Question

MATH225 Statistical Reasoning for the Health Sciences

Week 1 Assignment Comparing Sampling Methods

Question 1 A quality-assurance worker wants to
systematically sample 120 glass jars each day from a conveyor belt
in a factory that puts out 3,600 jars each day. If the worker will
select every kth jar, what is the best value of k for the worker to
use? Enter a whole number.

Question A quality manager at a manufacturing plant needs to
get a sample of widgets for monitoring the manufacturing processes.
He plans to choose one out of every N widgets produced. The plant
makes about 5100 widgets per day, and the quality team has enough
time to examine about 60 widgets each day. What value should the
manager use for N? Enter a whole number.

Question A town planner is interested in getting some
demographic data about the households in the city. The city has ten
wards that vary in size. Which sampling method is most appropriate?

The planner should randomly select households from the
population.

The planner should select one or two wards and choose all the
households in those wards.

The planner should randomly select households from each ward
so the proportions of the wards in the sample are about the same as
in the population.

The planner should get a list of all the households
alphabetically by owner, randomly choose a starting point, and then
choose every nth household in the list.

Question A television station plans to send a crew to a
polling center on an election day. Because they do not have time to
interview each individual voter, they decide to count voters
leaving the polling location and ask every 20th voter for an
interview. What type of sampling is this?

Simple random sampling

Cluster sampling

Stratified Sampling

Systematic sampling

Convenience sampling

Question A grocer receives cartons of 12 eggs in boxes of 100
cartons. In a particular month, the grocer receives 4 shipments of
eggs with 20 boxes in each shipment. The grocer wants to estimate
the proportion of cartons he receives this month that include at
least one broken egg. Which of the following sampling methods would
be most appropriate?

Obtain a stratified sample by examining 100 randomly selected
cartons from each of the 4 shipments.

Obtain a cluster sample by randomly selecting 3 boxes and
examining every carton in those 3 boxes.

Obtain a convenience sample by examining every carton on the
grocery store’s shelves one day.

Obtain a systematic sample by examining the top carton in the
top right corner of each box.

Question When is using a simple random sample appropriate?

A simple random sample should always be used if possible.

A simple random sample should be used if the population is
not well understood or there are no groups within the population
that need to be analyzed individually.

A simple random sample should be used when the population has
well-defined groups that are relatively homogeneous. This will make
sure each group is represented proportionally.

Question A manufacturer has three tool centers that each make
about 1000 tools every day. In order to implement better
quality-control procedures, the manager wants to start sampling the
tools made each day to be able to identify issues as quickly as
possible. Which sampling method would be most appropriate?

At the end of each day, select a random sample of 60 tools
from all the tools produced that day.

At the end of each day, select random samples of 20 tools
from the tools produced by each tool center that day.

Select the first 20 tools produced by each tool center on
each day.

Select every 50th tool produced by each tool center during
the day.

Select every 150th tool produced by any tool center during
the day.

Question The management of a large airline wants to estimate
the average time after takeoff taken before the crew begins serving
snacks and beverages on their flights. Assuming that management has
easy access to all of the information that would be required to
select flights by each proposed method, which of the following
would be reasonable methods of stratified sampling? Select all that
apply.

For each day of the week, randomly select 5% of all flights
that depart on that day of the
week.

Divide all flights into the following 4 groups on the basis
of scheduled departure time:before 9:00 am, 9:00 am to 1:00 pm,
1:00 pm to 5:00 pm, and after 5:00 pm. Randomly select 5% of the
flights in each group.

For each crew member the airline employs, randomly select 5
flights that the crew member works.

Divide the airports from which the airline’s flights depart
into 4 regions: Northeast, Northwest, Southwest, and Southeast.
Randomly select 5% of all flights departing from airports in each
region.

Question

A professor is interested in the average length of books in
her library. She has divided her books into a few different
categories: 235 books on mathematics, 290 books on sports, and 166
books on interior design. Rather than examining all the books, she
plans to use a stratified sample of 50 books. How many of the
sports books should she choose? Enter a whole number.

Question

Assume that 80 houses are present in the form of a grid
consisting of 10 columns and 8 rows. If a loud speaker is placed
just before the first row, which sampling method works the best to
select a sample of houses if we want to get an estimate of the
average loudness (measured in decibels) near all the 80 houses?

Simple Random Sampling

Stratified Sampling using the rows of the houses as strata

Cluster Sampling using the rows of the houses as clusters

Convenience Sampling

Determine Appropriate Sampling Methods

A representative sample is a sample that has the same
characteristics as the population from which it is drawn. Although
no sample will be exactly representative unless the entire
population is sampled, there are various methods that individually
vary in accuracy depending on sample conditions. A table of five
basic sampling methods and their description can be seen below. The
third columns shows an example of how each method might be used if
researchers want to find out which of two mayoral candidates is
favored by voters.

