Psychology 60
Spring 2010
Homework Assignment 4
1)
For a population with μ = 50, and σ = 10, find the standard error,
σ
X
, when:
a.
(1 point)
n = 4,
σ
X
=
σ
n
=
10
4
=
10
2
=
5
b.
(1 point)
n = 25,
σ
X
=
σ
n
=
10
25
=
10
5
=
2
c.
(1 point)
n = 100,
σ
X
=
σ
n
=
10
100
=
10
10
=
1
2)
(2 point)
The distribution of sample means is not always distributed normally. Under what
circumstances will the distribution of sample means
not
be normal?
The distribution of the sample means will be nonnormal if the population is
nonnormal and the sample size is smaller than about 35.
3)
For a population with σ = 20:
a.
(1 point)
How large a sample would be needed to have a standard error less than 10
points?
σ
X
<
10,
σ
n
,
20
n
∴
n
>
4
b.
(1 point)
How large a sample would be needed to have a standard error less than 4
points?
σ
X
<
4,
σ
n
,
20
n
∴
n
>
25
c.
(1 point)
How large a sample would be needed to have a standard error less than 2
points?
σ
X
<
2,
σ
n
,
20
n
∴
n
>
100
4)
A population has a mean of μ = 100 and a standard deviation of σ = 20. Find the z‐score for
each of the following
sample means
obtained from this population:
a.
(1 point)
X
= 102 for sample of 4 scores
z
X
=
X
−
μ
σ
X
,
z
X
=
102
−
100
σ
/
n
,
z
X
=
102
−
100
20 /
4
,
z
X
=
2
10
=
0.2
b.
(1 point)
X
= 102 for sample of 100 scores
z
X
=
X
−
μ
σ
X
,
z
X
=
102
−
100
σ
/
n
,
z
X
=
102
−
100
20 /
100
,
z
X
=
2
2
=
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 Spring '11
 PARRIS
 Psychology, Standard Deviation

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