MATH225 Week 1 Assignment Comparing Sampling Methods (July 2019)

MATH 225 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?