HW-pgs. 637-638 (10.13, 14, 17)
**READ pgs. 639,642-648**
www.westex.org HS, Teacher Website
2-7-14
Warm up—AP STATS
1. Regarding the problem at the end of class
yesterday, what is the confidence interval. Give
the answer to your calculation in context. Put
your ANSWERS on your note sheet from
YESTERDAY!
NYT article
Name_______________________________
Date__________
AP STATS
Chapter 10 Estimating with Confidence
10.1 Confidence Intervals (Day 3)
Objectives:

Identify three ways to make the margin of error smaller when constructing a
confidence interval.

Determine the sample size necessary to construct a level C confidence interval for
a population mean with a specified margin of error.

Identify the “warnings” about constructing confidence intervals.
The user chooses the confidence level, and the _________________________ follows
from this choice. We would like ________ confidence and also a ___________
margin of error. High confidence says that our method almost always gives
____________ answers. A small margin or error says that we have pinned down the
__________________ quite precisely.
The margin of error z *

gets smaller when
n
o z * gets __________________. Smaller z * is the same as smaller confidence level
C.
o σ gets __________________. Reducing σ is very difficult in practice, however.
o n gets __________________. Increasing the sample size n reduces the margin
of error for any fixed confidence level. Because we take the square root of n, we
must take ________ times as many observations in order to cut the margin of
error in half.
Make sure you understand the trade-offs between high confidence and a low margin of
error. For fixed, n, higher confidence implies a wider interval (the more certain you want
to be that you have captured the parameter). A small margin of error implies low
confidence and vice versa. Only by manipulating n can you control the margin of error.
In this section you will learn how to determine the sample size n needed to produce a
specified margin of error when constructing a confidence interval for a population mean.
You can arrange to have both high confidence and a small margin of error by taking
enough ____________.
Sample Size for a Desired Margin of Error
(when constructing a confidence interval for a population mean)
To determine the sample size n that will yield a confidence interval for a population mean
with a specified margin of error m, set the expression for the margin of error to be less
than or equal to m and solve for n:
z*

n
m
Always round up to the next whole number when finding n.
Notice that it is the size of the _____________ that determines the margin of
error. The size of the __________________ does not influence the sample size
we need. (This is true as long as the population is much larger than the sample.)
HW-pgs. 637-638 (10.13, 14, 17)
**READ pgs. 639,642-648**
Some Cautions
The recipe x  z *

n
for estimating an unknown population mean comes with the following
warnings:
1. The data must be an _______ from the population.
2. Different methods are needed for different designs. (The confidence interval
formula isn’t correct for probability samples more complex than an SRS. Correct
methods for other designs are available. We will not discuss confidence intervals
based on multistage, cluster, or stratified random samples. )
3. There is no correct method for inference from data haphazardly collected
with bias of unknown size. (Fancy formulas cannot rescue badly produced data.)
4. __________________ can distort the results. (Because x is strongly influenced
by a few extreme observations, outliers can have a large effect on the confidence
interval.)
5. The ____________ of the population distribution matters. (Examine your data
carefully for skewness and other signs of non-Normality.)
6. You must know the _____________
______________ of the population.
(This unrealistic requirement renders the interval x  z *

of little use in
n
statistical practice. We will learn in the next section what to do when  is
unknown.)
7. The margin of error in a confidence interval covers only ______________
sampling errors. (The margin of error is obtained from the sampling distribution
and indicates how much error can be expected because of ________ variation in
randomized data production. Practical difficulties, such as undercoverage and
nonresponse in a sample survey, can cause additional errors that may be larger than
the random sampling error. Remember this when reading the results of an opinion
poll or other sample surveys. The practical conduct of the survey influences the
trustworthiness of its results in ways that are not included in the announced
margin of error.)
Finally, you should understand what statistical confidence does not say. We are
95% confident that the mean IQ score for all Big City University freshman lies
between 107.8 and 116.2. That is, these numbers were calculated by a
________________ that gives correct results (captures the true population mean)
in 95% of all _______________ _____________. We cannot say that the
probability is 95% that the true ________ falls between 107.8 and 116.2.
No randomness remains after we draw one particular sample and get from it one
particular interval. The true mean either is or is not between 107.8 and 116.2.
The probability calculations of standard statistical inference describe how often the
method gives correct answers. (p. 637)
This last paragraph cannot be overemphasized. You should read it several times and come
back to it again and again. Our “confidence” is in the method used to construct an
interval, not in any particular interval constructed by that method.
10.15 Confidence level and margin of error-High School students who take the SAT
Mathematics exam a second time generally score higher than on their first try. The
change in score has a normal distribution with standard deviation σ = 50. A random
sample of 1000 students gain an average of x = 22 points on their second try.
a) Construct and interpret a 95% confidence interval for the mean score gain µ in the
population.
Parameter-Identify the population of interest and the parameter you want to draw
conclusions about.
Conditions-Choose appropriate inference procedure & verify the conditions for using it.
SRS:
Normality:
Independence:
Calculations-If the conditions are met, carry out the inference procedure.
Interpretation-Interpret your results in the context of the problem.
b) Calculate the 90% and 95% confidence interval for µ.