True or False: A simple random sample is always preferred because it obtains the same information as other sampling plans but requires a smaller sample size.

Verified step by step guidance

1. Understand the definition of a simple random sample (SRS): it is a sampling method where every member of the population has an equal chance of being selected, and each sample of a given size is equally likely to be chosen.
2. Recognize that while SRS is unbiased and straightforward, it does not always require a smaller sample size compared to other sampling methods; the sample size needed depends on the desired precision and variability in the population.
3. Consider other sampling plans such as stratified sampling or cluster sampling, which can sometimes provide more precise estimates or be more cost-effective, especially when the population is heterogeneous.
4. Note that the statement claims SRS obtains the same information as other sampling plans but with a smaller sample size, which is generally not true because other methods can be more efficient in certain contexts.
5. Conclude that the statement is false because SRS is not always preferred, nor does it always require a smaller sample size to obtain the same information as other sampling plans.

Key Concepts

Simple Random Sampling

Simple random sampling is a method where every member of the population has an equal chance of being selected. It is straightforward and unbiased but does not always guarantee the most efficient or smallest sample size for all study designs.

Sampling Efficiency and Sample Size

Sampling efficiency refers to how well a sampling method uses data to estimate population parameters. Some sampling plans, like stratified sampling, can achieve more precise estimates with smaller sample sizes compared to simple random sampling.

Comparison of Sampling Plans

Different sampling plans (e.g., stratified, cluster, systematic) have unique advantages depending on the population structure. Simple random sampling is not always preferred because other methods may provide better accuracy or require fewer resources.