AP Statistics!!! - Somerset Independent Schools

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AP Statistics!!!
Test Review 2013
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Sampling Error
◦ Occurs in the act of choosing the sample
◦ Undercoverage – certain members of population are
‘left out’
 Suppose we use poll people a group of people at a golf
tournament about how they feel about the Affordable
Care Act…

Non Sampling Error
◦ Occurs after sample is chosen
◦ Non response – cannot be surveyed or refuse to
answer question.
◦ Response Bias
◦ Poorly Worded Questions
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Which type of error is made when you use phone
calls to sample people, but you call during
working hours?
◦ Answer: Non Response (non sampling error)

Which type of error is made when you use a
telephone to sample people?
◦ Answer: Undercoverage (sampling error)

What type of error is shown below:
◦ Question: “How do you feel that the extremely
expensive Affordable Care Act will help your and
your family’s overall health and wellness?”
◦ Answer: It is a poorly worded question
(nonsampling error) and will UNDERESTIMATE the
support for the A.C.A.

Voluntary Response Sample
◦ Participants ‘choose’ or volunteer themselves (not random; very biased)

Convenience Sample
◦ We only include who is ‘convenient’ to survey. (not truly random; biased)

Simple Random Sample (SRS)
◦ Every person has an equal chance to be selected (“all the names are in ‘one
pot’”) DO NOT BREAK INTO GROUPS!!!

Stratified Random Sample
◦ Population is divided into groups or ‘strata’ that are made up of similar
individuals within each group. You do an SRS within each group.

Systematic Sample
◦ We sample every ‘kth’ person after the first person is randomly selected.

Multi-Stage Sample
◦ Done on a large scale; combining other types of sampling methods; you
sample to choose GROUPS, then sample within the groups.

Cluster Sample
◦ Population is divided into groups that don’t necessarily all look alike; the
clusters should ‘mirror the population; you sample to choose GROUPS, then
take a census within the group.
Review of Chapter 4 Vocab

Simple Random Samples (“chopping
through #’s)
◦ Labels
 9 people?
 10 people?
 100 people?
 57 people?
 124 people?

You have two dogs, each of whom have a
litter of 12 puppies. You want to determine
the amount of weight gain over 12 weeks
based on the type of food you give them. If
you give puppy food #1 to one dog’s 12
puppies and puppy food #2 to the other
dog’s 12 puppies and then compare the
weight gain after 12 weeks, what type of
experiment have you carried out?
◦ Answer: An experiment, but NOT completely
randomized


Puppies… continued…
Suppose you now give puppy food #1 to
an SRS of 6 puppies from one ‘momma
dog’ and an SRS of 6 puppies from the
other ‘momma dog’, with the remaining
12 puppies from the two ‘momma dogs’,
then what type of design have you used
now?
◦ Answer: Block Design, based on which
‘momma dog’
Explain Double-blind experiments
 …. Single-blind…


Suppose that you decide to do a survey in
Somerset to inquire about a ‘particular issue’.
You decide to select an SRS of 50 homes in
the city limits and you contact them for a
face-to-face interview that consists of 2
questions. What is the chance that all 50
homes just happened to be drawn from the
same neighborhood (Oaklawn)?
◦ Answer: the same chance as for any other set
of 50 homes….
S

You wish to do a survey of residents in the
state of Tennessee. You select an SRS of
100 adults heads of households in each
county in the state and ask their opinion
on the selected topic. What type of
sample is this?
◦ Answer: Stratified
Does the amount of sales of ice cream (in
dollars) accurately predict the number of
drowning's in Lake Michigan?
 Does ice cream CAUSE drownings?
 Consider what conclusion can be drawn?

◦ Answer: Lurking/confounding variable –
seasonal variation in temperature… hotter
it is, more ice cream consumed…. More
people swim…. Thus, more drownings…

An experiment will take place at Kroger, in
which participants will taste test each of
two kinds of sweet tea. What type of
design is this?
◦ Answer: Matched Pairs
I choose to do a survey at Somerset High
School. I randomly select 2 homerooms
per grade and ask every student in those
homerooms the selected question.
 What type of sample is this?