Method
Description Example

Simple random sample A simple random sample is selected
from a population in a way such that all samples of that size have
the same chance of being selected. However, a true simple random
sample can sometimes be difficult to obtain. Additionally,
researchers may sometimes wish to ensure that some distinguishable
characteristic of members in the population is not overrepresented
or underrepresented in their sample, as could occur by chance with
a simple random
sample.
The researchers could use a computer to randomly select telephone
numbers from all of those in use in the city, and then interview a
registered voter at each telephone number. (This procedure would
yield a sample that represents only those people who have a
telephone.)

Cluster
sampling
Cluster sampling involves dividing the population into groups,
randomly selecting several of these groups, and including every
individual from each of the selected groups in the sample. Cluster
sampling is more convenient and practical than simple random
sampling, but samples obtained by this method may be biased or
unrepresentative of the population if clusters are different from
each other with respect to the population being investigated. This
method is best employed when population groups are separated, and
it would be difficult to access all of the
groups. The
researchers could randomly select a few neighborhoods and interview
all the people in each one.

Stratified
sampling
Stratified sampling involves dividing the population into groups
called strata—usually on the basis of some characteristic other
than the response and explanatory variables—and randomly selecting
a proportionate number of individuals from each group. Stratified
sampling can produce a very good random representative sample, but
it can be complex to administer and requires a lot of information.
This sampling method is best applied when there are specific
subgroups of the population to investigate, like age groups or
ethnicities of people. Unlike even simple random sampling,
stratified sampling ensures that each group is represented in the
sample. The researchers
could take random samples from voters of each age range, where each
age range is a strata.

Systematic sampling
Systematic sampling involves selecting every kth individual from
the population, beginning at a randomly-selected starting point. If
a particular sample size is desired, the value of k should be small
enough to produce a sample of the desired size but not so small
that it produces an unrepresentative sample. Systematic sampling
usually is easy to administer and provides a good random sample,
but it may produce a biased sample if there is a pattern in the
population. This method is best employed when a stream of
representative individuals is
available. The
researchers could create a systematic sample by obtaining the voter
registration roster, starting at a randomly selected name, and
contacting every 500th person thereafter.

Convenience sampling Convenience sampling involves
selecting individuals from the population that are easily
accessible, or from which data are easily obtained. Convenience
samples can be easy and are often employed when limited resources
are available. However, convenience samples are not random and are
particularly prone to self-selection bias, which is when some
individuals are more likely to be included in the sample than
others because individuals with some characteristic (for example, a
strong opinion on a survey question) are more likely to choose to
participate. The
researchers might ask everyone visiting a store or website if they
would like to take a survey about candidate preference.

Question Explain why cluster sampling method is the
best when you want to estimate the IQ of all college-going 20 year
old students in your city.

Question A restaurant owner is interested in determining if
customers are satisfied with the new atmosphere. To determine this,
the owner leaves customer feedback cards at each table. Which
sampling method would be most appropriate?

a) Systematic sampling

b) Stratified sampling

c) Convenience sampling

Question

A town planner is interested in getting some demographic data
about the households in the city. The city has four wards with the
following numbers of households: ward A has 2,107, ward B has 903,
ward C has 1,505, and ward D has 1,499. The budget for the project
allows the planner to survey 100households. She plans to use a
stratified sampling method. What number of households should be
chosen from ward B? Enter a whole number.

Question

Assume that 80 houses are present in the form of a grid
consisting of 10 columns and 8 rows. If a loud speaker is placed
just before the first row, which sampling method works the best to
select a sample of houses if we want to get an estimate of the
average loudness (measured in decibels) near all the 80 houses?

Simple Random Sampling

Stratified Sampling using the rows of the houses as strata

Cluster Sampling using the rows of the houses as clusters

Convenience Sampling

Determine Appropriate Sampling Methods

A representative sample is a sample that has the same
characteristics as the population from which it is drawn. Although
no sample will be exactly representative unless the entire
population is sampled, there are various methods that individually
vary in accuracy depending on sample conditions. A table of five
basic sampling methods and their description can be seen below. The
third columns shows an example of how each method might be used if
researchers want to find out which of two mayoral candidates is
favored by voters.

Method
Description Example

Simple random sample A simple random sample is selected
from a population in a way such that all samples of that size have
the same chance of being selected. However, a true simple random
sample can sometimes be difficult to obtain. Additionally,
researchers may sometimes wish to ensure that some distinguishable
characteristic of members in the population is not overrepresented
or underrepresented in their sample, as could occur by chance with
a simple random
sample.
The researchers could use a computer to randomly select telephone
numbers from all of those in use in the city, and then interview a
registered voter at each telephone number. (This procedure would
yield a sample that represents only those people who have a
telephone.)

