 Honda
CRVs is at least 27 mpg (
μ
≥
27).
2.The mean cost for tuition at
fouryear private
universities in the U.S. is no more than $30,000 (
μ
≤
$30,000 ).
3.The mean thickness of the flange on a 22 inch I
beams is .500 inch (µ = 0.500).
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Example
1
:
A consumer advocacy group would like
to test Honda’s claim that the mean gas mileage is at
least 27 mpg (µ ≥ 27), against the opposite claim—
that the mean gas mileage is less than 27 (µ < 27).
The consumer advocacy group decides to take a
random sample of 36 2010 Honda CRVs and
determine their highway mpg.
It finds that the mean
highway mileage for the 36 cars was 26.7 mpg (
x
=26.7).
Assume that the standard deviation,
σ,
is
known to be
1.8 mpg.
How likely were they to get a
sample mean of 26.7 mpg or less) if in fact the true
highway mileage is 27 mpg or higher?
If the
probability is sufficiently small we’ll conclude that μ <
27 mpg.
Example 2
:
To test the claim made by the IOPU
(independent organization of private universities) that
the mean cost of tuition at private universities in the
U.S. is no more than $30,000 (µ ≤ $30,000 ) against
the opposite claim that the mean is greater than
$30,000 (µ > $30,000) fifty private universities were
randomly sampled and their annual tuition cost
recorded.
The mean cost for the sample was $31,550
(
x
= $31,550) with a standard deviation of $5,400 (s
= $5,400).
What is the probability of getting a sample
mean this high or higher if the claim that the tuition is
no more than $30,000 per year (µ ≤ $30,000 ) is true?
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 Fall '09
 Rollins
 Statistics, Null hypothesis, Type I and type II errors

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