WARM – UP
The population average height for Jamesville HS is 68 cm.
(σ = 2.341 cm). What is the probability that if you select 5
students, at least 2 of them will be taller than 71 cm?
x
(Assume Normality)
P z
1. What is the probability that a randomly selected student
ö
will be taller than 71 cm? æ 71- 68 ÷
P ççz >
= P (z > 1.2815)
÷
First : Find P(X > 71)
÷
çè
2.341 ø
Normalcdf(1.2815, E99) = 0.10 or 10%
2. Go to Line 15 and simulate 8 trials.
Single digits 0-9: 0 = Height > 71 cm
1 - 9 = Height < 71 cm.
Line 15: 76488 88899 15860 07370 13431 84041 69202 18912
1/8 = 0.125
Identify the type of sampling used in each example.
A researcher randomly selects 8 schools from one school district
with 38 schools and interviews all the teachers at each of the 8.
Cluster sampling
At a college there are 120 freshmen, 90 sophomores, 110 juniors,
and 80 seniors. A school administrator selects a random sample of
12 of the freshmen, a random sample of 9 of the sophomores, a
random sample of 11 of the juniors, and a random sample of 8 of
the seniors. She then interviews all the students selected.
Stratified sampling
At the local college a survey was being done on whether or not the
students liked the cafeteria food. The survey was located in the
college newspaper and was to be filled out and sent to the editing
office.
Voluntary Response sampling
At the end of each semester a local college requires a teacher's
evaluation. An evaluation survey is given to all students to fill out.
“Attempted” Census
Identify the type of sampling used in this example.
During a particular weekend, a reporter who manages many
apartment buildings, interviews almost everyone in his building.
The reporter finds that everyone, including himself, is satisfied with
the conditions with the apartment building.
Convenience sampling
A new clothing store in town emphasizing mainly children clothing.
Before opening, management had to decide whether to only carry
either men's, women's, boys', girls', or infants' clothing. After
performing representative sampling of potential customers from
each of these groups, it was decided to carry only children’s
clothing.
Stratified sampling
The human resources department of a large firm is behind schedule
in sampling the job satisfaction of the company's employees. In an
effort to catch-up, the HR manager quickly goes down an
alphabetical list of employees and e-mails a survey to every tenth
employee.
Systematic sampling
Identify the type of sampling used in this example.
The human resources department of a large firm is behind schedule
in sampling the job satisfaction of the company's employees. In an
effort to catch-up, the HR manager numbers the alphabetical list of
employees and uses a random number generator to select 20
employees
Simple Random Sample
WARM - UP
You want to conduct a survey about the opinions students
have with regards to AP Statistics. Describe the Bias the
may result from… Voluntary Response, Undercoverage,
Nonresponse , Response, or Poor Wording of the Question
1. Putting an ad in the Pony Express asking students to go to a
website and fill out a survey. Voluntary Response Bias
2. Asking the first 5 students who enter B211.
3. Randomly selecting 5 students and asking…“Everyone I
have asked just loves AP Stats, you would have to be dumb
not too. How do you feel about Stats? Poor Wording Bias
4. Randomly selecting 5 students who made 5 (100%) on the
AP Statistics exam.
5. Randomly selecting Statistics students from FACEBOOK.
Chapter 12 (continued)
Randomization
• Randomizing protects us from the influences of all the
features of our population, even ones that we may not
have thought about.
– Randomizing makes sure that on the average the
sample looks like the rest of the population.
• Bias: Any systematic failure of a sampling method to
represent the entire population.
• Randomization REDUCES Bias!
Simple Random Samples
• Samples drawn at random generally differ from
one another.
– Each draw of random numbers selects different
people for our sample.
– These differences lead to different values for the
variables we measure.
– Sample-to-sample differences are called Sampling
Variability.
Cluster and Multistage
Sampling (cont.)
• Sometimes we use a variety of sampling
methods together.
• Sampling schemes that combine several
methods are called Multistage Samples.
• Most surveys conducted by professional
polling organizations use some
combination of stratified and cluster
sampling as well as simple random
sampling.
Populations and Parameters
A value that represents a characteristic of a population is
called a population parameter.
(μ = Population Mean p = Population proportion.)
A value that is CALCULATED from sample data is called
a Statistic.
( x = sample mean, p̂ = sample proportion.)
HW Page 290 11-17, 21, 27, 28
Cautions in Sampling
1. Voluntary Response Bias: Individual with strong opinions
choose themselves
2. Undercoverage occurs when some groups in the population
are left out of the process of choosing the sample.
3. Nonresponse occurs when an individual chosen for the
sample can’t be contacted or refuses to cooperate.
4. Response Bias occurs when the behavior of the respondent
or interviewer leads to a systematic favoring of one response.
Respondents may lie or give an “expected” answer.
5. Poor Wording of the Question Bias occurs when the
question is confusing or leading.
Warm-Up: You invent a new chocolate bar and you want to
gather information about it’s likeability from the population of
US consumers. Using Undercoverage, Nonresponse,
Response Bias, Poor Wording, or Voluntary Response,
describe what is wrong with the following sampling methods?
A. You randomly select 10 households. Six are not home
and 4 slam the door in your face.
Nonresponse
B. You randomly select 10 individuals who all happen to be
new employees that work under you.
Response Bias
C. You randomly select 10 individuals who are all in the
Weight Watchers program. None of them have had
chocolate for 5 years but agree to eat yours.
Response Bias
Undercoverage, Nonresponse, Response Bias, Poor Wording, or
Voluntary Response
D. You randomly select 10 individuals from the Richardson
Phone Book and ask them to come in for a taste test.
Undercoverage
E. You put the bars along with a questionnaire next to a time
clock.
Voluntary Response
F.
You explain how extremely beneficial the candy is to
general health. You then ask them to taste it and comment
on its manifestation, its majestic consistency, and its
astounding eminence.
Poor Wording of the Question
Example
You want to conduct a survey about the opinions students
have with regards to AP Statistics. How would you select
5 individuals from this previous year statistics.
1. DARAIS, NATHAN A
2. DAVIS, MADISEN E
3. FARAGO, PETER
4. GOODWIN, JONATHAN J
5. GUNTER, AUSTIN S
6. KAWALSKY, ERIC M
7. LOEWENSTEIN, BEN N
8. MANDELBAUM, CAREN L
9. MICHELL, ANDREW R
10.MILLER, TYLER L
11.PIERCE, TAYLOR
12.REDLINGER, JOHN L
13.ROBINSON, CHAD B
14.SCHUTZA, EVAN J
15.SLATE, LEE
16.SMEJDIR, ANDREW D
17.STEPHENS, JOHN-MICHAEL
18.STIEG, ANNE M
19.WHALEY, CHLOE
20.WINER, LEMORE P
21.YANG, MATTHEW
22.ZACK, AARON E
• Work hard to avoid influencing responses.
Cluster and Multistage
Sampling
• Sometimes stratifying isn’t practical and simple
random sampling is difficult.
• Splitting the population into similar parts or
clusters can make sampling more practical.
– If we select one or a few clusters at random and
perform a census within each of them, this sampling
design called Cluster Sampling.
– If each cluster fairly represents the full population,
cluster sampling will give us an unbiased sample.