Worked solution P38-Easy-1. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Easy-2. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Easy-3. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Easy-4. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Easy-5. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Easy-6. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Easy-7. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Easy-8. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Easy-9. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Easy-10. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Easy-11. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Easy-12. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Easy-13. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Easy-14. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Easy-15. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Easy-16. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Easy-17. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Easy-18. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Easy-19. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Tough-1. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Tough-2. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Tough-3. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Tough-4. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Tough-5. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Tough-6. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Tough-7. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Tough-8. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Tough-9. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Tough-10. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Tough-11. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Tough-12. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Tough-13. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Tough-14. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Tough-15. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Tough-16. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Tough-17. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Tough-18. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Tough-19. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Toughest-1. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Toughest-2. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Toughest-3. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Toughest-4. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Toughest-5. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Toughest-6. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Toughest-7. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Toughest-8. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Toughest-9. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Toughest-10. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Toughest-11. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Toughest-12. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Toughest-13. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Toughest-14. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Toughest-15. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Toughest-16. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Toughest-17. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Toughest-18. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.

Worked solution P38-Toughest-19. State experimental units, treatments, response, assignment mechanism, comparison, replication, controls, and the intended scope of inference. With 120 units and four treatments, equal random assignment gives $120/4=30$ units per treatment before attrition. Interpretation: Random assignment balances lurking variables in expectation and supports a causal comparison; random sampling is what supports generalization. Validity: Interference should be limited, treatment implementation consistent, and response measurement blind where feasible. Error to reject: A large observational comparison is not automatically an experiment, because sample size does not replace random assignment.