FRQ teacher feedback:
For #1, your use of the “names in a hat” method of conducting an SRS is clear, but stumbles a bit at the end: “collect the data they need” is a little vague and doesn’t connect to this scenario. It should be clear that the 500 pieces of paper represent students (you do this in your first sentence) and that the selected students will be given the survey about quality of instruction. That second part isn’t clear in your response. On some rubrics, your response would still earn “E” (full credit); on others, it may be in jeopardy of being bumped to a “P” (partial credit)
For #2, you do a good job of explaining one purpose of a stratified sample (you are guaranteed to get results from each type of student), how that differs from an SRS (you might only get one group or the other), but then you describe how to implement the stratified sample. That wasn’t what the question asked: they want to know why the stratified sample is a good idea. The beginning of your answer starts down that road, but should go a little further in describing the fact that having results from the two different groups of students is good because their opinions about the quality of instruction may differ, which is the intent of the survey. Therefore, your response would likely get partial credit (“P”)
FRQ teacher feedback:
For part #1, I’m a little torn on whether you would earn “E” or “P”. Typically, the criteria for describing implementing a process like this are (1) clearly assign numbers to each individual, (2) generate a list of n unique numbers within the boundaries of the assigned numbers, (3) select individuals who correspond with the numbers. It is clear that you have fulfilled components (2) and (3)… what I’m stuck on is (1). Saying “randomly number the 30,000 students [with] an integer between 1 and 30,000” does not clearly indicate that each student is receiving a unique number label; your description being just “randomly” leaves open the possibility of multiple people being assigned the same number, for example. This can be alleviated by using a clear randomization method. For example, you could have said “From a list of the 30,000 students, randomize the order of names and then assign the first name on the list 1, second name 2, and so on until all students are numbered. [rest of your response here]”. Or - and here’s the annoying part - simply add the word “unique” before “integer between 1 and 30,000”, and you’re covered. So with all of that said (sorry for long-winded response), you’d likely earn “P” for this part.
Much shorter feedback for #2: you crushed it. You show a clear understanding of why stratification is useful in this context, and gave a reason why (“opinions… might be similar within their primary type of instruction”). “E” for this part!
FRQ teacher feedback:
For #1, your response is strong, but missing one small component: when you use the RNG to select 500 students without replacement (as you should), you must specify that you want the RNG to select 500 numbers within the range of 1-30,000. The way you’ve described it leaves us open to the possibility that 500 numbers will be generated, but not all 500 numbers will match the labels of students. Yes, it’s a small detail, but it’s been a part of rubrics for this type of question in the past. (The 3 things that are usually looked for: (1) give the population unique numbers, (2) generate n unique numbers within the range of the numbers from the population, (3) choose the [individuals] corresponding to those numbers and administer [thing].) Your response clearly does 2 of those 3 things, and would likely earn partial instead of full credit.
For #2, your response essentially summarizes the question (we’ll provide a more precise estimate of the proportion), without fully explaining why that happens. You mention that there will be “less variability”, but do not mention how stratifying the sample will do that. When explaining why we stratify (or block in experiments), it’s important to connect to the stratification/blocking variable to the response variable: in this case, that means explaining that the type of instruction a student receives may impact their opinion of the quality of that instruction (then insert a possible reason for this), which is why stratifying might help reduce variation: we’ll have separated the sample based on a factor that would influence the response, making our estimate more representative of the true population proportion.
FRQ Teacher Feedback
Very well done! For #1, you check all of the boxes that we as readers must look for - each individual is given a unique number, the numbers you generate are within the bounds of the numbers you assign, and you clearly indicate what is being done with the individuals selected.
For #2, you give a clear description of why stratification is done, in the context of the scenario. Nicely done!