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An outline of lecture 11 from math 1070-2 at the university of utah, focusing on statistical hypothesis testing for means. The lecture covers the assumptions, hypotheses, test statistic, p-value, and conclusion for testing means, using an example of weight change in girls with anorexia. The document also discusses the robustness of the test and calculating confidence intervals for the difference between two proportions.
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Lecture 11
Davar Khoshnevisan
Department of Mathematics
University of Utah
http://www.math.utah.edu/˜davar
April 9, 2008
Only 2 weeks left
I Complete the material of chapter 8:
I §8.3–§8.
I
Skip §8.5–§8.
I
§9.
Example 7, pp. 388–
I
Study different therapies for teenage girls with anorexia
I Weight measured before & after therapy
I
Variable: Weight change = wt after − wt before therapy
I n = 29 girls
I ¯ x = 3 .00 pounds, s = 7 .32 pounds
Continued
I Assumptions:
I Quant. var.
I Sampling not random [interpret results with care]
I
Normal population [could be... tentative]
I Hypotheses: [Is the test effective?]
I
H
0
: μ = 0 versus H a
: μ > 0
I Test statistic:
t =
x − μ
0
s /
n
I P -value: [Use t with n − 1 = 28 df]
I Conclusion: P -value 0.05 → reject H
0
[even for
a
: μ 6 = 0]
I
Point estimate for p
1
− p
2
is
p
1
p
2
I Fact:
p
1
p
1
n
1
p
2
p
2
n
2
I CI for p
1
− p
2
: [ n
1
and n
2
large]
(ˆ p
1
p
2
) ± z
p
1
p
1
n
1
p
2
p
2
n
2
pp. 429–
I Want difference between placebo & aspirin
I n
1
= 11034, n
2
= 11037 [large X]
p
1
p
2
p
1
p
2
I
p
1
p
1
n
1
p
2
p
2
n
2
I
95% CI for p
1
− p
2