HW-pgs. 624-625 (10.1 - 10.4),
**READ pgs. 626-632**
10.1-10.2 Quiz Next Wednesday
www.westex.org HS, Teacher Website
1-31-12
Warm up—AP Stats
A shipment of ice cream cones has the
manufacturer’s claim that no more than 15% of
the shipment will be defective (broken cones).
Dairy Heaven Distribution Center will receive a
shipment of 1 million cones. Use the Normal
approximation of the binomial distribution to
calculate the probability that in a shipment of 1
million cones, Dairy Heaven Distribution Center
will find more than 151,000 broken cones.
Name_________________________
AP Stats
Chapter 10 Estimating with Confidence
10.1 Confidence Intervals
Date________
Introduction
How long can you expect a AA battery to last? It wouldn’t be practical to determine the
lifetime of every AA battery. Instead, we select a sample of individuals (in this case
batteries) to represent the population, and we collect data from those individuals. The goal
of statistical inference is to infer from the sample data some conclusion about the
________________. Statistical Inference provides methods for drawing
_____________ about a _________________ from ___________ data.
We cannot be certain that our conclusions are correct – a different sample might lead to
different conclusions. Statistical inference uses the language of probability to express the
_______________ of our conclusions. Probability allows us to take chance ____________
into account and to correct our judgment by calculation.
We will learn about the two most common types of formal statistical inference.
 confidence intervals (for estimating the value of population parameter)
 significance tests (which assess the evidence for a claim about a population)
Both types of inference are based on the __________________ distributions of statistics.
Both report probabilities that state what would happen if we used the inference method
_________ _________.
The methods of formal inference require the _______-_____ behavior that probability
describes. Inference is most reliable when the data are produced by a properly randomized
design. When you use statistical inference, you are acting as if the data are a
___________ sample or come from a ______________ experiment. If this is not true,
your conclusions may be open to challenge. Formal inference cannot remedy the basic flaws
in producing data, such a voluntary response samples and uncontrolled experiments. Proceed
to formal inference only when you are satisfied that the data deserve such analysis.
Confidence Intervals: The Basics
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. *See Example 10.1 (p.618)
Objective: List the six basic steps in the reasoning of statistical estimation.
1. To estimate the unknown population mean µ, use the mean x of our _____________
_____________.
2. Although x is an _______________ estimate of µ, it will _________ be exactly
equal to µ, so our estimate has some _____________.
3. In repeated samples, the values of x follow (approximately) a ___________
distribution.
4. The 95 part of the _________________ rule for Normal distributions says that in
about 95% of all samples, the mean x for the sample with be within _____ standard
deviations of the population mean µ.
5. Whenever x is within two standards deviation of µ, µ is within two standard deviations
of x . This happens in about ______ of all possible samples. So the unknown µ lies
between x  2 x in about _____ of all samples.
6. If we estimate that µ lies somewhere in the interval from x  2 x we would be
calculating this interval using a method that “captures” the true ____ in about 95% of
all possible samples.
The big idea is that the sampling distribution of x tells us how big the error is likely to be
when we use x to estimate µ. *See Example 10.2 (pp.620-621) and Example 10.3 (p.621)
Think of a confidence interval as a range of population values for which our found sample
value is likely.
Caution! One of the most common mistakes students make on the AP Exam is misinterpreting
the information given by a confidence interval. Probabilities are long-run relative
frequencies, and the idea simply does not 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 (e.g. “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.
We cannot know whether our sample is one of the 95% (or 90% etc.) for which the
interval captures the true population parameter, or whether it is one of the unlucky 5% (or
10% etc.). The statement that we are “95% confident” that the unknown population
parameter lies in our interval is shorthand for saying, “We got these numbers by a method
that gives correct results 95% of the time.” A 95% confidence interval catches the
unknown parameter in 95% of all possible samples.
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.
The basic form of a confidence interval is estimate  margin of error.
The margin of error shows how __________ we believe our guess is, based on the
_____________ of the _______________.
Objective: Explain what is meant by a “level C confidence interval.”
A level C confidence interval for a parameter has two parts:
 A confidence interval calculated from the data, usually of the form
estimate  margin of error
 A confidence level C, which gives the probability that the interval will capture the
true parameter in repeated samples. That is, the confidence level is the success rate
for the method.
The confidence level states the probability that the method will give a correct answer. That
is, if you use many 95% confidence intervals, in the long run 95% of your intervals will
contain the true parameter value. You do not know whether a 95% confidence interval
calculated from a particular set of data contains the true parameter value.
We can choose the confidence level, usually 90% or higher because we want to be quite sure
of our conclusions. We will use C to stand for the confidence level in decimal form.
Be sure you understand the basis for our confidence. There are only two possibilities.
1. Our interval contains the true population parameter (µ or p ).
2. Our SRS was one of the few samples for which our statistic ( x or p̂ ) is not within 
the margin of error of the true parameter (µ or p ).
*See Figure 10.4 (p.622) (Make sure you understand this illustration)
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click on Confidence Interval
HW-pgs. 624-625 (10.1 - 10.4), **READ pgs. 626-632** 10.1-10.2 Quiz Next Wednesday
www.westex.org
HS, Teacher Website