MATH225N Week 1 Assignment: Comparing Sampling Methods

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?

Ans:

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

To study the mean respiratory rate of all people in his state, Frank samples the population by dividing the residents by towns and randomly selecting 12 of the towns. He then collects data from all the residents in the selected towns. Which type of sampling is used?

Ans:

Convenience sampling

Systematic sampling

Stratified sampling

Cluster sampling

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.

Ans:



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.

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.

Ans:

In order to study the shoe sizes of people in his town, Billy samples the population by dividing the residents by age and randomly selecting a proportionate number of residents from each age group. Which type of sampling is used?

Ans:

Systematic sampling

Stratified sampling

Convenience sampling

Cluster sampling

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

Ans:

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

To study the mean blood pressure of all people in her state, Christine samples the population by dividing the residents by towns and randomly selecting 9 of the towns. She then collects data from all the residents in the selected towns. Which type of sampling is used?

Ans:

Convenience sampling

Systematic sampling

Cluster sampling

Stratified sampling

Donald is studying the eating habits of all students attending his school. He samples the population by dividing the students into groups by grade level and randomly selecting a proportionate number of students from each group. He then collects data from the sample. Which type of sampling is used?

Ans:

Systematic sampling

Convenience sampling

Stratified sampling

Cluster sampling

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?

Ans:

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.

Q10

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?

Ans:

Simple random sampling

Cluster sampling

Stratified Sampling

Systematic sampling

Convenience sampling

Q11

In order to study the mean pulse rate of people in his town, Jerry samples the population by dividing the residents by regions and randomly selecting 12 of the regions. He collects data from all residents in the selected regions. Which type of sampling is used?

Cluster sampling

Convenience sampling

Stratified sampling

Systematic sampling

Q12

When is cluster sampling appropriate?

Ans:

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.

ANSWERS

Ans:

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

Ans:

Convenience sampling

Systematic sampling

Stratified sampling

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MATH225N Week 1 Assignment: Comparing Sampling Methods

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