HW-pgs. 632-633 (10.8, 10.10, 10.11)
**READ pgs. 633-637**
10.1-10.2 Quiz next THURSDAY 2-13-14
www.westex.org HS, Teacher Website
2-6-14
Warm up—AP Stats
NYT article
Name_____________________________
Date__________
AP STATS
Chapter 10 Estimating with Confidence
10.1 Confidence Intervals (Day 2)
Objectives:

State the three conditions that need to be present in order to construct a valid
confidence interval.

Explain what it means by the “upper p critical value” of the standard Normal
distribution.

For a known population standard deviation σ, construct a level C confidence interval
for a population mean.

List the four necessary steps in the creation of a confidence interval.
We will now learn how to calculate a level C confidence interval for the unknown mean µ of
a population. A very common error that students make on the AP Exam is to fail to
identify the conditions by which they are justified in constructing a confidence interval.
A question may direct you to “construct a confidence interval” without any specific
directions to justify it first. However, you must show that the conditions exist to
construct a valid confidence interval in order to get full credit on a question!
Be sure you check that the conditions for constructing a confidence interval are
satisfied before you perform any calculations.
Conditions for Constructing a Confidence Interval for µ
The construction of a confidence interval for a population mean µ is appropriate when
o the data come from an ______ from the population of interest. (______)
o the sampling distribution of x is approximately ___________________.
(________________)
o individual observations are _________________; when sampling without
replacement, the population size N is at least _____ times the
____________ size n. (_____________________)
To construct a level C confidence interval, we want to catch the central probability C
under a _____________ curve. To do that, we must go out z * standard deviations on
either side of the mean. Since any Normal distribution can be ___________________,
we can get the value z * from the standard Normal table.
It may be helpful to memorize the values of z * for C = 0.90, 0.95, 0.99.
Confidence level Tail area
z*
90%
95%
99%
0.050
0.025
0.005
1.645
1.960
2.576
Notice that for the 95% confidence we use z * = 1.960. This is more exact than the
approximate value z * = 2 given by the 68-95-99.7 rule.
Values z * that mark off a
specified area under the standard Normal curve are often called ________________
_______________ of the distribution.
Critical Values
The number z * with probability p lying to its _____________ under the standard
Normal curve is called the _____________ p critical value of the standard Normal
distribution.
Confidence Interval for a Population Mean (σ KNOWN)
Choose an ____ of size n from a population having ___________ mean µ and
____________ standard deviation σ. A level C confidence interval for µ is :
Here z * is the value that determines C between ____ and _____ under the standard
Normal curve. This interval is ____________ when the population distribution in Normal
and ________________ correct for large n in other cases.
Make sure that you understand the form of a confidence interval:
estimate  m arg in of error   estimate  critical value  s tan dard error 
See Example 10.5 (p.630) for an example of how to calculate a confidence interval.
Inference Toolbox (p.631)
Step 1: Parameter Identify the population of interest and the parameter you want to
draw conclusions about.
Step 2: Conditions Choose the appropriate inference procedure. Verify the conditions
for using it.
Step 3: Calculations
If the conditions are met, carry out the inference procedure.
Step 4: Interpretation Interpret your results in the context of the problem.
Remember the “three C’s”: conclusion, connection, and context.
All four steps in the process must be present in an inference problem on the AP
exam in order to receive full credit. We will use this four-step process throughout our
study of statistical inference.
Practice
10.7 Finding z*
Find z* for confidence level 97.5%
We can do this with our calculator or a table from our formula packet. In order to
understand what we are doing though it really helps to DRAW A PICTURE!!! (just like
from page 2 of our notes)
HW-pgs. 632-633 (10.8, 10.10, 10.11) *READ pgs. 633-637*10.1-10.2 Quiz next THURSDAY 2-13-14
10.9
Here
114
108
111
IQ Test Scores
are the IQ Test scores of 31
100 104 89
102 91
130 120 132 111
128
103 74
112 107 103
7th grade girls in
114 114 103
118 119 86
98
96
112
a midwestern school district:
105
72
112 93
Treat these girls as an SRS of all 7th grade girls in the school district. Suppose that the
standard deviation of IQ scores in this population is known to be σ = 15.
(a) Construct and interpret a 99% confidence interval for the mean IQ score in the
population. Follow the Inference Toolbox!
Step 1: Parameter Identify the population of interest and the parameter you want to
draw conclusions about.
Step 2: Conditions Choose the appropriate inference procedure. Verify the conditions
for using it.
SRS:
Normality:
Independence:
Step 3: Calculations
If the conditions are met, carry out the inference procedure.
Step 4: Interpretation
Interpret your results in the context of the problem.
Remember the “three C’s”: conclusion, connection, and context.