Download AP Stat Ch. 5 Day 1 Lesson Worksheet 08

AP STATISTICS
Chapter 5 – Producing Data
Section 5.1: Designing Samples
Day 1: Assignment (see syllabus)
Name _______________________
Date __________
Period _____
A. Review homework: Read Introduction to Chapter 5 (pp. 265-270)
Submit a description and example of these 3 things:
a) an observational study,
b) a statistical experiment, and
c) a statistical simulation
B. Key vocabulary: observational study, statistical experiment, statistical simulation,
population, census, sample, sample design,
bias in sampling - voluntary response sample, convenience sample,
cautions – undercoverage, nonresponse, response bias, question wording bias,
probability sampling, SRS – simple random sample, systematic random sample,
table of random digits (see back), strata, stratified random sampling,
multistage sampling and clusters, sample size and accuracy: larger = better!
C. The three basic models for producing data are observational studies, statistical experiments, and
statistical simulations. The focus today is designing and understanding observational studies.
Observational study – observe individuals and measure one or more variables of interest but
do not attempt to influence the responses.
Example:
Dr. Lehman would like to know what percent of the senior class wants to preserve
the . He obtains an alphabetized list of all the seniors, assigns them numbers from
001 to n, uses his handy dandy table of random digits to randomly select 50,
summons all selected students one by one to his office, hands each a slip of paper
with this on it:
Should be we preserve the ? Circle One: YES
NO
The student circles one, folds the slip of paper, and drops it in the bag.
Dr. Lehman counts the number of yes responses and determines proportion.
D. Some basics through the example above:
Population – all seniors at LHS: N=?
Individual - each senior is an individual member of the population
Variable – characteristic of the population being “measured”: yes or no on the question, in this case
Census - all seniors are (the entire population) asked the question; all N are asked
Sample - 50 of the seniors were selected from the whole population; n=50
Sample design – a simple random sample
E. Sample Design – The key to success!
“No amounting of torturing of the data can make it tell the truth if the sample design is bad!”
F. Good sample design increases the probability that the sample drawn from the population is
representative and that the data will be unbiased.
G. Bias in sampling is to be avoided at all cost! What to watch out for?
Bad designs:
Voluntary response “sampling”
“Call 1-800-YOU-TELL to express your opinion”
Convenience “sampling”
I ask you if seniors rule!
Cautions:
Under coverage – a sub part of the population is under represented
SRS of LHS students with n=40, but no seniors are randomly selected
Over coverage – if under coverage happens, then this will, too.
If the seniors are under represented, then another class must be over represented!
Response bias – “response” is influenced by the context or manner of data collection
Dr. Lehman watches you fill in your answer!
Non-response – individual selected is not measured for some reason
You decide to not respond to Dr. Lehman’s summons, or refuse to answer
Question wording bias – wording “pushes” response in a particular direction
“Only an idiot would want to mess with tradition!”
Should be we preserve the ? Circle One: YES
NO
H. Good sampling designs produce representative samples by using randomness (chance) – the good
methods use probability sampling. The idea is that a sample chosen using randomness (in the right way) is
likely to be representative and unbiased. The core idea behind each good design is that each individual in a
population being sampled has an equal probability of being chosen
Good designs:
Simple Random Sample (of size n): a sample obtained in such manner that all possible
samples of size n are equally likely
Put all individuals in the population in a bag, shake real well, draw n, measure
Stratified Random Sample: stratify the population on some defineable and
Important characteristic, then use a separate SRS in each strata
Divide LHS student body into classes and SRS each class
Systematic Random Sample: “list” all individuals, the systematically draw n from list
List all 250 frosh alphabetically, randomly select a number from 1 to 10, use as
starting point, then select every 10th one after that to get 25 individuals
Multistage Sampling with Clusters
Identify all elementary schools in Oregon, randomly select 10 of them, randomly
choose one 4th grade class from each school, measure all 4th graders in class.