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Question Video: Defining Stratified Random Sampling Mathematics

Which of the following is not true about stratified sampling? [A] Stratified random sampling is also called proportional random sampling. [B] Stratified random sampling allows researchers to obtain a sample population that best represents the entire population being studied. [C] Stratified sampling is the random selection of data from an entire population. [D] Stratified random sampling is a method of sampling that involves the division of a population into smaller subgroups known as strata. [E] The stratified random sample is a statistical measurement tool.

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Video Transcript

Which of the following is not true about stratified sampling? (A) Stratified random sampling is also called proportional random sampling. (B) Stratified random sampling allows researchers to obtain a sample population that best represents the entire population being studied. (C) Stratified sampling is the random selection of data from an entire population. (D) Stratified random sampling is a method of sampling that involves the division of a population into smaller subgroups known as strata. And (E) the stratified random sample is a statistical measurement tool.

We’re asked which of the options (A), (B), (C), (D), and (E) is not true about stratified sampling. So let’s begin by recalling when and how we might use stratified sampling. Recall that we use stratified random sampling when the population subdivides into distinct, nonoverlapping smaller subgroups, which we call strata. Random samples are then taken from each stratum and combined to form the overall sample from the population. And the size of the sample from each stratum reflects the stratum proportion of the whole population. So now let’s examine each of our options (A), (B), (C), (D), and (E) to see if they match our definition of stratified random sampling.

Beginning with option (A), this says stratified random sampling is also called proportional random sampling. We know that stratified random sampling is used when the population of interest is split into groups or strata. The size of the sample taken from each stratum reflects the proportion of the population represented by that stratum. It would therefore not be incorrect to give stratified random sampling an alternate name such as proportional random sampling. Option (A) is therefore true about stratified sampling.

Now let’s consider option (B). This says that stratified random sampling allows researchers to obtain a sample population that best represents the entire population being studied. In stratified random sampling, we know that when random samples are taken from each stratum, the stratum sample size reflects the stratum proportion of the whole population. This means that each of the different groups are represented proportionally within the final combined sample. No subgroup is therefore over- or underrepresented, and the sample reflects the proportion or makeup of the whole population. Such a sample will then best represent the entire population being studied. Option (B) is then also true about stratified sampling.

Now let’s consider option (C). This says stratified sampling is the random selection of data from an entire population. We know from our definition that stratified random sampling is used when the population subdivides into distinct nonoverlapping smaller subgroups or strata. Random samples are taken from each stratum and combined to form the overall sample. Option (C) however describes the random selection of data from an entire population that’s directly from the population. In this scenario then, there is no subdivision of the population before sampling. And this does not match with our definition of stratified random sampling. The statement in option (C) is therefore false about stratified sampling.

So now let’s consider option (D). This says that stratified random sampling is a method of sampling that involves the division of a population into smaller subgroups known as strata. In fact, this is exactly what’s specified in our definition of stratified random sampling. The population is subdivided into smaller groups or strata. We can then say that option (D) is true about stratified sampling.

And finally, let’s look at option (E). This says the stratified random sample is a statistical measurement tool. When we take a stratified random sample from a population, the proportional makeup of the population is represented in the sample size for each stratum. This means that the true makeup of the population is represented in any predictions or results gained from the sample data. So by this token, the stratified random sample is indeed a statistical measurement tool. Option (E) is therefore true about stratified sampling.

So we find that options (A), (B), (D), and (E) are true about stratified sampling and option (C) is not true about stratified sampling. Our answer is therefore option (C).

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