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

PROBLEMS 333
19. If other factors are held constant, explain how each of
the following influences the value of the independentmeasures
t statistic, the likelihood of rejecting the
null hypothesis, and the magnitude of measures of
effect size.
a. Increasing the number of scores in each sample.
b. Increasing the variance for each sample.
20. As noted on page 304, when the two population
means are equal, the estimated standard error for the
independent-measures t test provides a measure of
how much difference to expect between two sample
means. For each of the following situations, assume
that μ 1
= μ 2
and calculate how much difference
should be expected between the two sample means.
a. One sample has n = 6 scores with SS = 75 and the
second sample has n = 10 scores with SS = 135.
b. One sample has n = 6 scores with SS = 310 and the
second sample has n = 10 scores with SS = 530.
c. In part b, the samples have larger variability (bigger
SS values) than in part a, but the sample sizes are
unchanged. How does larger variability affect the
magnitude of the standard error for the sample
mean difference?
21. Two samples are selected from the same population. For
each of the following, calculate how much difference is
expected, on average, between the two sample means.
a. One sample has n = 4, the second has n = 6, and
the pooled variance is 60.
b. One sample has n = 12, the second has n = 15,
and the pooled variance is 60.
c. In part b, the sample sizes are larger but the pooled
variance is unchanged. How does larger sample
size affect the magnitude of the standard error for
the sample mean difference?
22. For each of the following, assume that the two
samples are obtained from populations with the same
mean, and calculate how much difference should be
expected, on average, between the two sample means.
a. Each sample has n = 4 scores with s 2 = 68 for
the first sample and s 2 = 76 for the second. (Note:
Because the two samples are the same size, the
pooled variance is equal to the average of the two
sample variances.)
b. Each sample has n = 16 scores with s 2 = 68 for
the first sample and s 2 = 76 for the second.
c. In part b, the two samples are bigger than in part a,
but the variances are unchanged. How does sample
size affect the size of the standard error for the
sample mean difference?
23. For each of the following, calculate the pooled variance
and the estimated standard error for the sample
mean difference
a. The first sample has n = 4 scores and a variance of
s 2 = 17, and the second sample has n = 8 scores
and a variance of s 2 = 27.
b. Now the sample variances are increased so that the
first sample has n = 4 scores and a variance of
s 2 = 68, and the second sample has n = 8 scores
and a variance of s 2 = 108.
c. Comparing your answers for parts a and b, how
does increased variance influence the size of the
estimated standard error?