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

SECTION 10.2 | The Null Hypothesis and the Independent-Measures t Statistic 309
This same structure is used for both the single-sample t from Chapter 9 and the new independent-measures
t that was introduced in the preceding pages. Table 10.1 identifies each
component of these two t statistics and should help reinforce the point that we made earlier
in the chapter; that is, the independent-measures t statistic simply doubles each aspect of
the single-sample t statistic.
TABLE 10.1
The basic elements of a t statistic for the single-sample t and the independent-measures t.
Single-sample
t statistic
Independentmeasures
Sample
Data
Hypothesized
Population
Parameter
Estimated
Standard
Error
Sample
Variance
M μ
Î s2
s 2 5 SS
n
df
(M 1
− M 2
) (μ 1
− μ 2
)
Î s2 s
p
2 p
1 s 2
n 1
n 5 SS 1 SS 1 2
p
df
2 1
1 df 2
LEARNING CHECK
ANSWERS
1. When the null hypothesis is true, what is measured by the estimated standard error
in the denominator of the independent-measures t statistic?
a. The standard distance between a sample mean and its population mean
b. The standard distance between two sample means selected from the same population
c. The actual distance between a sample mean and its population mean
d. The actual distance between two sample means
2. Which of the following is the correct null hypothesis for an independent-measures t test?
a. M 1
− M 2
= 0
b. M 1
− M 2
≠ 0
c. μ 1
− μ 2
= 0
d. μ 1
− μ 2
≠ 0
3. One sample from an independent-measures study has n = 4 with SS = 100. The
other sample has n = 8 and SS = 140. What is the pooled variance?
a. 53.33
b. 42.5
c. 24
d. 20
4. One sample from an independent-measures study has n = 9 with a variance of s 2 = 35.
The other sample has n = 3 and s 2 = 40. What is the df value for the t statistic?
a. 36
b. 12
c. 11
d. 10
1. B, 2. C, 3. C, 4. D