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

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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

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]

2. 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]

(ˆ 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 )