Question

In a particular county, car registration records for families show ownership of vehicles. There are 2,000 vehicles registered among 1,800 families. (Some families have only one vehicle while others have multiple vehicles.) Of these 2,000 vehicles, 1,500 are cars and 500 are light trucks. The following lists are available: The 2,000 families; the 1,800 vehicles; the 1,500 cars; the 500 light trucks. For each question, identify the sampling plan used to select the sample of vehicles.

(a) We select the vehicles that are listed 100th, 200th, 300th, etc., from the list of all vehicles.

A. Volunteer sample.
B. Stratified random sample.
C. Systematic sample.
D. Simple random sample.
E. Cluster sample.

(b) We randomly select 100 vehicles from the list of all vehicles.

A. Systematic sample.
B. Simple random sample.
C. Stratified random sample.
D. Cluster sample.
E. Volunteer sample.

(c) We randomly select 15 vehicles from the list of cars and 15 vehicles from the list of light trucks.

A. Volunteer sample.
B. Simple random sample.
C. Stratified random sample.
D. Cluster sample.
E. Systematic sample.

(d) We randomly select 25 families and include every vehicle that belongs to one of the selected families in our sample.

A. Simple random sample.
B. Cluster sample.
C. Stratified random sample.
D. Systematic sample.
E. Volunteer sample.

Answer 1

(a) We select the vehicles that are listed 100th, 200th, 300th, etc., from the list of all vehicles.

C. Systematic sample.

Reason : In a systematic sampling technique, we choose a random initial point and sample with a fixed interval. Like the interval in the question is 100

(b) We randomly select 100 vehicles from the list of all vehicles.

B. Simple random sample.

Reason : In Simple random sampling, we randomly select some x number of samples without any selection criterion

(c) We randomly select 15 vehicles from the list of cars and 15 vehicles from the list of light trucks.

C. Stratified random sample.

Reason : The population is divided into stratas of cars and light trucks. From these stratas, randomly 15 vehicles are selected.

(d) We randomly select 25 families and include every vehicle that belongs to one of the selected families in our sample.

B. Cluster sample.

Reason : In cluster sampling, naturally forming clusters are considered. Then these clusters are selected randomly and all the samples belonging to these clusters are selected. With respect to the given question, clusters of families are formed and all the vehicles belonging to these families are selected.