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

612 CHAPTER 18 | The Binomial Test
■ Assumptions for the Binomial Test
The binomial test requires two very simple assumptions.
1. The sample must consist of independent observations (see Chapter 8, page 244).
2. The values for pn and qn must both be greater than or equal to 10 to justify using
the unit normal table for determining the critical region.
LEARNING CHECK
1. What is the mean for the normal approximation to the binomial distribution with
n = 30 and p = .40?
a. .24
b. 7.2
c. 12
d. 18
2. What is the standard deviation for the normal approximation to the binomial
distribution with n = 100 and p = .20?
a. 16
b. 4
c. 2
d. 0.16
3. For a binomial test with p = q = 1 2 and n = 36, is a score of X = 24 sufficient to
reject the null hypothesis? Assume a two-tailed test with α = .05.
a. Yes, X = 24 is entirely in the critical region.
b. No, none of X = 24 is in the critical region.
c. No, X = 24 overlaps the critical boundary with the lower limit in the critical
region but the upper limit outside the critical region.
d. No, X = 24 overlaps the critical boundary with the upper limit in the critical
region but the lower limit outside the critical region.
ANSWERS
1. C, 2. B, 3. D
18.3 More about the Binomial Test: Relationship
with Chi-Square and the Sign Test
LEARNING OBJECTIVES
5. Explain the relationship between the chi-square test for goodness of fit and the
binomial test.
6. Recognize when a sign test is appropriate and be able to perform the necessary
computations.
You may have noticed that the binomial test evaluates the same basic hypotheses as the
chi-square test for goodness of fit; that is, both tests evaluate how well the sample proportions
fit a hypothesis about the population proportions. When a research study produces