1
1
Slide
Slide
Hypothesis Testing Part 2:
Where are we?
2
2
Slide
Slide
Orienting Ourselves:
We covered:
Descriptive
Statistics
•
How to describe
data:
•
Visually (table and
graphs)
•
Numerically
Probability
Inferential Statistics
•
Confidence Intervals
•
Testing hypotheses
about one
population
•
Testing hypotheses
Today’s Class
3
3
Slide
Slide
Statistical Inference About Means and
Proportions With Two Populations
Inferences About the Difference Between
Two Population Means: Independent Samples
Inferences About the Difference Between
Two Population Means:
Matched Samples
Inferences About the Difference Between
Two Population Proportions
4
4
Slide
Slide
Abortions and Mental Health:
Do abortions cause mental health
problems?
5/studyabortionsdontcausementalhe
althissues
From the world of research…
What were the two populations that were
being studied?
5
5
Slide
Slide
Illustrative Example:
Do people drive faster in Richmond or in
Surrey?
o
How would you test this?
6
6
Slide
Slide
Estimating the Difference Between
Two Population Means
m
1
–
m
2
= difference between
the mean speeds
x
1

x
2
= Point Estimate of
m
1
–
m
2
Population 1
Traffic Speed Richmond
m
1
= average speed of
driver in Richmond
Population 1
Traffic Speed Richmond
m
1
= average speed of
driver in Richmond
Population 2
Traffic Speed, Surrey
m
2
= average speed
of driver in
Surrey
Population 2
Traffic Speed, Surrey
m
2
= average speed
of driver in
Surrey
Surrey Sample
Simple random sample
of
n
2
Surrey drivers
x
2
= average speed among
Surrey Sample
Richmond sample
Simple random sample
of
n
1
Richmond drivers
x
1
= average speed among
Richmond sample
7
7
Slide
Slide
Inferences About the Difference Between
Two Population Means
Hypothesis Tests About
m
1
–
m
2
:
µ
1
≤ µ
2
:
µ
1
>µ
2
OneTailed
:
µ
1
= µ
2
:
µ
1
≠µ
2
TwoTailed
8
8
Slide
Slide
?
=
´
?
1
−
´
?
2
√
?
1
2
?
1
+
?
2
2
?
2
Test Statistic
Inferences About the Difference Between
Two Population Means
9
9
Slide
Slide
Difference Between Two Population
Means:
s
1
and
s
2
Unknown
Example:
Do people in Surrey drive faster than
people in Richmond?
Sample Size
Sample Mean
Sample Std. Dev.
Sample #1
Surrey
Sample #2
Richmond
24 drivers
2
8 drivers
65 km/hr
63 km/hr
2.56
km/hr
1.81
km/hr
10
10
Slide
Slide
Point estimate of
m
1

m
2
=
Point Estimate of
m
1

m
2
where:
m
1
= average speed of Surrey drivers
m
2
= average speed of Richmond drivers
= 65  63
=
2 km/hr
Okay.
So there’s a 2 km /hr difference between the
two sample averages.
Does that mean there’s a
difference between the average speed among the
population of Richmond and Surrey drivers?
x
x
1
2

11
11
Slide
Slide
Wait.
Why are we using ‘t’ instead of ‘z’?
And if we’re using a t distribution, how are
we going to calculate degrees of freedom?
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 Fall '14
 ALIHASSANLOU