Chapter 9: Introduction to
the t statistic

The t Statistic
•
allows researchers to
use sample data
to test
hypotheses about an
unknown population
mean
.
•
does not require any knowledge of the
population standard deviation (needed when
using z-score)
•
can be used to test hypotheses about a
completely unknown
population; that is,
both
μ
and
σ
are unknown
, and the only available
information about the population comes from the
sample.

The t Statistic
•
required for a hypothesis test using t-stat
–
a sample
–
a reasonable hypothesis about the population
mean.

The t StatisticTwo general situations where the t-statistic is used in hypothesis testing:
1. to determine whether or not a treatment causes a change in a population mean. –must know the value of μfor the original, untreated population–Obtain a sample from the population –the treatment is administered to the sample–If the resulting sample mean is significantly different from the original population mean, can conclude that the treatment has a significant effect

The t Statistic
2.a hypothesized valuefor an unknown population mean is derived from a theory or other prediction–Obtain a sample from the population–the t statistic is used to compare the actual sample mean with the hypothesized population mean–significant difference indicates that the hypothesized value for μshould be rejected

The Estimated Standard Error and
the t Statistic
•
sampling error
(discrepancy or "error"
between the sample mean and the
population mean) is expected
•
Is the discrepancy observed between
sample mean and population mean
significant?
–
Find out through hypothesis testings

The Estimated Standard Error and
the t Statistic
Two alternatives to consider in hypothesis testing:
1.
Discrepancy
between M and
μ
is
simply due
to sampling error
and not resulting from
treatment effect OR
2.Discrepancy between M and
μ
more than
what
is expected by
sampling error alone
, therefore
the
sample mean significantly different from
the population mean

The Estimated Standard Error and
the t Statistic
•
The critical first step for the t statistic