Questions: 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. 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. 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. 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.

Solution Steps

Stratified sampling involves dividing the population into distinct subgroups (strata) based on certain characteristics. A sample is then drawn from each stratum, either proportionally or equally, depending on the sampling method.

Option A states that a simple random sample is drawn from one stratum at random, and all other strata are excluded. This is incorrect because stratified sampling requires sampling from all strata, not just one.

Option B claims that a stratified sample is constructed by selecting a stratum at random and then selecting a random individual from within that stratum, which may result in unequal sampling across strata. This is incorrect because stratified sampling typically ensures that all strata are represented, either proportionally or equally, depending on the design.

Option C states that the number of individuals sampled from each stratum should be proportional to the size of the strata in the population. This is correct for proportional stratified sampling, where the sample size from each stratum reflects the stratum's size in the population.

Option D claims that sampling the same number of people from each stratum results in a representative sample at a lower cost than a simple random sample. This is incorrect because equal-sized strata do not necessarily reflect the population's proportions, and cost-effectiveness depends on the sampling design, not just the stratum size.

Final Answer