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Find the mean number of points for the basketball
team and the standard deviation.
Player
Points
St. Dev.
John
5
1
Tim
8
2
Ed
12
4
Marcus
10
3
Demetrius
14
4
Inference Test of
Difference of Means
Section 11.1
Experiment
 Separate – boys & girls.
 Take Pulse rates
Remember….
 Independent

Selection of one sample does not influence
the selection of the other sample
So if we want to estimate the difference in means
between two populations…..
 The point estimate is:
 So
For the difference of means what is the standard
deviation?
The properties of the sampling
distribution of x  x
1
 
x
 x
1
1
x2
x2


2
1   2
1
2
n1
2
2

n2
 If n1 and n2 are sufficiently large or the
populations normal, then the distribution will
be approximately normal.
So what is the z-score for the difference
in boys and girls pulse rates?
Remember: Use t test if σ is unknown
 T-Test statistic
t
x
1

 x 2   1   2 
2
s1
n1
Use boxplot to check
for normal if samples
are small & data
given.
2

s2
n2
So is there a difference between
boys and girls?
Assumptions:

D.F. is a little more complicated!
s
s 



n
n
2 
 1
2
1
df 
2
2
2
2
2
s 
s 




n
n
 1 
 2 

n1  1
n2  1
2
1
2
2
A conservative estimate of the P-value can be found
by using a df = smaller of either n1-1 or n2-1.
Let’s try one!
College financial aid offices expect students to
use summer earnings to help pay for college.
But how large are these earnings? One large
university studied this by asking a random
sample of 1296 students who had summer jobs
how much they earned. They were then
separated into two groups based on gender. Is
there a difference in the amount males and
females earn?
Amounts different for males &
females?
n
mean
st. dev.
Males
675
$1884.52
$1368.37
Females
621
$1360.39
$1037.46
Parameter:
 1 = true mean amount males earned
 2 = true mean amount females earned
Hypothesis
or
Assumptions
1. Random: samples chosen randomly
2. Approximately normal: n1>30 and n2>30.
3. Independent: more than 6750 males and
6210 females
Name
Use a 2 sample T test
of means since σ is
unknown
Test Statistic
Obtain a P-value
P-value = tcdf (7.81, ∞., 620)*2 ≈ 0
Now to finish it up!
Make a decision
Reject the Ho since p-value(0) < α (0.05)
State a conclusion
There’s sufficient evidence to support the claim
that there is a difference in the amounts
earned by males and females.
Pooling the Data
 If you prove the standard deviations are equal
then you can pool the data together.
 You don’t want to do this….it’s another type
of hypothesis test to prove standard
deviations equal
 Never Pool!
The Formula Sheet
If you bought a used camera in good condition from a friend, would you
pay the same as you would if you bought the same item from a stranger.
Friend
Stranger
275
260
300
250
260
175
300
130
255
200
275
225
290
240
300
Don’t forget the boxplot to show
normal!
Homework
 Worksheet #1
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