AP Statistics
10.1 Confidence Intervals: The Basics
Objectives: Distinguish between a point estimate and an interval estimate
Explain what is meant by margin of error
Explain what is meant by level C confidence interval
Do Now:
Read 10.1 Introduction, and fill in the blanks below:
Statistical Inference:
CAUTION: When you use inference, you are acting as if the data are a RANDOM SAMPLE or
come from a RANDOMIZED experiment.
Recall:
𝒙̅
=
, 𝒙̅ =
, Central Limit Thm. if for _______________ Distributions
A Level “C” confidence interval for a parameter has two parts
 A confidence level interval calculated from the data

A confidence interval C gives the probability that the interval will capture the true parameter
value in repeated samples
BIG IDEA: sampling distribution of x̅ tells us how big the error is when we use x̅ to estimate 
Exercise 10.5 (pg. 626)
Confidence Interval for a population Mean (when  is known)
Depends on three important conditions
1. SRS our data must come from a Simple Random Sample
2. Normality  sample mean is at least approx. Normal. Remember to consider the
CLT when assessing Normality.
3. Independence  Make sure samples are independent and REQUIRE N  10n
BE SURE TO CHECK THAT THESE CONDITIONS ARE SATISFIED BEFORE YOU PERFORM ANY
CALCULATIONS
AP Tip  you must show that the conditions exist to construct a valid confidence interval in order to
get full credit. If there is a question to whether one of the conditions is met, remember to make note
as to why it is questionable and proceed with calculations.
Critical Values (z*) The number z* with probability p lying to its right under the standard Normal
Curve
Confidence Level
90%
95%
99%
Tail Area
.05
.025
.005
Z*
1.645
1.960
2.576
Calculator: STAT  Test  7: ZInterval
Confidence Interval for a Populations Mean (when  is known)
Interval is exact when the population distribution is Normal and approximately correct for large n in
other cases (Central Limit Thm.)
KEYS TO SUCCESS  Confidence Intervals
1. PARAMETER  Identify the pop of interest and the parameter you want to draw
conclusions about.
2. CONDITIONS  Choose the appropriate inference procedure. Verify ALL conditions for
using it.
3. CALCULATIONS  Carry out the calculations
4. INTERPRETATION  Remember to talk about your conclusion, your calculations and the
context of the problem (THE 3 C’s)
You Try: Exercise 10.9 (pg. 632)
How Confidence Intervals Behave
The margin of Error is
and this will get smaller when
1. z* gets smaller
2.  gets smaller
3. n gets larger
Determine Sample Size
If you have a desired margin of error (m) you can use the following to determine the
sample size:
Cautions:
1. Data MUST be an SRS (you will learn different methods for different designs)
2. There is no correct method for inference when data is haphazardly collected with bias of
unknown size. Always keep this in mind when setting up a study
3. Outliers can distort the results; remember this is mean-based analysis
4. Shape Matters!!!
5. You MUST know 
Exercise 10.13 (pg. 637)
Exercise 10.14 (pg. 637)
HW: #10.19 – 10.26
On Your Own:
Independently complete the following example. Hand in to the blue bin when complete and
begin working on your HW.
The average price of 40 recently purchased Darien homes (taken via an SRS) was $730,000.
Assume that the true standard deviation of Darien home prices (of homes recently purchased) is  =
$60,000. Construct a 95% confidence interval for the true average price of all recently purchased
homes in Darien.
On Your Own:
Independently complete the following example. Hand in to the blue bin when complete and
begin working on your HW.
The average price of 40 recently purchased Darien homes (taken via an SRS) was $730,000.
Assume that the true standard deviation of Darien home prices (of homes recently purchased) is  =
$60,000. Construct a 95% confidence interval for the true average price of all recently purchased
homes in Darien.