Topics for Today
More on the framework of Hypothesis
Testing
Hypotheses evaluating a single mean
Test Statistics
Stat203
Fall 2011 – Week 8 Lecture 1
Page 1 of 25
Hypothesis Testing
_______ is the method to evaluate the veracity
of hypotheses based on data.
Why do we do this?
Research is about ________________.
Hypothesis testing doesn’t give us the
answers, but tells us what side the ________
leans to.
Stat203
Fall 2011 – Week 8 Lecture 1
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Elements of Hypothesis Testing
There are 4 primary Elements to Hypothesis
testing:
1.
2.
3.
4.
________ __________
________________ _________
_____________________
____________ __________
Last lecture we gave a high – level
introduction to these.
Now some more details.
Stat203
Fall 2011 – Week 8 Lecture 1
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Hypotheses for a Single Mean
The following are examples of ________
__________ for a single mean.
First we’ll state the ________ hypothesis in
words, then state the ____ and
_________interms of statistics (ie: parameters
and numbers).
The research hypothesis is also often called
the ___________ hypothesis, and denoted H_
or H_.
Stat203
Fall 2011 – Week 8 Lecture 1
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Example 1: A newspaper article claims that
preschool children aged 3 to 5 watch an
average of 23.5 hours of television per week.
A researcher at a university thinks this is an
overestimate and plans to randomly select 60
children and measure their TV activity.
Research Hypothesis:
Individual:
Population:
Variable of interest:
Parameter:
Statistical null and research (alternative)
hypotheses:
Stat203
Fall 2011 – Week 8 Lecture 1
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Example 2: A labour union claims that the
average wage for their members is $30,000/yr.
You have a number of friends in this union and
believe this is too low.
Research Hypothesis:
Individual:
Population:
Variable of interest:
Parameter:
Statistical null and research (alternative)
hypotheses:
Stat203
Fall 2011 – Week 8 Lecture 1
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Example 3: The Survey of Study Habits and
Attitudes (SSHA) is a psychological test that
measures students’ attitude toward school and
study habits. The mean score for US college
students is 115. A teacher suspects that older
students have better attitudes toward school
and gives the SSHA to 25 mature (> 30 years
old) students.
Research Hypothesis:
Individual:
Population:
Variable of Interest:
Parameter:
Stat203
Fall 2011 – Week 8 Lecture 1
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Statistical Null and alternative hypotheses:
Stat203
Fall 2011 – Week 8 Lecture 1
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In all three of the preceeding examples, we
are given some value of µ and pose a
question.
We then would gather data and determine
whether the data provides evidence
 supports the null hypothesis
or
 does not support the null hypothesis
Let’s reconsider these examples, and consider
values of the sample mean which would either
support or contradict the null hypothesis.
Stat203
Fall 2011 – Week 8 Lecture 1
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Possible values of X
Example
Kids TV
watching
supporting H0
not supporting H0

Union member
wages
Study Habits &
Attitude
Stat203
Fall 2011 – Week 8 Lecture 1
Page 10 of 25
One-Sided and Two-Sided Hypotheses
Each of these examples involved hypotheses
that are “_________”
A _________ hypothesis is used when our
research hypothesis is concerned only with a
single ‘_________’.
eg:
- union members make more than …
- children watch less than …
- scores of mature students are higher than
…
If we are ___ concerned about a specific
direction we can use a _______ hypothesis;
so we accumulate ________ against the null if
our sample mean is ________ or _______!
Stat203
Fall 2011 – Week 8 Lecture 1
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Example4: A cable company’s service
technicians are expected to complete installation
of a cable box within 45 minutes. One of the
managers reviews the last 20 service calls to see
if the installation time is different than 45 minutes.
Research Hypothesis:
Individual:
Population:
Variable of interest:
Parameter:
Statistical null and research (alternative)
hypotheses:
Stat203
Fall 2011 – Week 8 Lecture 1
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Calculating a Test Statistic
Once we have defined our hypotheses, and
collected our data, we need some way to
_______ how much support our sample gives
___ or _______ the _______________.
We do this using a ______________.
We’ve considered values of the sample mean
which support the null and alternative
hypothesis for the earlier examples …
consider the first example.
Stat203
Fall 2011 – Week 8 Lecture 1
Page 13 of 25
Time watching TV
[ Remember, the CLT means that as long as the
researcher takes a large enough sample, the mean
will be normally distributed! ]
So, if H0 is true, what’s the µ for the
distribution of the sample mean? Mark it on
the x-axis.
Stat203
Fall 2011 – Week 8 Lecture 1
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Select one of the possible values of the
sample mean which did not support the null
and draw it on the figure on the preceeding
page.
Now … we just have to figure out __________
it was that we could have obtained this sample
mean.
Because, even though a particular value of the
mean doesn’t support the null, we have to
decide if it is enough evidence to call the mean
false and ‘______’ the ____ hypothesis in
favor of the ___________.
Stat203
Fall 2011 – Week 8 Lecture 1
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Evidence against the Null
So, we have a normal distribution centered at
23.5 (thanks to the CLT) and we want to know
the ___________ that we could have obtained
that particular sample mean.
In other words, if the null was true, is it likely
that the researcher would have observed such
a small sample mean?
Is it ________ that the true mean is smaller
than 23.5?
Consider this visually in the following applet.
http://www.intuitor.com/statistics/T1T2Errors.html
Stat203
Fall 2011 – Week 8 Lecture 1
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How Likely is our Sample Mean
To determine whether the sample mean we
observed is very unlikely, we could just use zscores and find a tail probability … right?
X  0
z
 n
Stat203
Fall 2011 – Week 8 Lecture 1
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[ minor aside on notation:
the mean value specified in the null
hypothesis is usually denoted as µ0
from the preceeding examples:
TV watching: µ0 = ____
Union salaries: µ0 = _______
Study Habits: µ0 = ___
Cable Installation: µ0 = __ ]
Stat203
Fall 2011 – Week 8 Lecture 1
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But … one thing is missing in this equation.
_____!
So, we’ll have to use the ______ standard
deviation s instead … and so we use the tdistribution again:
X  0
t n 1 
s n
t
Stat203
Fall 2011 – Week 8 Lecture 1
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In this setting, t is now the test statistic, for a
hypothesis test of a single mean!
The process is called the ______ for a single
mean and is probably the most widely used of
all statistical inference methods!
Let’s Try this out!
Stat203
Fall 2011 – Week 8 Lecture 1
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Example 5: Mean age of people in this class.
Research Hypothesis:
Individual:
Population:
Variable of interest:
Parameter:
Statistical null and research (alternative)
hypotheses:
Stat203
Fall 2011 – Week 8 Lecture 1
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Test Statistic:
Chance of obtaining our sample if the null is
true:
Conclusion?
Stat203
Fall 2011 – Week 8 Lecture 1
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P-values: the ______ of obtaining the test
statistic we observed (or something more
_______) if the ____ hypothesis is ____.
What is ‘likely’ and ‘unlikely’?
Stat203
Fall 2011 – Week 8 Lecture 1
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Topics for Today
Framework of Hypothesis Testing
- 4 Step Process
o Define Hypothesis
o Calculate Test statistic
o Calculate p-value
o Conclusion
Hypotheses evaluating a single mean
- one-sided hypotheses
- two-sided hypotheses
Test Statistics
- t-test for a single mean
Stat203
Fall 2011 – Week 8 Lecture 1
Page 24 of 25
Reading
First Section of Chapter 7
Stat203
Fall 2011 – Week 8 Lecture 1
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