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

240 CHAPTER 8 | Introduction to Hypothesis Testing
3. What is a likely outcome for a hypothesis test if a treatment has a very small effect?
a. a Type I error
b. a Type II error
c. correctly reject the null hypothesis
d. correctly fail to reject the null hypothesis
ANSWERS
1. A, 2. C, 3. B
8.3 More about Hypothesis Tests
LEARNING OBJECTIVES
6. Explain how the results of a hypothesis test with a z-score test statistic are reported
in the literature.
7. Describe the assumptions underlying a hypothesis test with a z-score test statistic.
8. Explain how the outcome of a hypothesis test is influenced by the sample size,
standard deviation, and difference between the sample mean and the hypothesized
population mean.
■ A Summary of the Hypothesis Test
In Example 8.1 we presented a complete example of a hypothesis test evaluating the effect
of waitresses wearing red on male customers tipping behavior. The 4-step process for that
hypothesis test is summarized as follows.
STEP 1
State the hypotheses and select an alpha level. For this example, the general
population of men, left an average tip of μ = 15.8 percent with σ = 2.4 percentage points
when the waitress wore a white shirt. Therefore, the hypotheses are:
H 0
: μ with red shirt
= 15.8 (the red shirt has no effect)
H 1
: μ with red shirt
≠ 15.8 (the red shirt does have an effect)
We set α = .05.
STEP 2
STEP 3
STEP 4
Locate the critical region. For a normal distribution with α = .05, the critical region
consists of sample means that produce z-scores in the extreme tails of the distribution
beyond z = ±1.96.
Compute the test statistic (the z-score). We obtained an average tip of M = 16.7
percent for a sample of n = 36. With a standard error of σ M
= 0.4, we obtain z = 2.25.
Make a decision. The z-score is in the critical region, which means that this sample
mean is very unlikely if the null hypothesis is true. Therefore, we reject the null hypothesis
and conclude that wearing a red shirt did have an effect on the men’s tipping.
The following section explains how the results from this hypothesis test would be
presented in a research report.