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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
:

ð
3
:
2
Þ

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 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 % conﬁdence interval about the mean.

Now that you know how to ﬁnd the value of t in the formula for the conﬁdence

interval about the mean, let’s explore how you ﬁnd this conﬁdence interval using

Excel.

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