Questions: 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. Within stratified samples, the number of individuals sampled from each stratum should be proportional to the size of the strata in the population. 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. 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. 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.

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. Within stratified samples, the number of individuals sampled from each stratum should be proportional to the size of the strata in the population. 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. 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. 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.
Transcript text: 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. Within stratified samples, the number of individuals sampled from each stratum should be proportional to the size of the strata in the population. 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. 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. 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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Solution

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Solution Steps

To determine whether the statement is true or false, we need to understand the concept of stratified sampling. In stratified sampling, the population is divided into distinct subgroups, or strata, and samples are drawn from each stratum. The number of individuals sampled from each stratum is typically proportional to the size of the stratum in the population, not necessarily equal. Therefore, the correct answer is A.

Step 1: Understanding Stratified Sampling

Stratified sampling involves dividing a population into distinct subgroups, known as strata, and then drawing samples from each stratum. The primary goal is to ensure that the sample accurately reflects the population's composition.

Step 2: Evaluating the Statement

The statement in question suggests that the number of individuals included within each stratum must be equal. However, in stratified sampling, the number of individuals sampled from each stratum is typically proportional to the size of the stratum in the population. This means that larger strata will have more individuals sampled than smaller strata.

Step 3: Analyzing the Options
  • Option A: False. Within stratified samples, the number of individuals sampled from each stratum should be proportional to the size of the strata in the population. This is the correct understanding of stratified sampling.
  • Option B: True. This option incorrectly states that equal sampling from each stratum is representative, which is not necessarily true.
  • Option C: False. This option describes a method that does not align with the principles of stratified sampling.
  • Option D: False. This option describes a random process that does not ensure representation from all strata.

Final Answer

The correct answer is \(\boxed{\text{A}}\).

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