Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

198 CHAPTER 7 | Probability and Samples: The Distribution of Sample Means
TABLE 7.1
All the possible samples
of n = 2 scores that can
be obtained from the
population presented in
Figure 7.1. Notice that
the table lists random
samples. This requires
sampling with replacement,
so is possible to
select the same score
twice.
Scores
Sample Mean
Sample First Second (M)
1 2 2 2
2 2 4 3
3 2 6 4
4 2 8 5
5 4 2 3
6 4 4 4
7 4 6 5
8 4 8 6
9 6 2 4
10 6 4 5
11 6 6 6
12 6 8 7
13 8 2 5
14 8 4 6
15 8 6 7
16 8 8 8
Remember that our
goal in this chapter is to
answer probability questions
about samples with
n > 1.
2. The distribution of sample means is approximately normal in shape. This is a
characteristic that is discussed in detail later and is extremely useful because we
already know a great deal about probabilities and the normal distribution
(Chapter 6).
Finally, you should realize that we can use the distribution of sample means to achieve
the goal for this chapter, which is to answer probability questions about sample means. For
example, if you take a sample of n = 2 scores from the original population, what is the
probability of obtaining a sample with a mean greater than 7? In symbols,
p(M > 7) = ?
Because probability is equivalent to proportion, the probability question can be restated
as follows: Of all the possible sample means, what proportion has values greater than 7? In
this form, the question is easily answered by looking at the distribution of sample means.
All the possible sample means are pictured (see Figure 7.2), and only 1 out of the 16 means
has a value greater than 7. The answer, therefore, is 1 out of 16, or 1
16 .
4
Frequency
3
2
FIGURE 7.2
The distribution of sample
means for n = 2. The distribution
shows the 16 sample
means from Table 7.1.
1
0
0 1 2 3 4 5 6 7 8 9
Sample means