AP Statistics!!! - Somerset Independent Schools

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AP Statistics!!!
Chapter 4 Review

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

Sampling Error
◦ Occurs in the act of choosing the sample
◦ Undercoverage – certain members of
population are ‘left out’

Non Sampling Error
◦ Occurs after sample is chosen
◦ Non response – cannot be surveyed or refuse
to answer question.
◦ Response Bias
◦ Poorly Worded Questions

Stratified Sampling: One type of sampling is
called stratified sampling. Groups or classes
inside a population that share a common
characteristic are called strata. Example: In the
population of all undergraduate college students,
some strata might be freshman, sophomores,
juniors, or seniors. Other strata might be men
or women or in-state students or out-of-state
students, and so on. In this method, the
population if divided into at least two distinct
strata. Then a (simple) random sample (SRS) of
a certain size is drawn from each stratum.

Systematic Sampling: This is another
popular method of sampling. In this method,
it is assumed that the elements of the
population are arranged in some natural
sequential order. Then we select a (random)
starting point and select every kth element
for our sample. For example, to obtain a
systematic sample of 20 students going
through the cafeteria line at lunch, we could
pick a random number between, say 0 and
10.

Cluster Sampling: Cluster sampling is a method
used extensively by government agencies and certain
private research organizations. In cluster sampling
we begin by dividing the demographic area into
sections. Then we randomly select the sections or
clusters. Depending on the size of the cluster, every
member of the cluster or a random sample of
members of the cluster is included in the sample. For
example, in conducting a survey of school children in
a large city, we could first randomly select 30 schools
and then include all the children from each school or
a random sample of children from each school.

Convenience Sampling: This type of sampling simply
uses results or data that are conveniently and readily
obtained. In some cases, this may be all that is available,
and in many cases, it is better than no information at all.
However, convenience sampling does run the risk of being
severely biased. For instance, consider a newsperson who
wishes to get the ‘opinions of the people’ about a proposed
seat tax to be imposed on tickets to all sporting events.
The revenues from the seat tax will then be used to
support the local symphony. The newsperson stands in
front of a classical music store at noon and surveys the
first five people coming out of the store who will cooperate.
This method of choosing a sample will produce some
opinions, and perhaps some human interest stories, but it
certainly has bias.


Categorize the type of sampling method
used in each of the following situations.
(simple random (SRS); stratified;
systematic; cluster, multi-stage or
convenience)
◦ To conduct a pre-election opinion poll on the latest
school board election, samples of 5 households
from each telephone prefix (first three digits of the
phone numbers) in the voting district were called.


ANSWER: Multi-Stage
Categorize the type of sampling
method used in each of the following
situations.
 (simple random (SRS); stratified;
systematic; cluster, multi-stage or
convenience)



To conduct a study on depression among the
elderly, a sample of 30 patients in one nursing
home was used.
ANSWER: Convenience




Categorize the type of sampling method
used in each of the following situations.
(simple random (SRS); stratified;
systematic; cluster, multi-stage or
convenience)
Subscribers to the magazine Sound Alive were
assigned numbers. Then a sample of 30 subscribers
was selected by using a random number table. The
subscribers in the sample were invited to rate new
compact disc players for a “What a Subscribers Think”
column.
ANSWER: Simple Random (SRS)
Categorize the type of sampling
method used in each of the following
situations.
 (simple random (SRS); stratified;
systematic; cluster, multi-stage or
convenience)



To maintain quality control in a brewery, every
20th bottle of beer coming off the production line
was opened and tested.
ANSWER: Systematic


Categorize the type of sampling method
used in each of the following situations.
(simple random (SRS); stratified;
systematic; cluster, multi-stage or
convenience)

To judge the appeal of a proposed television sitcom, a
random sample of 10 people from each of three
different age categories were selected and those
chose were asked to rate a pilot show.

ANSWER: Stratified
Modern Managed Hospitals (MMH) is a national forprofit chain of hospitals. Management wants to
survey patients discharged this past year to obtain
patient satisfaction profiles. They wish to use a
sample of such patients. Several sampling
techniques are described below: Categorize each
technique as:
 (simple random sample, stratified sample,
multi-stage, systematic sample, cluster sample,
or convenience sample).

◦ Obtain a list of patients discharged from all MMH facilities.
Divide the patients according to length of hospital stay (3
days or less, 3-7 days, 8-14 days, more than 14 days).
Draw simple random samples from each group.

ANSWER: Stratified
Modern Managed Hospitals (MMH) is a national forprofit chain of hospitals. Management wants to
survey patients discharged this past year to obtain
patient satisfaction profiles. They wish to use a
sample of such patients. Several sampling
techniques are described below: Categorize each
technique as:
 (simple random sample, stratified sample,
multi-stage, systematic sample, cluster sample,
or convenience sample).
 Obtain lists of patients discharged from all MMH
facilities. Number these patients, and then use a
random number table to obtain the sample.
 ANSWER: Simple Random (SRS)



Modern Managed Hospitals (MMH) is a national
for-profit chain of hospitals. Management wants
to survey patients discharged this past year to
obtain patient satisfaction profiles. They wish to
use a sample of such patients. Several sampling
techniques are described below: Categorize each
technique as:
(simple random sample, stratified sample,
multi-stage, systematic sample, cluster
sample, or convenience sample).

