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ADM2304
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Lecture 7

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Administration

ADM2304

Tony Quon

Fall

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—> There is good evidence that the avg. bill in Munic. II exceeds $80
1) H : µ − µ = 0
e.g, Is there evidence of a difference in avg. monthly bills? 0 1 2
H : µ − µ ≠ 0
a 1 2
2) α = 0.05
df = 40.13 3) UnequalVariance version:
(x1− x 2−0 115−98
4) To determine whether to reject, we need to look at the tstat 2 2 = 2 2 = 2.37
s1 s2 30 18
row in the t-table with 40 degrees of freedom + +
n 1 n 2 25 21
t.01,40= 2.423> t stat> t.025,40= 2.021
⇒ 2×.01< P− value< 2×.025
—> There is evidence at the 5% signiﬁcance level of a difference in avg. monthly bills between
municipalities
3) EqualVarianceversion:
2 2 2 2
2 (n1−1)s1+(n −2)s 2 (25−1)30 +(21−1)18
sp= = = 638.2
n1+ n2−2 25+ 21−2
s = 25.26
p
(x1− x2)−0 115−98
stat = = 2.2
1 1 1 1
sp n +n 25.26 25 + 21
1 2
4) To determine whether to reject, we need to look at the row in the t-table with .01.402.423> tstat .025,402.021
44 degrees of freedom. However, the text only gives rows for d.f. 40 and 45 ⇒ 2×.01< P−value< 2×.025
—> In this case the conclusion in both the pooled and the unpooled version was
to reject the null so….
—> There is evidence at the 5% signiﬁcance level of a difference in avg. monthly bills between
municipalities
Non-independent Populations:
Subjec “Before” “After” Differenc
Matched Pairs t-Test: t e
—> Two linked measurements - i.e. “before” and “after”
1 … … d1
2 … … d2
3 … … d3
… … … …
n … … d
n Method: H0:µd= 0 Teststatisticstat d −0
—> Compute the mean and SD of the differences and perform a one sd/ n
H :µ ≠ 0 (or >,stat
e.g, Learning Evaluation or rejec0 H stattα/2,n-1stat −α/2,n-1
Subjec Pre-test Post-test Post-Pre
t
1 30 29 -1 d =1.45
2 28 30 2

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