Which of the following sampling methods would MOST likely result in a representative sample?

A county in Illinois is conducting a survey to determine the mean annual income per household. The county is 427sq mi (2.65q km).

Which of the following sampling methods would MOST likely result in a representative sample?
A . A stratified phone survey of 100 people that is conducted between 2:00 p.m. and 3:00 p.m.
B . A systematic survey that is sent to 100 single-family homes in the county
C . Surveys sent to ten randomly selected homes within 5mi (8km) of the county’s office
D . Surveys sent to 100 randomly selected homes that are reflective of the population

View Answer

Answer: D

Explanation:

Surveys sent to 100 randomly selected homes that are reflective of the population. This is because a random sample is a type of sample that is selected by using a random method, such as a lottery or a computer-generated number, which ensures that every element in the population has an equal chance of being selected. A random sample can result in a representative sample, which means that the sample reflects the characteristics and diversity of the population. By sending surveys to 100 randomly selected homes that are reflective of the population, the analyst can ensure that the sample is representative of the county’s households and their income levels. The other sampling methods are not likely to result in a representative sample.

Here is why:

A stratified phone survey of 100 people that is conducted between 2:00 p.m. and 3:00 p.m. would result in a biased sample, which means that the sample favors or excludes certain groups or elements in the population. By conducting the survey only between 2:00 p.m. and 3:00 p.m., the analyst would miss out on people who are not available or reachable at that time, such as those who are working or sleeping. This could affect the representativeness and generalizability of the sample. A systematic survey that is sent to 100 single-family homes in the county would result in an unrepresentative sample, which means that the sample does not reflect the characteristics and diversity of the population. By sending surveys only to single-family homes, the analyst would ignore other types of households, such as apartments, condos, or mobile homes. This could affect the accuracy and reliability of the sample.

Surveys sent to ten randomly selected homes within 5mi (8km) of the county’s office would result in a small sample, which means that the sample size is too low to capture the variability and diversity of the population. By sending surveys only to ten homes within a limited area, the analyst would miss out on many households that are located in different parts of the county. This could affect the precision and confidence of the sample.