QQuestionBiology
QuestionBiology
Determine whether the following statement is true or false. Explain.
When obtaining a stratified sample, the number of individuals included within each stratum must be equal.
Choose the correct answer below.
A. False. When taking a stratified sample, a simple random sample is drawn from one stratum at random. All other strata will not be included in the sample.
B. True. Sampling the same number of people from each stratum will result in a sample that is representative of the population at a lower cost than a simple random sample.
C. False. Within stratified samples, the number of individuals sampled from each stratum should be proportional to the size of the strata in the population.
D. False. A stratified sample is constructed by successively selecting a stratum at random and then selecting a random individual from within that stratum. With this process, it is unlikely that all strata will be sampled from the same number of times.
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Step 1:Let's solve this step by step:
Step 2:: Understand Stratified Sampling
Stratified sampling is a sampling technique where the population is divided into subgroups (strata) based on shared characteristics, and then samples are drawn from each stratum.
Step 3:: Analyze the Key Requirement of Stratified Sampling
The critical point is that the number of individuals sampled from each stratum should be proportional to the size of that stratum in the original population. This ensures the sample represents the population accurately.
Step 4:: Evaluate the Statement
The statement claims that the number of individuals in each stratum must be equal. This is incorrect.
Step 5:: Reasoning
- In stratified sampling, strata can have different sizes - The sampling from each stratum should reflect the stratum's proportion in the total population - If each stratum had an equal number of individuals sampled, it would not accurately represent the population's composition
Step 6:: Identify the Correct Answer
The correct answer is C: False. Within stratified samples, the number of individuals sampled from each stratum should be proportional to the size of the strata in the population.
Final Answer
In stratified sampling, the sample size from each stratum should be proportional to the stratum's size in the population, not equal in absolute numbers.
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