Chapter6.1 - Chapter 6 Introduction to Inference This...

Chapter 6: Introduction to Inference
This chapter concerns inference procedures for
the population average. You will learn about
confidence intervals and significance tests to
learn about a population average
μ
. The world
uses both of these methods and you need to
know both also.
6.1 Estimating with Confidence
If the entire population of SAT scores has mean
and standard deviation
σ
, then in repeated
samples of size 500 the sample mean
x
has
a N( ,
500
) distribution. Let us suppose
that we know that the standard deviation of
SATM scores in California population is
100 =
. In repeated sampling the sample
mean
x
follows the normal distribution
centered at the unknown population mean
and having standard deviation
5 . 4
500
100
= =

x
The 68-95-99.7 rule says that the probability is
about 0.95 that
x
will be within 9 points (
× 2
) of the population mean score .

We say that we are 95% confident that the
unknown mean score for a California seniors lies
between
452 9 461 9 = - = - x
and
470 9 461 9 = + = + x
.
Figure 6.2
x
=461 lies within
9 ±
of
μ
in 95% of
all samples, so also lies within
9 ±
of
x
in
samples from more than 250,000 high school
seniors in California.

Confidence intervals
We will use C to stand for the confidence level in
decimal form. For example, a 95% confidence
level corresponds to C =0.95.
Confidence Interval
A level C confidence interval for a parameter
is an interval computed from sample data by a
method that has probability C of producing an
interval containing the true value of the