Psych 100A
Winter 2010
Lecture 8: Statistical Inference
1.Interval estimate (recap)
2.Hypothesis testing: tests of
significance
•
Example
•
Notations and definitions
3.Test for
,
known
1

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1. Interval estimates
•
How accurate are the point estimates?
Example:
Suppose a city manager in Los Angeles
wants to know the mean income (
) of 25,000
families living in South Los Angeles.
She
i t
i
900 ( )
f
ili
“ t
d
” d
interviews
900 (n)
families “at random” and
finds that the
sample mean = $14,400
.
Based
on past study, she knows that the population SD
(
) of incomes equals $9,000.
P bl
P t
“ i
t k ”
b
th
Problem:
Put a “give or take” number on the
point estimator (ie, the sample mean).
x
?
2

Solution:
Although the exact distribution of
incomes for this community is unknown
incomes for this community is unknown,
1. Sampling distribution of mean incomes
is
normally distributed
with mean
and
)
(
~
2
n
N
x
variance
2
/n due to central limit theorem.
Or,
,
2. Magnitude of
chance errors
in
sample mean
when repeatedly drawing a random sample of
size 900 from all 25,000 families is
300
$
000
9
$
900
,
n
3
Chance error
in
sample mean
is called
3. Chance error
standard error
.
3

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