◦ Answer: Cluster… (sample, then census)
I decide to do a large-scale sample using
Gallup. I want to gather information
about feelings about a potential major
candidate for the U.S. presidency. I then
select 10 states, and then within those 10
states, I select 2 AREA CODES and then
select 200 people randomly from those
AREA CODES to be a part of the survey…
 What type of sample is this?

◦ ANSWER: Multi-stage

I decide to do a survey at the University
of Alabama. I decide to divide the
student population into groups based on
the following criteria
◦ In state and in what 5 different regions from
AL they are from
◦ Out-of-state
◦ I then do random samples within each of the 6
groups.
◦ What type of sample have I done?
◦ ANSWER: Stratified
Why is doing an SRS of 100 people
preferable to doing an SRS of just 10
people?

At a certain university, students who live in dormitories eat
at a common dining hall. Recently, some students have
been complaining about the quality of the food service
there. The dining hall manager decides to do a survey to
estimate the proportion of students living in the
dormitories who think the quality of food should be
improved. One evening, the manager asked the first 100
students entering the dining hall to answer the following
question:
Many students believe that the food served in the dining hall needs improvement. Do
you think that the quality of food services here needs improvement, even though that
would increase the cost of the meal plan?
_____ Yes _____ No ______ No Opinion.
FRAPPY #1: ‘DORM FOOD’
a.
In this setting, explain how bias may have been
introduced based on the way this convenience
sample was selected and suggest how the
sample could have been selected differently to
avoid that bias.
a.
In this setting, explain how bias may have been
introduced based on the way the question
was worded and suggest how it could have
been worded differently to avoid that bias.



Questions…

INTENT: Measures student knowledge of:
◦ How bias affects sample selection.
◦ How wording of question affects sample results.

Scoring Criteria:
◦ Part a:
 Must correctly explain how this type of sampling method
will introduce bias.
 Must create a better sampling method that would
avoid/lessen bias.
◦ Part b:
 Must explain how the wording of the question introduced
bias.
 Must offer a better way to word the question.
SCORING CRITERIA & INTENT

Part a:
◦ The issue is that the first 100 people who enter the
dining hall are likely individuals who like the food the
most, simply because they are there and are FIRST to be
in line.
◦ ANSWERS must show a better design (RANDOM);
but should not simply resort to a census or a
‘better’ convenience sample.
 “I would have a dining hall employee hand a survey to
every 10th person who is line all day long and ask them to
answer the question.”
 “I would do a stratified sample of all the dorms on
campus. Within each dorm randomly select rooms based
on their assigned room number and ask them the
question.”
Model Solution

Part b:
◦ TWO WAYS OF LOOKING AT IT…
 The question is a ‘leading question’ in that it suggests
that other students have already expressed there
disapproval of the food in the dining hall, which would
make students chooses ‘yes’
 The question also suggest rising costs of the meal plan,
which would cause students to answer ‘no’
◦ BETTER WAY:
 “It would be best to leave out the part stating how
other students feel and the part about the increase in
costs and just ask: “Do you think the quality of food
services here needs improvement?”
Model Solution

An apartment building has nine floors and
each floor has four apartments. The
building owner wants to install new
carpeting in eight apartments to see how
well it wears before she decides whether
to replace the carpet in the entire
building.
AP Statistics – Chapter 4 FRAPPY Practice #4
2011 AP Statistics Exam Question #3
The figure below shows the floors of apartments in the building with their apartment numbers.
Only the nine apartments indicated with an asterisk (*) have children in the apartment.
a. For convenience, the apartment building owner wants to use a
cluster sampling method, in which the floors are clusters, to select
the eight apartments. Describe a process for randomly selecting
eight different apartments using this method.

b. An alternative sampling method would be to select a stratified
random sample of eight apartments, where the strata are
apartments with children and apartments with no children. A
stratified random sample of size eight might include two randomly
selected apartments with children and six randomly selected
apartments with no children. In the context of this situation, give
one statistical advantage of selecting such a stratified sample as
opposed to a cluster sample of eight apartments using the floors as
clusters.
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