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

150 CHAPTER 5 | z-Scores: Location of Scores and Standardized Distributions
Notice that the set of
z-scores is considered
to be a sample and the
variance is computed
using the sample formula
with df 5 n 2 1.
The variance for the sample of z-scores is
s z
5
SS
n 2 1 5 4 4 5 1.00
Finally, the standard deviation for the sample of z-scores is s 2 5
z
Ï1.00 5 1.00. As
always, the distribution of z-scores has a mean of 0 and a standard deviation of 1. ■
LEARNING CHECK
1. For a sample with M = 60 and s = 8, what is the z-score corresponding to X = 62?
a. 2
b. 4
c. 0.25
d. 0.50
2. For a sample with a standard deviation of s = 5, what is the z-score corresponding
to a score that is located 10 points below the mean?
a. −10
b. +2
c. −2
d. cannot answer without knowing the mean
3. If a sample with M = 60 and s = 8 is transformed into z-scores, then the resulting
distribution of z-scores will have a mean of ______ and a standard deviation of _____.
a. 0 and 1
b. 60 and 1
c. 0 and 8
d. 60 and 8 (unchanged)
ANSWERS
1. C, 2. C, 3. A
5.7 Looking Ahead to Inferential Statistics
LEARNING OBJECTIVE
9. Explain how z-scores can help researchers use the data from a sample to draw
inferences about populations.
Recall that inferential statistics are techniques that use the information from samples to
answer questions about populations. In later chapters, we will use inferential statistics to
help interpret the results from research studies. A typical research study begins with a question
about how a treatment will affect the individuals in a population. Because it is usually
impossible to study an entire population, the researcher selects a sample and administers
the treatment to the individuals in the sample. This general research situation is shown in
Figure 5.10. To evaluate the effect of the treatment, the researcher simply compares the