Devry MATH225 Week 1 Assignment Comparing Sampling Methods Latest 2019 JULY Question # 00603498 Subject: Mathematics Due on: 08/08/2019 Posted On: 08/08/2019 08:22 AM Tutorials: 1 Rating: 5.0/5

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?