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

SECTION 10.3 | Hypothesis Tests with the Independent-Measures t Statistic 311
t distribution
df 5 14
FIGURE 10.3
The critical region for the
independent–measures
hypothesis test in Example
10.2 with df = 14 and
α = .05.
Reject H 0
t 5 22.145
t 5 0
Reject H 0
t 5 12.145
The t distribution for df = 14 is presented in Figure 10.3. For α = .05, the critical region
consists of the extreme 5% of the distribution and has boundaries of t = +2.145 and
t = −2.145.
STEP 3
Caution: The pooled
variance combines the
two samples to obtain a
single estimate of variance.
In the formula, the
two samples are combined
in a single fraction.
Caution: The standard
error adds the errors
from two separate samples.
In the formula, these
two errors are added as
two separate fractions. In
this case, the two errors
are equal because the
sample sizes are the same.
Obtain the data and compute the test statistic. The data are as given, so all that
remains is to compute the t statistic. As with the single-sample t test in Chapter 9, we recommend
that the calculations be divided into three parts.
First, find the pooled variance for the two samples:
s 2 5 SS 1 SS 1 2
p
df 1
1 df 2
60 1 66
5
7 1 7 5 126
14 5 9
Second, use the pooled variance to compute the estimated standard error:
s 5 sM1 2M 2
d Î s2 9 8 1 9 8
Third, compute the t statistic:
= Ï2.25
= 1.50
1
n 1
1 s2 2
n 2
5Î
t 5 sM 1 2 M 2 d 2 sm 1 2m 2 d
s sM1 2M 2
d
5
5 24
1.5 522.67
s8 2 12d 2 0
1.5
STEP 4
Make a decision. The obtained value (t = −2.67) is in the critical region. In this example,
the obtained sample mean difference is 2.67 times greater than would be expected if