Cluster
sampling
Cluster sampling involves dividing the population into groups,
randomly selecting several of these groups, and including every
individual from each of the selected groups in the sample. Cluster
sampling is more convenient and practical than simple random
sampling, but samples obtained by this method may be biased or
unrepresentative of the population if clusters are different from
each other with respect to the population being investigated. This
method is best employed when population groups are separated, and
it would be difficult to access all of the
groups. The
researchers could randomly select a few neighborhoods and interview
all the people in each one.

Stratified
sampling
Stratified sampling involves dividing the population into groups
called strata—usually on the basis of some characteristic other
than the response and explanatory variables—and randomly selecting
a proportionate number of individuals from each group. Stratified
sampling can produce a very good random representative sample, but
it can be complex to administer and requires a lot of information.
This sampling method is best applied when there are specific
subgroups of the population to investigate, like age groups or
ethnicities of people. Unlike even simple random sampling,
stratified sampling ensures that each group is represented in the
sample. The researchers
could take random samples from voters of each age range, where each
age range is a strata.

Systematic sampling
Systematic sampling involves selecting every kth individual from
the population, beginning at a randomly-selected starting point. If
a particular sample size is desired, the value of k should be small
enough to produce a sample of the desired size but not so small
that it produces an unrepresentative sample. Systematic sampling
usually is easy to administer and provides a good random sample,
but it may produce a biased sample if there is a pattern in the
population. This method is best employed when a stream of
representative individuals is
available. The
researchers could create a systematic sample by obtaining the voter
registration roster, starting at a randomly selected name, and
contacting every 500th person thereafter.

Convenience sampling Convenience sampling involves
selecting individuals from the population that are easily
accessible, or from which data are easily obtained. Convenience
samples can be easy and are often employed when limited resources
are available. However, convenience samples are not random and are
particularly prone to self-selection bias, which is when some
individuals are more likely to be included in the sample than
others because individuals with some characteristic (for example, a
strong opinion on a survey question) are more likely to choose to
participate. The
researchers might ask everyone visiting a store or website if they
would like to take a survey about candidate preference.

Example

Question

Explain why cluster sampling method is the best when you want
to estimate the IQ of all college-going 20 year old students in
your city.

Question

A restaurant owner is interested in determining if customers
are satisfied with the new atmosphere. To determine this, the owner
leaves customer feedback cards at each table. Which sampling method
would be most appropriate?

a) Systematic sampling

b) Stratified sampling

c) Convenience sampling

Question When is cluster sampling appropriate?

Cluster sampling is a good choice when the population has
multiple distinct groups that are each likely to be representative
of the population as a whole.

Cluster sampling is a good choice when the population has
multiple distinct groups that are internally homogenous but not
representative of the population as a whole.

Cluster sampling is useful if the population is not well
understood or there are no groups within the population that need
to be analyzed individually.

Cluster sampling is a useful method when the individuals in
the population are generated in a continuous stream, like on an
assembly line.

Question

A television station wants to report on a local election. The
station has three crews that can be used during the day for
collecting data. What sampling method would be appropriate?

The crews should go to three of the station’s offices in the
city and ask people to call the station to report how they voted.

The station should randomly select three polling centers and
send one crew to each. The crews should interview people as they
leave the polls.

The station should randomly select a set of voters from the
city at the beginning of the day and ask them each how they voted
as they leave their polling centers.

The crews should visit the polling centers in a sequence,
interviewing the next 10 voters to leave each center.

Question

Assume that 80 houses are present in the form of a grid
consisting of 10 columns and 8 rows. If a loud speaker is placed
just before the first row, which sampling method works the best to
select a sample of houses if we want to get an estimate of the
average loudness (measured in decibels) near all the 80 houses?

Simple Random Sampling

Stratified Sampling using the rows of the houses as strata

Cluster Sampling using the rows of the houses as clusters

Convenience Sampling

Determine Appropriate Sampling Methods

A representative sample is a sample that has the same
characteristics as the population from which it is drawn. Although
no sample will be exactly representative unless the entire
population is sampled, there are various methods that individually
vary in accuracy depending on sample conditions. A table of five
basic sampling methods and their description can be seen below. The
third columns shows an example of how each method might be used if
researchers want to find out which of two mayoral candidates is
favored by voters.

Method
Description Example

Simple random sample A simple random sample is selected
from a population in a way such that all samples of that size have
the same chance of being selected. However, a true simple random
sample can sometimes be difficult to obtain. Additionally,
researchers may sometimes wish to ensure that some distinguishable
characteristic of members in the population is not overrepresented
or underrepresented in their sample, as could occur by chance with
a simple random
sample.
The researchers could use a computer to randomly select telephone
numbers from all of those in use in the city, and then interview a
registered voter at each telephone number. (This procedure would
yield a sample that represents only those people who have a
telephone.)

