Describe a circumstance in which stratified sampling would be ...

Question

Describe a circumstance in which stratified sampling would be an appropriate sampling method.

Accepted Answer

Hello there. Today we are going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Select the scenario in which stratified sampling would be the most appropriate technique. OK. So it appears for this particular problem we're asked to look at our multiple choice answers, and we're asked to determine which of our multiple choice answers describes the scenario in which stratified sampling would be the most appropriate technique to use. So now that we know what we're ultimately trying to solve for, let's take a moment to read off our multiple choice answers to see what our final answer might be. A is drawing a single large random sample from the entire student body without regard to faculty. B is choosing several dormitories at random and surveying every student in those dormitories. C is selecting every 10th name from the from the student registry to estimate mean test scores. And finally, D is estimating mean test scores. In a university where performance varies systematically by faculty, engineering, arts, science, so students are grouped by faculty and sampled from each faculty. OK. So with that in mind, our first step that we need to take in order to solve this problem is we need to recall and state the method. So what method are we trying to recall and state? Well, we're focused based on what the prom tells us to focus on. We're focused on stratified sampling. So we need to recall and define what stratified sampling is. So as we should recall, stratified sampling partitions the population into strata that are hoogeneous, meaning the same and consistent throughout. And once again, this strata is hoogeneously. Internal, so it's homogeneous internally, meaning it's the same throughout internally, and the samples within each stratum. OK. So with that in mind, so once again, to quickly recap here, stratified sampling partitions the population into strata, strata that are hoogeneous internally, and samples within each stratum. So our second step now is we need to recall and state the appropriate criterion, so the appropriate criteria for stratified sampling. So we are allowed to use stratified sampling, as we should recall, when the subgroups with different means are known and are identifiable, which improves estimate when you're estimating precision. So it improves estimate precision. So with that in mind, our 3rd step now at this stage is we need to recall and match. So we need to recall what we know about stratified sampling, and we need to match the scenario given to us by the problem itself. To our multiple choice answers. So we need to match the definition of stratified sampling to the scenario that is listed in our multiple choice answer. So which multiple choice answer scenario correctly represents stratified sampling. So we need to note faculties. So specifically, The one multiple choice answer or answers that mention faculty are multiple choice answer letter A and multiple choice answer letter D. And we need to note that when we are noting faculties such as engineering, arts and science, we need to note that these are identifiable subgroups with different performance levels, so they suit the strata condition, the strata criteria. So with that in mind, we can eliminate multiple choice answer letter A because it doesn't mention any specific subgroups. So we can eliminate multiple choice answer letter A. So that's looking, so so far our final answer could be B, C, or D. So moving right along here to our fourth step now. We need to now recall and describe a we need to recall how we could describe a sampling plan by saying the students in each faculty, specifically in each faculty subgroup, and then from that point, we then therefore need to draw samples from each faculty either proportionally or with special allocation. OK. So with that in mind, our 5th step now is we need to give proportional allocation formulas. We need to recall and use the the given proportional allocation formula by stating the following formula, which states that N subscript H. Specifically, lowercase n subscript H is equal to N subscript H divided by N multiplied by lowercase n. With capital N subscript H, N, and lowercase n defined as before. So with that said, our 6th step now is we need to recall and state that the benefit by saying stratified sampling reduces variance of the estimated mean test scores compared with simple random sampling when between strata variability is large. So that will mean for our 7th and final step, we need to recall and note that a drawback will be that saying if faculty membership is misclassified or if students take courses from across different faculties, that will mean as a result that strata may be ill-defined and the method will be less effective. So based on this information, our correct and final answer without a doubt will have to be multiple choice answer letter D, which is once again estimating mean test scores in a university where performance varies systematically by faculty, parenthes engineering, arts, science, so students are grouped by faculty and sampled from each faculty. So multiple choice answer letter D is the only scenario that divides the data into subgroups, and we need to note that B and C are incorrect because D is the only scenario that most accurately captures stratified sampling based on our prior knowledge and the definition. Of stratified sampling. So that is why C and B are wrong because only D accurately represents the subgroups and also mentions the importance of estimating mean test scores or mean scores. In this case, they're doing the mean of test scores. So in so once again, stratified sampling. Emphasizes this, the importance of performing the mean and dividing data points into subgroups. So with that said, we've officially solved for this problem. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Describe a circumstance in which stratified sampling would be an appropriate sampling method.

Key Concepts

Stratified Sampling

Population Heterogeneity

Appropriate Circumstances for Stratified Sampling

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