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

332 CHAPTER 10 | The t Test for Two Independent Samples
Counting Money
Counting Paper
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a. Is there a significant difference in reported pain
between the two conditions? Use a two-tailed test
with α = .01.
b. Compute Cohen’s d to estimate the size of the
treatment effect.
15. In a classic study in the area of problem solving,
Katona (1940) compared the effectiveness of two
methods of instruction. One group of participants was
shown the exact, step-by-step procedure for solving a
problem and was required to memorize the solution.
Participants in a second group were encouraged to
study the problem and find the solution on their own.
They were given helpful hints and clues, but the exact
solution was never explained. The study included the
problem in the following figure showing a pattern of
five squares made of matchsticks. The problem is to
change the pattern into exactly four squares by moving
only three matches. (All matches must be used,
none can be removed, and all the squares must be the
same size.) After 3 weeks, both groups returned to be
tested again. The two groups did equally well on the
matchstick problem they had learned earlier. But when
they were given new problems (similar to the matchstick
problem), the memorization group had much
lower scores than the group who explored and found
the solution on their own. The following data demonstrate
this result.
Memorization of
the Solution
Find a Solution
on Your Own
n = 8 n = 8
M = 10.50 M = 6.16
SS = 108 SS = 116
a. Is there a significant difference in performance on
new problems for these two groups? Use a twotailed
test with α = .05.
b. Construct a 90% confidence interval to estimate
the size of the mean difference.
Incidentally, if you still have not discovered the
solution to the matchstick problem, keep trying.
According to Katona’s results, it would be very poor
teaching strategy for us to give you the answer. If you
still have not discovered the solution, however, check
Appendix C at the beginning of the problem solutions
for Chapter 10 and we will show you how it is done.
16. A researcher conducts an independent-measures study
comparing two treatments and reports the t statistic as
t(25) = 2.071.
a. How many individuals participated in the entire
study?
b. Using a two-tailed test with α = .05, is there a
significant difference between the two treatments?
c. Compute r 2 to measure the percentage of variance
accounted for by the treatment effect.
17. In a recent study, Piff, Kraus, Côté, Cheng, and
Keitner (2010) found that people from lower social
economic classes tend to display greater prosocial
behavior than their higher class counterparts. In one
part of the study, participants played a game with an
anonymous partner. Part of the game involved sharing
points with the partner. The lower economic class
participants were significantly more generous with
their points compared with the upper class individuals.
Results similar to those found in the study, show that
n = 12 lower class participants shared an average of
M = 5.2 points with SS = 11.91, compared to an
average of M = 4.3 with SS = 9.21 for the n = 12
upper class participants.
a. Are the data sufficient to conclude that there is
a significant mean difference between the two
economic populations? Use a two-tailed test with
α = .05
b. Construct an 80% confidence interval to estimate
the size of the population mean difference.
18. Describe the homogeneity of variance assumption
and explain why it is important for the independentmeasures
t test.