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Statistical Hypothesis Testing for Means: Spring 2008 Lecture 11 by Davar Khoshnevisan, Exams of Mathematics

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.

Typology: Exams

Pre 2010

Uploaded on 08/31/2009

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Math 1070-2: Spring 2008
Lecture 11
Davar Khoshnevisan
Department of Mathematics
University of Utah
http://www.math.utah.edu/˜davar
April 9, 2008
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Download Statistical Hypothesis Testing for Means: Spring 2008 Lecture 11 by Davar Khoshnevisan and more Exams Mathematics in PDF only on Docsity!

Math 1070-2: Spring 2008

Lecture 11

Davar Khoshnevisan

Department of Mathematics

University of Utah

http://www.math.utah.edu/˜davar

April 9, 2008

This week’s reading

Only 2 weeks left

I Complete the material of chapter 8:

I §8.3–§8.

I

Skip §8.5–§8.

I

§9.

Anorexia example

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

Anorexia example

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]

  1. 5 % = 0. 025 > P -value > 0. 01 = 1 % [middle]

I Conclusion: P -value  0.05 → reject H

0

[even for

H

a

: μ 6 = 0]

CI for p

− p

I

Point estimate for p

1

p

2

is

p

1

p

2

I Fact:

SE =

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]

p

1

p

2

) ± z

p

1

p

1

n

1

p

2

p

2

n

2

An example

pp. 429–

I Want difference between placebo & aspirin

I n

1

= 11034, n

2

= 11037 [large X]

I ˆ

p

1

p

2

I ˆ

p

1

p

2

I

SE =

p

1

p

1

n

1

p

2

p

2

n

2

0. 017 × 0. 983

0. 009 × 0. 991

I

95% CI for p

1

p

2

0. 008 ± ( 1. 96 × 0. 0015 ) = ( 0. 005 , 0. 011 )