Question

Which of the following methods describes stratified sampling?

A. Each person is assigned a three digit number (from 000 to 999). On a Random Digit Table, numbers are read, three at a time. The first hundred three-digit numbers read will represent the people in the sample.
B. To make the sampling frame a more manageable size, only people with birthdays from June 1 to December 31 will be considered. From that reduced sampling frame, the method described in Answer Choice A will be used.
C. Every man in the sampling frame will be assigned 8 sequential 4-digit numbers (from 0000 to 3999; example: 0000, 0001, 0002, 0003, 0004, 0005, 0006, 0007), and every woman in the sampling frame will be assigned 12 sequential 4-digit numbers (from 4000 to 9999; example: 4000, 4001, 4002, 4003, 4004, 4005, 4006, 4007, 4008, 4009, 4010, 4011). From a Random Digit Table, groupings of 4 numbers will be read and the first 100 subjects with their number read will be in the sample (duplicate selections will be ignored).
D. From an alphabetized list of people in the sampling frame, the first hundred are selected.
E. Each man in the sampling frame is assigned two sequential three-digit numbers (from 000 to 999; example: 000, 001). From a Random Digit Table, groupings of three numbers at a time are read. The first 40 three-digit numbers will represent the men selected (duplicate selections will be ignored). Then, each woman in the sampling frame will be assigned two sequential three-digit numbers (from 000 to 999; example: 000, 001). From a Random Digit Table, groupings of three numbers at a time are read. The first 60 three-digit numbers will represent the women selected (duplicate selections are ignored). These 40 men and 60 women will together form the sample of 100 people.

Answer 1

Stratified sampling is a method where a population is divided into strata and samples are taken from each of these groups separately. Option E describes stratified sampling, as men and women are sampled separately, maintaining representation from each gender. This method ensures representativeness and allows for the analysis of separate strata.

Step-by-step explanation:

The method that describes stratified sampling is a method where a population is divided into separate groups, known as strata, and a sample is then taken from each stratum. In stratified sampling, each stratum is sampled as an independent sub-population, where individual elements are randomly selected.

In the context of the given options, the answer that best corresponds to stratified sampling would be Option E. Here, each man and each woman in the sampling frame is assigned two sequential three-digit numbers. A random digit table is then used to select random numbers representing the men and the women separately, making it possible to control the proportion of men and women in the sample, and ensuring representation from each subgroup of the population.

It is important for stratified sampling that the strata are mutually exclusive and collectively exhaustive, meaning every population element must be assigned to one and only one stratum and all the population elements must be covered by the strata. Examples of strata could include gender, age groups, income levels, etc. This approach enhances the representativeness of the sample and allows for accurate analysis of each stratum separately.