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

PROBLEMS 363
b. Now assume that the sample mean difference is
M D
= 10, and once again visualize the sample
distribution. Use a two-tailed hypothesis test with
α = .05 to determine whether it is likely that this
sample came from a population with μ D
= 0.
c. Explain how the size of the sample mean difference
influences the likelihood of finding a significant
mean difference.
19. A sample of difference scores from a repeatedmeasures
experiment has a mean of M D
= 3 with a
standard deviation of s = 4.
a. If n = 4, is this sample sufficient to reject the null
hypothesis using a two-tailed test with α = .05?
b. Would you reject H 0
if n = 16? Again, assume a
two-tailed test with α = .05.
c. Explain how the size of the sample influences the
likelihood of finding a significant mean difference.
20. Participants enter a research study with unique
characteristics that produce different scores from
one person to another. For an independent-measures
study, these individual differences can cause problems.
Identify the problems and briefly explain how
they are eliminated or reduced with a repeatedmeasures
study.
21. In the Chapter Preview we described a study
showing that students had more academic problems
following nights with less than average sleep
compared to nights with more than average sleep
(Gillen-O’Neel, Huynh, & Fuligni, 2013). Suppose
a researcher is attempting to replicate this study
using a sample of n = 8 college freshmen. Each
student records the amount of study time and amount
of sleep each night and reports the number of
academic problems each day. The following data
show the results from the study.
Number of Academic Problems
Student
Following Nights
with Above
Average Sleep
Following Nights
with Below
Average Sleep
A 10 13
B 8 6
C 5 9
D 5 6
E 4 6
F 10 14
G 11 13
H 3 5
a. Treat the data as if the scores are from an independent-measures
study using two separate samples,
each with n = 8 participants. Compute the pooled
variance, the estimated standard error for the
mean difference, and the independent-measures
t statistic. Using a two-tailed test with α = .05, is
there a significant difference between the two sets
of scores?
b. Now assume that the data are from a repeatedmeasures
study using the same sample of n = 8
participants in both treatment conditions. Compute
the variance for the sample of difference scores,
the estimated standard error for the mean difference
and the repeated-measures t statistic. Using a
two-tailed test with α = .05, is there a significant
difference between the two sets of scores? (You
should find that the repeated-measures design substantially
reduces the variance and increases the
likelihood of rejecting H 0
.)
22. The previous problem demonstrates that removing
individual differences can substantially reduce
variance and lower the standard error. However, this
benefit only occurs if the individual differences are
consistent across treatment conditions. In problem 21,
for example, the participants with the highest scores
in the more-sleep condition also had the highest
scores in the less-sleep condition. Similarly, participants
with the lowest scores in the first condition
also had the lowest scores in the second condition.
To construct the following data, we started with
the scores in problem 21 and scrambled the scores
in treatment 1 to eliminate the consistency of the
individual differences.
Number of Academic Problems
Student
Following Nights
with Above
Average Sleep
Following Nights
with Below
Average Sleep
A 10 13
B 8 14
C 5 13
D 5 5
E 4 9
F 10 6
G 11 6
H 3 6
a. Treat the data as if the scores are from an independent-measures
study using two separate samples,
each with n = 8 participants. Compute the pooled