Question

A researcher planning a survey of heads of households in a particular state has census lists for each of the 23 counties in that state. He plans to obtain a random sample from each of the counties rather than grouping all census lists together and obtaining a sample from the entire group. Which of the following statements about the resulting stratified sample are true?

1. It is not a simple random sample.
2. It will help to avoid samples that do not represent the population.

III. It provides comparative information (e.g. mean salary of County X vs County Y) that a simple random sample would not provide.

1. I only
2. I and II
3. I and III
4. I, II, and III
5. None of the above

Answer 1

l. It is not a simple random sample.

This statement is true, as this is a stratified random sample, here, we are picking a random sample from each of the counties, instead of picking a sample from the entire group.

II. It will help to avoid samples that do not represent the population.

This statement is false, as stratified random sampling also won't remove the samples that do not represent the population. It can be done with the help of cluster sampling.

III. It provides comparative information ( e.g mean salary of county X vs county Y) that a simple random sample would not provide.

This statement is true. Here, as we are picking 23 different samples, one from each county, the samples from each county can be compared. But in a simple random sample, this us not possible, as the sample is picked from one entire group.

Hence, the correct option is:

C. I and III