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

266 CHAPTER 8 | Introduction to Hypothesis Testing
treatment effect and plans to use a two-tailed hypothesis
test with α = .05.
a. Compute the power of the test if the researcher uses
a sample of n = 9 individuals. (See Example 8.6.)
b. Compute the power of the test if the researcher
uses a sample of n = 16 individuals.
20. A researcher plans to conduct an experiment evaluating
the effect of a treatment. A sample of n = 9
participants is selected and each person receives the
treatment before being tested on a standardized dexterity
task. The treatment is expected to lower scores
on the test by an average of 30 points. For the regular
population, scores on the dexterity task form a normal
distribution with μ = 240 and σ = 30.
a. If the researcher uses a two-tailed test with
α = .05, what is the power of the hypothesis test?
b. Again assuming a two-tailed test with α = .05,
what is the power of the hypothesis test if the
sample size is increased to n = 25?
21. Research has shown that IQ scores have been increasing
for years (Flynn, 1984, 1999). The phenomenon
is called the Flynn effect and the data indicate that the
increase appears to average about 7 points per decade.
To examine this effect, a researcher obtains an IQ test
with instructions for scoring from 10 years ago
and plans to administers the test to a sample of
n = 25 of today’s high school students. Ten years
ago, the scores on this IQ test produced a standardized
distribution with a mean of μ = 100 and a
standard deviation σ = 15. If there actually has been
a 7-point increase in the average IQ during the past
10 years, then find the power of the hypothesis test
for each of the following.
a. The researcher uses a two-tailed hypothesis test
with α = .05 to determine if the data indicate a
significant change in IQ over the past 10 years.
b. The researcher uses a one-tailed hypothesis test
with α = .05 to determine if the data indicate a
significant increase in IQ over the past 10 years.
22. Briefly explain how increasing sample size influences
each of the following. Assume that all other factors
are held constant.
a. The size of the z-score in a hypothesis test.
b. The size of Cohen’s d.
c. The power of a hypothesis test.
23. Explain how the power of a hypothesis test is influenced
by each of the following. Assume that all other
factors are held constant.
a. Increasing the alpha level from .01 to .05.
b. Changing from a one-tailed test to a two-tailed test.