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DSC 211
CLASS NOTES 21, page 1
Comparing Two Populations
REVIEW
Target Population: e.g., Customer Incomes (X)
MOD 1:
Questions (1 or 2sided) about:
across k categories
Analysis: 6 Step Hypothesis Testing
"Conclusion About
Specific Question (one or twosided)
the Claim"
1
Ho & Ha > Ha is same as the question
IN SHORT:
2
Test Stat
Is sample
Sample evidence inconclusive. Cannot conclude (Ha)
3
Alpha = usually 0.05
inconsistent
4
Reject Rule > Use TINV, CHIINV, NORMINV
with Ho ?
Reject rule is consistent with Ha.
If so, then
5
Calculate the Test Stat (from the sample results)
"yes" to
NOW:
Part 2 of our DSC 211 Course
pvalue > Use TDIST, CHIDIST, NORMDIST
bus question.
Comparing 2 or more Populations
6
Reject Ho or Do not reject Ho
Issue:
Population 1
Data:
Assembly
Plant 1 Assembly Times
Plant 2 Assembly Times
Times at
2 Plants
BQues:
Question (another way to state it):
Do the sample results provide evidence that the averages are different?
1
2
because we know its distribution
(2) If
Ho is true: t distribution
with df we can calculate
with df =
3
alpha = .05
4
Reject Ho if t < (low neg value) or t > (high pos value)
2sided Hyp
Use =TINV(.05,df)
5
from the two sample results
calculate these 1st four values
df =
use formula above to calc df
t=
use formula above to calc t
pvalue=
use TDIST with the t and df just calculated
Sample (n)
> Test Statistic
:
tTest for Mean, t
= (xbar  mu
o
) / (s/n^.5)
μ
 average income & some value, mu
o
ChiSq Test for Variance, ChiSq
= (n1)*s^2/var
o
σ
2
or var
 variability of incomes & a value, var
o
Normal Test for Prop, pbar
with stdev = (p
o
*(1p
o
)/n)^.5
p
 proportion of incomes > some value, p
o
ChiSq Goodness of Fit Test, ChiSq
= Sum of (fe)^2/e
p1,p2,p3, .
..
 distribution of incomes
First  comparing means (
μ
's)
xbar
1
xbar
2
Sample from 1 (n
1
)
s
1
^2
Sample from 2 (n
2
)
s
2
^2
μ
1
 ave time
μ
2
 ave time
Common question, "Are the assembly times different?" Which usually means >
Are
μ
1
and
2
different?
(Or, Do
μ
1
and
μ
2
differ by more or less than D?)
(Ques could be Is
μ
1
greater than
μ
2
?)
Ho:
μ
1
=
μ
2
,
(or,
μ
1

μ
2
= D, where
D=0
in this case)
Ha:
μ
1
<>
μ
2
,
Test Statistic. (1)
t = [(xbar
1
xbar
2
)  0]
(
(s
1
2
/n
1
+ s
2
2
/n
2
)^0.5
(s
1
^2/n
1
+ s
2
^2/n
2
)^2
(s
1
^2/n
1
)^2/(n
1
1) + (s
2
^2/n
2
)^2/(n
2
1)
xbar
1
=
xbar
2
=
s
1
^2=
s
2
^2=
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View Full Documentcan (cannot) conclude . . .
6
Reject or Do Not Reject Ho.
NOTE:
We will do calculations manually with the following example.
However, in practice we will use excel's tool:
Example:
Issue:
Two possible methods of assembly for new product.
Two Sample t Test> Unequal Variances
Question:
From data gathered using the two methods, can we conclude that the avg assembly times differ?
[If so, how?]
Data:
Samples of 25 randomly selected workers; recorded assembly times for each.
May not be explicit.
6.29
min
6.02
min
Diff =
0.27
What do you think about bus question
1. Hypotheses:
just looking at xbars  before Analysis?
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 Spring '07
 Dunne
 Variance

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