Choose a representation
Allocate a proportional sample using each stratum share. Compute response relative to people invited. For a block design, count the assignments within each block and multiply across distinct blocks. Compare changes from baseline when initial measurements differ.
Worked example: follow the quantity
A school has 60 juniors and 90 seniors. A stratified sample of 15 students is allocated proportionally. How many sampled students should be juniors? Use the junior population share as the sampling weight. Multiply that share by the total planned sample size. Substitute the given numbers: 15 × 60 ÷ (150) = 6. Therefore the requested value is 6.
Contrast a plausible mistake
For that example, the tempting answer 9 follows this error: Allocate the senior share to juniors. The requested quantity is 6. Explain why the wrong operation changes the mathematical object, not merely the arithmetic.
A second representation
An experiment has 3 labeled blocks, each containing 3 distinct volunteers. Exactly 2 volunteers in each block receive treatment and the remaining volunteer receives control. How many different treatment assignments are possible across all blocks? Within one block, choose the control volunteer in 3 ways; this uniquely determines the unordered pair receiving treatment. Multiply the 3 choices across all 3 labeled blocks; no ordering of the two treated volunteers is recorded. Substitute the given numbers: 3^3 = 27. Therefore the requested value is 27.
Transfer before checking
A school has 80 juniors and 120 seniors. A stratified sample of 20 students is allocated proportionally. How many sampled students should be juniors? Try without viewing the answer. Check: 8. Use the junior population share as the sampling weight. Multiply that share by the total planned sample size. Substitute the given numbers: 20 × 80 ÷ (200) = 8.
Scope and conditions
Random sampling supports population description; random assignment supports a treatment comparison under a sound experiment. A calculated effect alone does not establish either design property. These original practice tasks sample the official topic; they do not certify complete coverage or a predicted ACT score.
A school has 60 juniors and 90 seniors. A stratified sample of 15 students is allocated proportionally. How many sampled students should be juniors?
- Use the junior population share as the sampling weight.
- Multiply that share by the total planned sample size.
- Substitute the given numbers: 15 × 60 ÷ (150) = 6.
- Therefore the requested value is 6.
Compare the other answer choices
Allocate only one of the five ratio parts instead of the two parts belonging to juniors.
Split the sample equally between the two strata and round the junior allocation down to a whole person.
Allocate the senior share to juniors.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
ACT Mathematics content