Cluster
sampling
Cluster sampling involves dividing the population into groups,
randomly selecting several of these groups, and including every
individual from each of the selected groups in the sample. Cluster
sampling is more convenient and practical than simple random
sampling, but samples obtained by this method may be biased or
unrepresentative of the population if clusters are different from
each other with respect to the population being investigated. This
method is best employed when population groups are separated, and
it would be difficult to access all of the
groups. The
researchers could randomly select a few neighborhoods and interview
all the people in each one.

Stratified
sampling
Stratified sampling involves dividing the population into groups
called strata—usually on the basis of some characteristic other
than the response and explanatory variables—and randomly selecting
a proportionate number of individuals from each group. Stratified
sampling can produce a very good random representative sample, but
it can be complex to administer and requires a lot of information.
This sampling method is best applied when there are specific
subgroups of the population to investigate, like age groups or
ethnicities of people. Unlike even simple random sampling,
stratified sampling ensures that each group is represented in the
sample. The researchers
could take random samples from voters of each age range, where each
age range is a strata.

Systematic sampling
Systematic sampling involves selecting every kth individual from
the population, beginning at a randomly-selected starting point. If
a particular sample size is desired, the value of k should be small
enough to produce a sample of the desired size but not so small
that it produces an unrepresentative sample. Systematic sampling
usually is easy to administer and provides a good random sample,
but it may produce a biased sample if there is a pattern in the
population. This method is best employed when a stream of
representative individuals is available.The researchers could
create a systematic sample by obtaining the voter registration
roster, starting at a randomly selected name, and contacting every
500th person thereafter.

Convenience sampling Convenience sampling involves
selecting individuals from the population that are easily
accessible, or from which data are easily obtained. Convenience
samples can be easy and are often employed when limited resources
are available. However, convenience samples are not random and are
particularly prone to self-selection bias, which is when some
individuals are more likely to be included in the sample than
others because individuals with some characteristic (for example, a
strong opinion on a survey question) are more likely to choose to
participate. The
researchers might ask everyone visiting a store or website if they
would like to take a survey about candidate preference.

Example

Question Explain why cluster sampling method is the best when
you want to estimate the IQ of all college-going 20 year old
students in your city.

Question A restaurant owner is interested in determining if
customers are satisfied with the new atmosphere. To determine this,
the owner leaves customer feedback cards at each table. Which
sampling method would be most appropriate?

a) Systematic sampling

b) Stratified sampling

c) Convenience sampling

Question An executive for a large national restaurant chain
with multiple locations in each of 513 counties wants to personally
sample the cleanliness of the chain’s restaurants throughout the
country by visiting restaurants. The executive wants a good-quality
sample but wants to minimize travel time and expenses. Which of the
following sampling methods would be most appropriate?

Obtain a convenience sample by visiting the 100 restaurants
that are closest to the executive’s office.

Obtain a systematic sample by selecting every 20th restaurant
from a list that orders all restaurants by date of opening.

Obtain a stratified sample by visiting 1 randomly selected
restaurant in every county.

Obtain a cluster sample by randomly selecting 20 counties and
visiting every restaurant within those counties.

Question To study the mean head size of all people in her
state, Jacqueline collects data from 20 people in her town. Which
type of sampling is used?

Cluster sampling

Stratified sampling

Systematic sampling

Convenience sampling

Question In reference to different sampling methods, is the
following statement true or false?

Cluster sampling includes the steps: divide the population
into groups; use simple random sampling to identify a proportionate
number of individuals from each group.

True

False

Question A school district’s superintendent wants to
administer a test of life skills to a sample of students. The
superintendent has ample time and resources to conduct the study,
as well as access to detailed information about all students’
addresses, courses, grades, and attendance. Which of the following
would be the worst sampling method for the superintendent to use?

Cluster sampling

Convenience sampling

Stratified sampling

Systematic sampling

Question When considering different sampling methods, cluster
sampling includes the steps: _______.

use simple random sampling to select a set of groups; every
individual in the chosen groups is included in the sample

list the members of the population; use simple random
sampling to select a starting point in the population; let k =
(number of individuals in the population)/(number of individuals
needed in the sample); choose every kth individual in the list
starting with the one that was randomly selected

divide the population into groups; use simple random sampling
to identify a proportionate number of individuals from each group

identify individuals of the population that are easily
accessible; obtain data from these individuals

Question When is stratified sampling appropriate?

Stratified sampling is a good choice when the population has
multiple distinct groups that are each likely to be representative
of the population as a whole.

Stratified sampling is a good choice when the population has
multiple distinct groups that are internally homogenous but not
representative of the population as a whole.

Stratified sampling is a useful method if the population is
not well understood or there are no groups within the population
that need to be analyzed individually.

Stratified sampling is a useful method when the individuals
in the population are generated in a continuous stream, like on an
assembly line.

Question In reference to different sampling methods, is the
following statement true or false?

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