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

606 CHAPTER 18 | The Binomial Test
population. In this case, the null hypothesis would simply specify that there is no
difference between the two populations. Suppose that national statistics indicate
that 1 out of 12 drivers will be involved in a traffic accident during the next year.
Does this same proportion apply to 16-year-olds who are driving for the first time?
According to the null hypothesis,
H 0
: For 16-year-olds, p = p(accident) = 1 12
(Not different from
the general population)
Similarly, suppose that last year, 30% of the freshman class failed the college writing
test. This year, the college is requiring all freshmen to take a writing course. Will the
course have any effect on the number who fail the test? According to the null hypothesis,
H 0
: For this year, p = p(fail) = 30%
(Not different from last year’s class)
■ The Data for the Binomial Test
For the binomial test, a sample of n individuals is obtained and you simply count how many
are classified in category A and how many are classified in category B. We focus attention
on category A and use the symbol X to stand for the number of individuals classified in
category A. Recall from Chapter 6 that X can have any value from 0 to n and that each value
of X has a specific probability. The distribution of probabilities for each value of X is called
the binomial distribution. Figure 18.1 shows an example of a binomial distribution where
X is the number of heads obtained in four tosses of a balanced coin.
■ The Test Statistic for the Binomial Test
As we noted in Chapter 6, when the values pn and qn are both equal to or greater than
10, the binomial distribution approximates a normal distribution. This fact is important
because it allows us to compute z-scores and use the unit normal table to answer probability
questions about binomial events. In particular, when pn and qn are both at least 10, the
binomial distribution will have the following properties.
1. The shape of the distribution is approximately normal.
2. The mean of the distribution is μ = pn.
0.375
Probability
0.250
0.125
FIGURE 18.1
A binomial distribution for the
number of heads obtained in
four tosses of a balanced coin.
0
1 2
Number of heads
in 4 coin tosses
3 4