Statistics 400
Section 7.2
Confidence intervals for means
The Statistical End Goal:
draw conclusions about the data we have
collected and analyzed.
Every time we estimate
μ
using statistic
X
,
we will never get the same
answer.
•
Due to sampling variability
Need to provide intervals around the estimated statistics.
For example:
Draw a random sample of size n from N(
μ
,
σ
2
). Estimate
μ
using statistic
X
.
Repeat your experiment to make sure you get similar results each time.
Note, however, that each time you will end up with different answers that
are very close to each other.
You want to provide a range of values where we think
X
will occur. In
addition to providing a range of values, you want to attach some level of
confidence to the range you calculate.
Recall: Density Curves:
Used to represent a distribution of random variables.
Density of
X
:
Ping Ma
Lecture 26
Fall 2005
 1 
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentInterpretation:
Confidence Intervals:
Form: estimate
±
margin of error
Estimate:
Whatever statistic we are estimating:
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '05
 TBA
 Statistics, Normal Distribution, $324, 1.96 99%, $34,076, 1.645 95%

Click to edit the document details