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3.1.5 Finding the Value for t in the Conﬁdence Interval Formula
Objective : To ﬁnd the value for t in the conﬁdence interval
formula
The correct formula for the conﬁdence interval about the mean for different
sample sizes is the following:
X
ts
e
(3.2)
:
:
To use this formula, you ﬁnd the sample mean, X , and add to it the value of
t times the s.e. to get the upper limit of this 95% conﬁdence interval. Also, you take
the sample mean , X , and subtract from it the value of t times the s.e. to get the lower
limit of this 95% conﬁdence interval. And, you ﬁnd the value of t in the table given
in Appendix E of this topic in the following way:
Objective : To ﬁnd the value of t in the t-table in Appendix E
Before we get into an explanation of what is meant by “the value of t,” let’s give
you practice in ﬁnding the value of t by using the t-table in Appendix E.
Keep your ﬁnger on Appendix E as we explain how you need to “read” that table.
Since the test in this chapter is called the “conﬁdence interval about the mean
test,” you will use the ﬁrst column on the left in Appendix E to ﬁnd the critical value
of t for your research study (note that this column is headed: “ sample size n” ).
To ﬁnd the value of t , you go down this ﬁrst column until you ﬁnd the sample
size in your research study, and then you go to the right and read the value of t for
that sample size in the “critical t column” of the table (note that this column is the
column that you would use for the 95% conﬁdence interval about the mean).
For example, if you have 14 people in your research study, the value of t is 2.160.
If you have 26 people in your research study, the value of t is 2.060.
If you have more than 40 people in your research study, the value of t is always
1.96.
Note that the “critical t column” in Appendix E represents the value of t that you
need to use to obtain to be 95% conﬁdent of your results as “signiﬁcant” results.
Throughout this topic, we are assuming that you want to be 95% conﬁdent in the
results of your statistical tests . Therefore, the value for t in the t-table in Appendix E
tells you which value you should use for t when you use the formula for the 95%