Figure 6-1 (p. 162) The role of probability in inferential statistics. Probability is used to predict what kind of samples are likely to be obtained from a population. Thus, probability establishes a connection between samples and populations.

1
Figure 6-1 (p. 162)The role of probability in
inferential statistics. Probability is used to
predict what kind of samples are likely to be
obtained from a population. Thus, probability
establishes a connection between samples and
populations. Inferential statistics rely on this
connection when they use sample data as the basis
for making conclusions about populations.
2
Figure 6-2 (p. 166)A frequency distribution
histogram for a population that consists of N
10 scores. The shaded part of the figure
indicates the portion of the whole population
that corresponds to scores greater than X 4.
The shaded portion is two-tenths (p 2/10) of
the whole distribution.
3
Figure 6-3 (p. 168)The normal distribution. The
exact shape of the normal distribution is
specified by an equation relating each X value
(score) with each Y value (frequency). The
equation is (? and e are mathematical
constants.) In simpler terms, the normal
distribution is symmetrical with a single mode in
the middle. The frequency tapers off as you move
farther from the middle in either direction.
4
Figure 6-4 (p. 168)The normal distribution
following a z-score transformation.
5
Figure 6-5 (p. 169)The distribution for Example
6.2.
6
Figure 6-6 (p. 170)A portion of the unit normal
table. This table lists proportions of the normal
distribu-tion corresponding to each z-score
value. Column A of the table lists z-scores.
Column B lists the proportion in the body of the
normal distribution up to the z-score value.
Column C lists the proportion of the normal
distribution that is located in the tail of the
distribution beyond the z-score value. Column D
lists the proportion between the mean and the
z-score value.
7
Figure 6-7 (p. 171) The distributions for
Example 6.3A6.3C.
8
Figure 6-8 (p. 173) The distributions for
Examples 6.4A and 6.4B.
9
Figure 6-9 (p. 175)The distribution of SAT
scores. The problem is to find the probability of
proportion of the distribution corresponding to
scores greater than 6.50.
10
Figure 6-10 (p. 176) The distribution for
Example 6.6.
11
Figure 6-11 (p. 177) The distribution for
Example 6.7.
12
Figure 6-12 (p. 177) Determining probabilities
or proportions for a normal distribution is shown
as a two-step process with z-scores as an
intermediate stop along the way. Note that you
cannot move directly along the dashed line
between X values and probabilities or
proportions. Instead, you must follow the solid
lines around the corner.
13
Figure 6-13 (p. 178)The distribution of SAT
scores. The problem is to locate the score that
separates the top 15 from the rest of the
distribution. A line is drawn to divide the
distribution roughly into 15 and 85 sections.
14
Figure 6-14 (p. 179)The distribution of SAT
scores. The problem is to find the scores that
determine the middle 80.
15
Figure 6-15 (p. 181) The distribution for
Example 6.10A. The proportion for the shaded area
provides the percentile rank for X 114.
16
Figure 6-16 (p. 181) The distribution for
Example 6.10B. The proportion for the shaded area
provides the percentile rank for X 92.
17
Figure 6-17 (p. 182)The distribution for
Example 6.11.
18
Figure 6-18 (p. 183)The z-scores corresponding
to the first, second, and third quartiles in a
normal distribution.
19
Figure 6-19 (p. 186) The binomial distribution
showing the probability for the number of heads
in 2 tosses of a balanced coin.
20
Figure 6-20 (p. 187) Binomial distributions
showing probabilities for the number of heads (a)
in 4 tosses of a balanced coin and (b) in 6
tosses of a balanced coin.
21
Figure 6-21 (p. 188)The relationship between
the binomial distribution and the normal
distribution. The binomial distribution is always
a discrete histogram, and the normal distribution
is a continuous smooth curve. Each X value is
represented by a bar in the histogram or a
section of the normal distribution.
22
Figure 6-22 (p. 189) The binomial distribution
(normal approximation) for the number of males in
a sample of n 48 psychology majors. The shaded
area corresponds to the probability of obtaining
exactly 14 males when the probability of
selecting a male is p ¼. Note that the score X
14 is defined by its real limits.
23
Figure 6-23 (p. 190) A diagram of a research
study. One individual is selected from the
population and receives a treatment. The goal is
to determine whether or not the treatment has an
effect.
24
Figure 6-24 (p. 191) Using probability to
evaluate a treatment effect. Values that are
extremely unlikely to be obtained from the
original population are viewed as evidence of a
treatment effect.