1
Psych 100A
Winter 2010
Lecture 10: Hypothesis testing &
Power Analysis
1. Test for
,
known
2. Computation of power
3. Relationships among
, power and
n
4. Power curves
12.Tests of significance are about one question and
that question is always the same:
HT: notations and definitions (continued)
“How easy is it to explain the difference
How easy is it to explain the difference
between the observed data (sample statistic)
and the expected outcome (H
O
) by chance
alone.”
2
3. Theorem: hypothesis test for
,
2
known
If x
1
, x
2
, …, x
n
is a random sample from a
normal population or a large random sample from
any population with known variance
2
, then do
O
H
:
A
.
2
.
1
:
versus
n
x
z
TS
:
.
3
2
.
3
.
2
.
1
:
if
reject
CR
error
I
type
3
•
Example (Kuzma). Boys of a certain age have a
mean weight of 85 lb.
A complaint was made that,
in a municipal children’s home, the boys are
underfed.
As one bit of evidence, all 25 boys of a
given age were weighed and
lb.
94
.
80
•
Suppose it is known that
= 11.6 lb.
•
At a significance level
= 0.05, what do you
conclude about the complaint?
4
•
Solution.
1. H
O
:
= 85 lb versus H
A
:
< 85 lb.
2. Data:
3. Assumptions:
a. SRS of 25 boys
b
Weights normally distributed
lb.
94
.
80
74
.
1
25
6
.
11
85
95
.
80
b. Weights normally distributed
c.
= 11.6 lb.
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 Winter '10
 FIRSTENBERG,I.
 Power, Null hypothesis, Statistical hypothesis testing

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