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

274 CHAPTER 9 | Introduction to the t Statistic
Caution: The t distribution table printed in this book has been abridged and does
not include entries for every possible df value. For example, the table lists t values for
df = 40 and for df = 60, but does not list any entries for df values between 40 and 60.
Occasionally, you will encounter a situation in which your t statistic has a df value that
is not listed in the table. In these situations, you should look up the critical t for both of
the surrounding df values listed and then use the larger value for t. If, for example, you
have df = 53 (not listed), look up the critical t value for both df = 40 and df = 60 and
then use the larger t value. If your sample t statistic is greater than the larger value listed,
you can be certain that the data are in the critical region, and you can confidently reject
the null hypothesis.
LEARNING CHECK
1. Which of the following is a fundamental difference between the t statistic and a
z-score?
a. The t statistic uses the sample mean in place of the population mean.
b. The t statistic uses the sample variance in place of the population variance.
c. The t statistic computes the standard error by dividing the standard deviation by
n – 1 instead of dividing by n.
d. All of the above are differences between t and z.
2. Which of the following terms is not required when using the t statistic?
a. n
b. σ
c. df
d. s or s 2 or SS
3. How does the shape of the t distribution compare to a normal distribution?
a. The t distribution is flatter and more spread out, especially when n is small.
b. The t distribution is flatter and more spread out, especially when n is large.
c. The t distribution is taller and less spread out, especially when n is small.
d. The t distribution is taller and less spread out, especially when n is small.
ANSWERS
1. B, 2. B, 3. A
9.2 Hypothesis Tests with the t Statistic
LEARNING OBJECTIVES
3. Conduct a hypothesis test using the t statistic.
4. Explain how the likelihood of rejecting the null hypothesis for a t test is influenced by
sample size and sample variance.
In the hypothesis-testing situation, we begin with a population with an unknown mean and
an unknown variance, often a population that has received some treatment (Figure 9.3).
The goal is to use a sample from the treated population (a treated sample) as the basis for
determining whether the treatment has any effect.