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Learning Objectives
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Describe the hypothesis testing process
Distinguish the types of hypotheses
Explain hypothesis testing errors
Solve hypothesis testing problems
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One population mean
One population proportion
One & two-tailed tests
Statistical Methods
Statistical
Statistical
Methods
Methods
Descriptive
Descriptive
Statistics
Statistics
Inferential
Inferential
Statistics
Statistics
Estimation
Estimation
Hypothesis
Hypothesis
Testing
Testing
What’s a Hypothesis?
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A belief about a
population parameter
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Parameter is population
mean, proportion,
variance
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Must be stated
before analysis
I believe the mean GPA
of this class is 3.5!
© 1984-1994 T/Maker Co.
Null Hypothesis
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What is tested
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Has serious outcome if incorrect decision made
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Always has equality sign: =, , or 
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Designated H0
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Pronounced ‘H sub-zero’ or ‘H oh’
Example
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H0: m  3
Alternative Hypothesis
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Opposite of null hypothesis
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Always has inequality sign: , <, or >
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Designated H1
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Example
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H1: m < 3
Basic Idea
Sampling Distribution
It is unlikely
that we would
get a sample
mean of this
value ...
... therefore,
we reject the
hypothesis
that m = 50.
... if in fact this were
the population mean
20
mm == 50
50
H0
Sample
Sample Mean
Mean
Level of Significance
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Defines unlikely values of sample statistic if
null hypothesis is true
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Designated a (alpha)
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Called rejection region of sampling distribution
Typical values are .01, .05, .10
Selected by researcher at start
Rejection Region (One-Tail Test)
Sampling Distribution
Level of Confidence
Rejection
Rejection
Region
Region
a
1-a
Nonrejection
Nonrejection
Region
Region
Critical
Critical
Value
Value
Ho
Ho
Value
Value
Sample
Sample Statistic
Statistic
Rejection Regions (Two-Tailed
Test)
Sampling Distribution
Level of Confidence
Rejection
Rejection
Region
Region
1/2
1/2 aa
Rejection
Rejection
Region
Region
1-a
Nonrejection
Nonrejection
Region
Region
Critical
Critical
Value
Value
1/2
1/2 aa
Ho
Ho
Sample
Sample Statistic
Statistic
Value
Critical
Value Critical
Value
Value
Errors in
Making Decision
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Type I error
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Reject true null hypothesis
Has serious consequences
Probability of Type I error is a
• Called level of significance
Type II error
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Do not reject false null hypothesis
Probability of Type II error is b (Beta)
Truth
Ho:
Ho:
Decision
Ha:
Ha:
Decision Results
H0: Innocent
Jury Trial
H00 Test
Actual Situation
Actual Situation
Verdict
Innocent Guilty Decision H00 True
Innocent Correct
Guilty
Error
Error
Do Not
Reject
H00
Correct
Reject
H00
1-a
H00
False
Type II
Error
(b)
Type I
Power
Error (a) (1 - b)
a & b Have an
Inverse Relationship
You can’t reduce both
errors simultaneously!
b
a
H0 Testing Steps
n
State H0
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Set up critical values
n
State H1
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Collect data
n
Choose a
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Compute test statistic
n
Choose n
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Make statistical decision
n
Choose test
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Express decision
p-Value
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Probability of obtaining a test statistic more
extreme ( or  than actual sample value
given H0 is true
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Called observed level of significance
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Smallest value of a H0 can be rejected
Used to make rejection decision
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If p-value  a, do not reject H0
If p-value < a, reject H0