Introduction to Experimental Design Practice Test

A principal wants to test whether a new tutoring program improves algebra test scores. One hundred 9th-grade students who are currently enrolled in algebra are available. The principal labels the students 1–100 and uses a random number generator to select 50 students to receive tutoring; the remaining 50 do not receive tutoring. After 6 weeks, all students take the same algebra test; the response variable is test score. Which statement best describes what the random number generator is used for in this study?

A school nurse wants to test whether a new 5-minute breathing routine reduces students’ test anxiety. She recruits 80 volunteers from the school (students who sign up after an announcement). Each student completes a short anxiety survey (0–40) right before a practice exam. Then the nurse uses a random number generator to assign 40 students to do the breathing routine and 40 students to sit quietly for 5 minutes (control). All students then take the same practice exam and complete the same anxiety survey immediately afterward; the response variable is the change in anxiety score (after − before). Which feature of this study allows the nurse to make a cause-and-effect conclusion about the routine’s effect on anxiety?