Randomly select some MMH facilities from each of five
geographic regions, and then take random samples from
each of these hospital discharge lists.

ANSWER: Multi-Stage




Modern Managed Hospitals (MMH) is a national
for-profit chain of hospitals. Management wants
to survey patients discharged this past year to
obtain patient satisfaction profiles. They wish to
use a sample of such patients. Several sampling
techniques are described below: Categorize each
technique as:
(simple random sample, stratified sample,
systematic sample, cluster sample, or
convenience sample).
At the beginning of the year, instruct each MMH facility to
survey every 500th patient discharged.
ANSWER: Systematic
Modern Managed Hospitals (MMH) is a national forprofit chain of hospitals. Management wants to
survey patients discharged this past year to obtain
patient satisfaction profiles. They wish to use a
sample of such patients. Several sampling
techniques are described below: Categorize each
technique as:
 (simple random sample, stratified sample,
multi-stage, systematic sample, cluster sample,
or convenience sample).
 Randomly selected some MMH facilities and from each
of the facilities, ask every person from a discharge list
their satisfaction level.
 ANSWER: Cluster Sample





Modern Managed Hospitals (MMH) is a national
for-profit chain of hospitals. Management wants
to survey patients discharged this past year to
obtain patient satisfaction profiles. They wish to
use a sample of such patients. Several sampling
techniques are described below: Categorize each
technique as:
(simple random sample, stratified sample,
systematic sample, cluster sample, or
convenience sample).
Instruct each MMH facility to survey 10 discharged patients
this week and send in the results.
ANSWER: Convenience

An important part of employee compensation is a
benefits package that might include health insurance,
life insurance, child car, vacation days, retirement
plan, parental leave, bonuses, etc. Suppose you
want to conduct a survey of benefit packages
available in private businesses in Hawaii. You want a
sample size of 100. Some sampling techniques are
described below. Categorize each technique as:
(simple random (SRS); stratified, systematic,
cluster, multi-stage, or convenience).
◦ Assign each business in the Island Business Directory a
number and then use a random number table to select the
businesses to be included in the sample.

ANSWER: Simple Random (SRS)

An important part of employee compensation is a
benefits package that might include health insurance,
life insurance, child car, vacation days, retirement
plan, parental leave, bonuses, etc. Suppose you
want to conduct a survey of benefit packages
available in private businesses in Hawaii. You want a
sample size of 100. Some sampling techniques are
described below. Categorize each technique as:
(simple random (SRS); stratified, systematic,
cluster, multi-stage, or convenience).
Send a team of five research assistants to Bishop Street in downtown
Honolulu. Let each assistant select a block or building and interview an
employee from each business found. Each researcher can have the rest
of the day off after getting responses from 20 different businesses.
 ANSWER: Convenience




An important part of employee compensation is a
benefits package that might include health insurance,
life insurance, child car, vacation days, retirement
plan, parental leave, bonuses, etc. Suppose you
want to conduct a survey of benefit packages
available in private businesses in Hawaii. You want a
sample size of 100. Some sampling techniques are
described below. Categorize each technique as:
(simple random (SRS); stratified, systematic,
cluster, multi-stage, or convenience).
Use the postal ZIP Codes to divide the state into regions. Pick
a random sample of 10 ZIP Codes areas and then pick a
random sample of 10 businesses in each ZIP Code area.
ANSWER: Multi-Stage



An important part of employee compensation is a benefits
package that might include health insurance, life insurance,
child car, vacation days, retirement plan, parental leave,
bonuses, etc. Suppose you want to conduct a survey of
benefit packages available in private businesses in Hawaii.
You want a sample size of 100. Some sampling techniques
are described below. Categorize each technique as:
(simple random (SRS); stratified, systematic, cluster,
multi-stage, or convenience).
Use the Island Business Directory. Number all the
businesses. Select a stating place at random, and then use
every 50th business listed until you have 100 businesses.
ANSWER: Systematic



An important part of employee compensation is a
benefits package that might include health insurance,
life insurance, child car, vacation days, retirement
plan, parental leave, bonuses, etc. Suppose you
want to conduct a survey of benefit packages
available in private businesses in Hawaii. You want a
sample size of 100. Some sampling techniques are
described below. Categorize each technique as:
(simple random (SRS); stratified, systematic,
cluster, multi-stage, or convenience).
Group the businesses according to type: medical, shipping,
retain, manufacturing, financial, construction, restaurant,
hotel, tourism, other. Then select a random sample of 10
businesses from each business type.
ANSWER: Stratified
An important part of employee compensation is a
benefits package that might include health insurance,
life insurance, child car, vacation days, retirement
plan, parental leave, bonuses, etc. Suppose you
want to conduct a survey of benefit packages
available in private businesses in Hawaii. You want a
sample size of 100. Some sampling techniques are
described below. Categorize each technique as:
(simple random (SRS); stratified, systematic,
cluster, multi-stage, or convenience).
 You randomly selected several city blocks and survey
EVERY business located within that city block
 ANSWER: Cluster


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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