Question

(17 points) 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 randomly select 100 vehicles 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 select the vehicles that are listed 100th, 200th, 300th, etc., from the list of all vehicles. A. Simple random sample, B. Stratified random sample. C. Volunteer sample

Answer 1

Let's first understand the different types of sampling methods:

1. Simple random sampling

In a simple random sample, every member of the population has an equal chance of being selected. Your sampling frame should include the whole population.

2. Systematic sampling

Systematic sampling is similar to simple random sampling, but it is usually slightly easier to conduct. Every member of the population is listed with a number, but instead of randomly generating numbers, individuals are chosen at regular intervals.

3. Stratified sampling

This sampling method is appropriate when the population has mixed characteristics, and you want to ensure that every characteristic is proportionally represented in the sample.

You divide the population into subgroups (called strata) based on the relevant characteristic (e.g. gender, age range, income bracket, job role).

From the overall proportions of the population, you calculate how many people should be sampled from each subgroup. Then you use random or systematic sampling to select a sample from each subgroup.

4. Cluster sampling

Cluster sampling also involves dividing the population into subgroups, but each subgroup should have similar characteristics to the whole sample. Instead of sampling individuals from each subgroup, you randomly select entire subgroups.

5. Volunteer Sampling

A voluntary sample is made up of people who self-select into the survey.

(a) Option D : Simple random sample

(b) Option E : Systematic sample

(c) Option C: Stratified random sample ( because we have two mixed characteristics i.e cars and trucks and we want them in equal proportion i.e. 15 each)

(d) Option B: Cluster Sample