 In
Chapter 10 we tested a parameter from a
population represented by a sample against a
known population ( p  p0 ).
 In chapter 11 we will test a parameter from
two samples to find if they come from the
same or different populations (i.e. p1  p2 ).
 We will be given two sets of sample data
from the experiment.
 If
the data from the two samples do not come
from the same individuals, the two sets are
independent.
 If the data from one sample comes from the
same individuals as the second sample and the
data are paired, the two sets are said to be
dependent.
 Dependent samples are said to be matched
pairs.

Determine whether the following samples are
independent or dependent:





A. A researcher wishes to compare salaries of men vs. women
and takes the data from married couples.
B. A comparison of history grades from a four year university
vs. a two year community college is made using a sample of
100 students from each type of institution.
C. The effectiveness of a weight loss program is determined
by taking the before and after weights from 50 people using
the program.
D. A comparison is made of weights of men ages 21 to 30 and
weights of men 31 to 40, by collecting data from 50 men in
each group.
E. The performance of two fuels is compared by using the two
fuels in each of 20 vehicles and measuring certain parameters.
 The
procedure is the same as it was for one
sample hypothesis testing.
 The test statistic and the p-value are found
using STAT TESTS 2-PropZTest.
 Example:
 Given: x1  368, n1  541, x2  351, n2  593
 Test the hypothesis
p1  p2 to a
significance of 0.10
 BMI
index is used to determine if men and
women were normal weight. 750 men and
750 women ages 20 to 25 were surveyed.
203 men and 270 women were considered
normal according to the index. Test the
claim that there is a difference between men
and women that are considered normal to a
significance of 0.10.
 The
procedure is the same as one sample
hypothesis testing.
 The test statistic and the p-value are found using
STAT TESTS 2-SampTTest.
 Given:
n1  25, x1  50.2, s1  6.4
n2  18, x 2  42.0, s2  9.9
Test the claim that 1  2 to a significance of
0.05.
Do students who first attend a community
college and then transfer to a 4 year college
take longer to graduate than students who
only attend a 4 year college. To find out the
following data was collected:
 Students who started at a 2 year college:

n1  268, x1  5.43, s1  1.162

Students who started at a 4 year college:

Test the claim that transfer students take
longer to a significance of 0.01.
n2  1145, x2  4.43, s2  1.015
 Another
method of testing hypothesis is using
Confidence Interval.
 A  B to see if H0  A  B should
 Testing
be rejected or fail to reject.


If 0 is in the Confidence Interval (the lower level
is negative and the upper level is positive), then
Fail to Reject the Null.
If the 0 is outside the Confidence Interval (both
sides of the Interval is positive or both sides are
negative), the Reject the Null.
 Data
is matched pairs. The data is normally
given as a table.
 The strategy is to test the difference between
the two values of individuals using a one sample
test (TTEST).
 As an example:
After
125
134
156
105
143
148
Before
130
126
151
108
150
148
-5
8
5
-3
-7
0
Difference

after  before implies after  before  0 or
 diff  0
 Procedure:
 1.
Put “after” values in L1, and “before”
values in L2. Go to the header of L3 and
enter “l1-l2” and click enter.
 2. STATS TESTS TTest Data. Enter
0  0,
List = L3, Freq = 1, and
.
H1
 3. The average difference
is
, s is
d
x
d
x
 4. As usual the test statistic and p-values are
the t and p, respectively.
s
 Are
sons normally taller than their fathers?
 To test this the following data was collected:
Father
70.3
67.1
70.9
66.8
72.8
70.4
71.8
Son
74.1
69.2
66.9
69.2
68.9
70.2
70.4
Father
70.1
69.9
70.8
70.2
70.4
72.4
Son
69.3
75.8
72.3
69.2
68.6
73.9
 Test
the claim that sons’ height is > fathers’ or
that the bottom row is bigger so that
 father  son or  father  son  0 or d  0
 The
Critical Value for 2 Sample Hypothesis
Tests of Standard Deviation is the F
distribution. It looks like the Chi Squared
distribution.
 The Notation for the Critical Value is
Fsi gnificance,column,row
 For
a Right Tailed Test:
FRight  F ,n11,n21
 For
a left Tailed Test:
FLeft  F
Left
 For
1
 F ,n 21,n11
a Two Tailed Test:
 Use the formulas above but the significance
will be  / 2
 The
Test Statistic is found by
s12
F0  2
s2

The Test Statistic and p-value is found with
 STAT
TESTS 2-SampFTest
 Given
the following, test the claim that the
standard deviation of the population
represented by sample 1 is greater than that
of sample 2 (i.e. 1   2 ) to a significance of
0.01.
 Given
the sample data:
n  26, s  9.9
n  21, s  6.4
1
1
2
2
 Do
students who plan for financial aide have
more variability in SAT scores than students
who do plan financial aid. To find out the
following data was collected.
n  26, s  119.4
n  31, s  123.1
 Test
1
1
2
2
the claim that those planning financial aid
(sample 1) had less variability than those that
did not 1   2 to a significance of 0.05.