Download chapter 10: introduction to inference - Hatboro

Name _______________________________
AP STATISTICS CHAPTER 8: ESTIMATING WITH CONFIDENCE
Confidence Intervals:
A _____________________ is a statistic that
provides an estimate of a population parameter. The
value of that statistic from a sample is called a
_______________________. Ideally, a
_________________ is our ____________________
at the value of an unknown parameter.
A Confidence interval for a population characteristic
is an ________ of ________________for the
characteristic. It is constructed so that, with a chosen
______________ of _______, the value of the
characteristic will be ___________ inside the
_______.
Formula for Confidence Interval:
Margin of error:
3 ways to make Margin of error smaller:
Confidence Level:
Interpretations (2 different ways )
What are 3 things you should NOT say?
What are the conditions required to construct a
Confidence Interval?
Name _______________________________
AP STATISTICS CHAPTER 8: ESTIMATING WITH CONFIDENCE
SOME COMMON CONFIDENCE LEVELS AND THEIR z*
VALUES
1. Confidence level 90%
2. Confidence level 95%
3. Confidence level 99%
Other z* values can be found
STEPS IN CONSTRUCTING A CONFIDENCE INTERVAL.
1.
2.
3.
4.
5.
One-Sample z interval for a Population
Proportion.
When the standard deviation of a statistic is estimated
from data, the result is called the
_______________________ of the statistic.
Name _______________________________
AP STATISTICS CHAPTER 8: ESTIMATING WITH CONFIDENCE
Example: The Gallup Youth Survey asked a random
sample of 439 U.S. teens aged 13 to 17 whether they
thought young people should wait to have sex until
marriage. Of the sample, 246 said “Yes”. Construct
and interpret a 95% confidence interval for the
proportion of all teens who would say “Yes” if asked
this question.
Example: The present packaging system produces
10% defective cereal boxes. Using a new system, a
random sample of 200 boxes had 11 defects. Does
the new system produce fewer defects? Construct a
confidence interval to answer this question.
Sample Size for Desired Margin of Error
Example: A company has received complaints about
its customer service. The managers intend to hire a
consultant to carry out a survey of customers. Before
contacting the consultant, the company president
wants some idea of the sample size that she will be
required to pay for. One critical question is the
degree of satisfaction with the company’s customer
service, measure on a five-point scale. The president
wants to estimate the proportion p of customers who
are satisfied (that is, who choose either “satisfied” or
“very satisfied,” the two highest levels on the fivepoint scale). She decides that she wants the estimate
to be within 3% at a 95% confidence level. How
large a sample is needed?
SUMMARY/QUESTIONS TO ASK IN CLASS
Name _______________________________
AP STATISTICS CHAPTER 8: ESTIMATING WITH CONFIDENCE
One Sample z interval for a Population Mean
Example: A random sample of the SAT math scores
of 500 California high school students yields a mean
of 461. We know that the standard deviation for all
seniors is 100. Construct a 95% confidence interval
for the mean of all California students. Comment on
the meaning of this interval.
Example: A test for the level of potassium in the
blood is not perfectly precise. Suppose that repeated
measurements for the same person on different days
vary normally with s = 0.2. A random sample of
three has a mean of 3.2. What is a 90% confidence
interval for the mean potassium level
Choosing the Sample Size
Example: The heights of HH male students is
normally distributed with s = 2.5 inches. How large a
sample is necessary to be accurate within + .75
inches with a 95% confidence interval?
SUMMARY/QUESTIONS TO ASK IN CLASS
Name _______________________________
AP STATISTICS CHAPTER 8: ESTIMATING WITH CONFIDENCE
The t Distributions
When the
of a statistic is
estimated from the data, the result is called the
of the statistic, and is
given by
.
When we use this estimator, the statistic that results
does not have a normal distribution, instead it has a
new distribution, called the
.
The variability of the t-statistic is controlled by the
.
The number of
is equal to
.
ASSUMING NORMALITY?
USING THE t PROCEDURES
1.
2.
3.
4.
SUMMARY/QUESTIONS TO ASK IN CLASS
Name _______________________________
AP STATISTICS CHAPTER 8: ESTIMATING WITH CONFIDENCE
Example: A manufacturer of high-resolution video terminals must control the tension on the mesh of fine wires that
lies behind the surface of the viewing screen. Too much tension will tear the mesh, and too little will allow wrinkles.
The tension is measured by an electrical device with output readings in millivolts (mV). Some variation is inherent
in the production process. Here are the tension readings from a random sample of 20 screens from a single day’s
production:
Construct and interpret a 90% confidence interval for the mean tension μ of all the screens produced on this day.
Environmentalists, government officials, and vehicle manufacturers are all interested in studying the auto exhaust
emissions produced by motor vehicles.
The major pollutants in auto exhaust from gasoline engines are hydrocarbons, carbon monoxide, and nitrogen oxides
(NOX). Researchers collected data on the NOX levels (in grams/mile) for a random sample of 40 light-duty engines
of the same type. The mean NOX reading was 1.2675 and the standard deviation was 0.3332.


(a) Construct and interpret a 95% confidence interval for the mean amount of NOX emitted by light-duty
engines of this type.
(b) The environmental Protection Agency (EPA) sets a limit of 1.0 gram/mile for NOX emissions. Are you
convinced that this type of engine has a mean NOX level of 1.0 or less? Use your interval from (a) to
support your answer.
SUMMARY/QUESTIONS TO ASK IN CLASS
Name _______________________________
AP STATISTICS CHAPTER 8: ESTIMATING WITH CONFIDENCE
Example : The times of first sprinkler activation (seconds) for a series of fire-prevention sprinklers were as follows:
27
30
24
41
33
22
24
27
27
23
28
35
22
Construct a 95% confidence interval for the mean activation time for the sprinklers.
An inference procedure is called _____________ if the probability calculations involved in that procedure remain
fairly accurate when a condition for using the procedure is violated.
SUMMARY/QUESTIONS TO ASK IN CLASS