Transcript confidence interval for a population mean

Chapter 10:
Estimating with Confidence
The Practice of Statistics
Third Edition
Yates, Moore & Starnes
Chapter Objectives
• Describe statistical inference
• Describe the basic form of all confidence intervals
• Construct and interpret a confidence interval for a population
mean (including paired data) and for a population proportion
• Describe a margin of error, and explain ways in which you can
control the size of the margin of error
• Determine the sample size necessary to construct confidence
interval for a fixed margin of error
• Compare and contrast the t distribution and the Normal
distribution
• List the conditions that must be present to construct a
confidence interval for a population mean or a population
proportion
• Explain what is meant by the standard error, and determine the
standard error of x-bar and the standard error of p-hat.
Introduction Objectives
• Explain what is meant by statistical
inference
• Explain how probability is used to make
conclusions about statistical inference
Readability Activity
• We want to infer from the sample data some
conclusion about the population
• Excel function to select 14 pages
=RANDBETWEEN(13,341)
31, 34, 45, 48, 70, 132, 133, 181, 183, 257,
281, 282, 284, 306, 307
Confidence intervals
Significance tests
!
When you use statistical inference, you are acting as if the
data are a random sample or come from a randomized
experiment
Today’s 10.1 Objectives
There are more objectives for this section, but
here are today’s:
• List the (six) basic steps in the reasoning of
statistical estimation
• Distinguish between a point estimate and an
interval estimate
• Identify the basic form of all confidence
intervals
• Explain what is meant by margin of error
Inference is the process of trying to say
something about a population from information
we can get from a sample.
Sample values (____________) vary but the
population values (_____________) do not.
Any given sample value may or may not be
helpful in understanding a population value.
Only by considering our sample as one of many
such samples can we draw inferences.
(Examples 10.1-10.3 illustrate this process.)
Six Steps of Estimation
from
page
619
Confidence Interval Applet
of publisher’s website
may be helpful in clarifying steps 4 & 5.
One of the most common mistakes students make on the
AP Exam is misinterpreting the information given by a
confidence interval. There seems to be an almost
irresistible urge to attach meaning in terms of probability
to a found interval.
Probabilities are long-run relative frequencies, and the
idea simply doesn’t apply to a found interval. An
already constructed interval either does or does not
contain the population value.
While it is correct to give the meaning of “confidence” in
terms of probability (that is, “the probability that my
method of constructing intervals will capture the true
population value is 0.95”), it is never correct to interpret
a found interval using the language of probability.
IMPORTANT:
In a confidence interval,
our “confidence” is in the procedure used to generate the interval.
That is, we are “confident” that an interval so constructed will
contain the true population value 95% (or whatever the
appropriate confidence level) of the time.
Confidence Interval Applet (p 623-4)
Activity 10B
Practice:
P 624-626
10.1
10.2
10.5
10.6