I.
Sampling
Distributions
A. All the values that the
statistic can take
B. The probability of getting
each value under the assumption that it resulted from chance alone
C.Null-Hypothesis Population
1.
2.
3.
It
is used to
4.
2
Approaches
a)
Empirical
Sampling -
b)
A
Priori -
II.
The
Normal Deviate (z) Test
A. Sampling Distribution of the
Mean
1.
2.
3.
4
characteristics
a)
Is
a distribution of scores where
(1)
(2)
(3)
b)
Has
a mean =
c)
Has
a standard deviation
d)
Is
normally shaped, depending on
(1)
(2)
(3)
B. Example:
1.
Population
mean = 75, sd = 16, N = 100
2.
Determine
sampling distribution of the mean
a)
Mean
=
b)
Standard
Error of Estimate =
(1)
=
16/ square root of 100
(2)
=
16/10 therefore
(3)
=
1.6
c)
Transform
to Z obt
(1)
Z
obt =
(2)
=
72 - 75/1.6
(3)
= -1.88
d)
Determine
Probability, From to Table A, column C
(1)
=
0.0301
(2)
Compare
to Alpha = .05
(3)
.0301
< .05, therefore reject the null hypothesis - accept the alternate
hypothesis, independent var affects dependent var
C.Preferred Solution - Using Zobt and the Critical
Region for Rejection of Ho
1.
Critical
Region for rejection of the null hypothesis -
2.
Critical
Value of a statistic -
3.
Determine
Zcrit by using table A in reverse
a)
1
tail - Zcrit = 1.645, since left side of dist, actually -1.645
b)
2
tails - Zcrit = +/- 1.96
c)
If
absolute value of Zobt >= absolute value of Zcrit, reject null hyp
d)
So
for our example, reject 1 tail, fail to reject 2 tail
III.
When
is Z test Appropriate
A.
B.
C.The sampling distribution of the mean should be
normally distribution - true if
1.
2.