Practice Experimental Design in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The deliberate planning of a study in which the researcher imposes treatments on subjects and measures responses, using control groups, randomization, replication, and (where possible) blinding to establish cause-and-effect relationships.

You want to know if a fertilizer helps plants grow. You can't just give it to some plants and hope for the best—you need a plan: a group that gets the fertilizer, a group that doesn't (control), random assignment so the groups are fair, enough plants so one weird result doesn't fool you (replication), and ideally the person measuring growth doesn't know which group is which (blinding).

Example 1

medium
Design an experiment to test whether caffeine improves test performance. Identify: explanatory variable, response variable, control group, treatment group, and how to control for confounders.

Example 2

hard
A study wants to test three fertilizer types (A, B, C) on crop yield across 12 fields. Design a completely randomized design (CRD) and a randomized block design (RBD) if the 12 fields have 4 different soil quality levels.

Example 3

easy
A teacher tests two teaching methods. She teaches Group A (morning) with Method 1 and Group B (afternoon) with Method 2. Identify the confounding variable and explain how to fix the design.

Example 4

hard
What is a placebo, and why is blinding important? Describe the placebo effect quantitatively: if 30% of placebo patients improve, what must a drug achieve to demonstrate its own effect?
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