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

Statistics is one of the most practical and essential courses that you will take, and a primary goal of this popular text is to make the task of learning statistics as simple as possible. Straightforward instruction, built-in learning aids, and real-world examples have made STATISTICS FOR THE BEHAVIORAL SCIENCES, 10th Edition the text selected most often by instructors for their students in the behavioral and social sciences. The authors provide a conceptual context that makes it easier to learn formulas and procedures, explaining why procedures were developed and when they should be used. This text will also instill the basic principles of objectivity and logic that are essential for science and valuable in everyday life, making it a useful reference long after you complete the course.

Statistics is one of the most practical and essential courses that you will take, and a primary goal of this popular text is to make the task of learning statistics as simple as possible. Straightforward instruction, built-in learning aids, and real-world examples have made STATISTICS FOR THE BEHAVIORAL SCIENCES, 10th Edition the text selected most often by instructors for their students in the behavioral and social sciences. The authors provide a conceptual context that makes it easier to learn formulas and procedures, explaining why procedures were developed and when they should be used. This text will also instill the basic principles of objectivity and logic that are essential for science and valuable in everyday life, making it a useful reference long after you complete the course.

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608 CHAPTER 18 | The Binomial Test

2. If pn = 40 and qn = 20, then what is the shape of the binomial distribution?

a. Normal

b. Positively skewed

c. Negatively skewed

d. Cannot be determined without additional information

3. A binomial distribution has p = 4/5. How large a sample would be necessary to

justify using the normal approximation to the binomial distribution?

a. At least 10

b. At least 13

c. At least 40

d. At least 50

ANSWERS

1. C, 2. A, 3. D

18.2 An Example of the Binomial Test

LEARNING OBJECTIVES

3. Perform all of the necessary computations for the binomial test.

4. Explain how the decision in a binomial test can be influenced by the fact that each

score actually corresponds to an interval in the distribution.

The binomial test follows the same four-step procedure presented earlier with other examples

for hypothesis testing. The four steps are summarized as follows.

STEP 1

STEP 2

STEP 3

STEP 4

State the hypotheses. In the binomial test, the null hypothesis specifies values for the

population proportions p and q. Typically, H 0

specifies a value only for p, the proportion

associated with category A. The value of q is directly determined from p by the relationship

q = 1 − p. Finally, you should realize that the hypothesis, as always, addresses the probabilities

or proportions for the population. Although we use a sample to test the hypothesis,

the hypothesis itself always concerns a population.

Locate the critical region. When both values for pn and qn are greater than or equal to

10, the z-scores defined by Equation 18.1 or 18.2 form an approximately normal distribution.

Thus, the unit normal table can be used to find the boundaries for the critical region.

With α = .05, for example, you may recall that the critical region is defined as z-score

values greater than +1.96 or less than −1.96.

Compute the test statistic (z-score). At this time, you obtain a sample of n individuals

(or events) and count the number of times category A occurs in the sample. The number

of occurrences of A in the sample is the X value for Equation 18.1 or 18.2. Because the two

z-score equations are equivalent, you may use either one for the hypothesis test. Usually

Equation 18.1 is easier to use because it involves larger numbers (fewer decimals) and it is

less likely to be affected by rounding error.

Make a decision. If the z-score for the sample data is in the critical region, you reject

H 0

and conclude that the discrepancy between the sample proportions and the hypothesized

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