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

SECTION 8.1 | The Logic of Hypothesis Testing 235
In general, a large value for a test statistic like the z-score indicates a large discrepancy
between the sample data and the null hypothesis. Specifically, a large value indicates that
the sample data are very unlikely to have occurred by chance alone. Therefore, when we
obtain a large value (in the critical region), we conclude that it must have been caused by
a treatment effect.
LEARNING CHECK
1. A sample of n = 16 individuals is selected from a population with μ = 40 and
σ = 12, and a treatment is administered to the sample. After treatment, the sample
mean is M = 42. How does this sample compare to samples that should be obtained
if the treatment has no effect?
a. It is an extreme value that would be very unlikely if the treatment has no effect.
b. It is much the same as samples that would be obtained if the treatment has no
effect.
c. The mean is noticeably larger than would be expected if the treatment has no
effect but it is not quite an extreme sample.
d. There is no way to compare this sample with those that would be obtained if the
treatment had no effect.
2. A researcher selects a sample of n = 20 from a normal population with μ = 80 and
σ = 20, and a treatment is administered to the sample. If a hypothesis test is used to
evaluate the effect of the treatment, what is the null hypothesis?
a. μ = 80
b. M = 80
c. μ ≠ 80
d. M ≠ 80
3. What is the correct decision in a hypothesis if the data produce a z-score that is in
the critical region?
a. Reject H 0
b. Fail to reject H 0
c. Reject H 1
d. Fail to reject H 1
4. A researcher administers a treatment to a sample of n = 25 participants and uses a
hypothesis test to evaluate the effect of the treatment. The hypothesis test produces a
z-score of z = 1.77. Assuming that the researcher is using a two-tailed test,
a. The researcher should reject the null hypothesis with α = .05 but not with α = .01.
b. The researcher should reject the null hypothesis with either α = .05 or α = .01.
c. The researcher should fail to reject H 0
with either α = .05 or α = .01.
d. Cannot answer without additional information.
ANSWERS
1. B, 2. A, 3. A, 4. C