Inferences About Means of Two Independent Samples

Chapter 11

Homework: 1, 2, 3, 4, 6, 7

Pooled Variance: n1 n2

Unequal sample sizes weight each variance bigger n ---> more weight

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222

2112

dfdf

sdfsdfspooled

Pooled Variance

since df = n - 1

2

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nn

snsnspooled

Example

What effect does the amount of sleep the night before an exam have on exam performance?

Dependent variable independent variable

Grp 1: 4 hrs sleep (n = 6) Grp 1: 8 hrs sleep (n = 7) ~

Example

1. State Hypotheses

H0:1 = 2 or 1 - 2 = 0

H1:1 2 or 1 - 2 0

2. Set criterion for rejecting H0:

nondirectional

= .05

df = (n1 + n2 - 2)

= (6 + 7 - 2) = 11

t CV = + 2.201 ~

Example

3. select sample, compute statistics

do experiment

mean exam scores for each group Group 1: X1 = 14 ; s1= 3

Group 2: X2 = 19; s2= 2 compute

s2pooled

s X1- X2

tobs ~

Example

compute s2pooled

2

11

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nn

snsnspooled

compute s X1- X2

compute test statistic

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2 1121 nn

ss pooledXX

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XX

obs s

XXt

[df = n1 + n2 - 2]

Example

4. Interpret

Is tobs beyond tCV?

If yes, Reject H0. Practical significance?

pooled

obs

s

XXd

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