Asignación aleatoria a grupos → se puede hablar de causa y efecto.
Selección aleatoria de la muestra → se puede generalizar a la población.
Estudio observacional → solo asociación.
Estrategia paso a paso
Busca dos cosas en el enunciado: ¿hubo asignación aleatoria? ¿hubo selección aleatoria?
Trampas habituales
Generalizar a “todas las personas” resultados de voluntarios.
Ejemplo resuelto
Experimento con asignación aleatoria de voluntarios: “la app probablemente mejora el sueño en personas parecidas a las del estudio” (no “en todo el mundo”).
Preguntas de ejemplo
Intenta responder antes de abrir la solución. Las preguntas están en el idioma del examen.
Pregunta 1
Dificultad fácil≈ 1 min
A survey of $1{,}500$ randomly selected high school students in a state found that students who reported eating breakfast every day had higher average grades than students who did not. Which of the following conclusions is most appropriate?
AA. Eating breakfast every day causes students in the state to earn higher grades.
BB. Earning higher grades causes students to eat breakfast every day.
CC. Among high school students in the state, eating breakfast every day is associated with higher grades.
DD. Eating breakfast every day is associated with higher grades for all students in the country.
Ver respuesta y explicación
Respuesta correcta: C. Among high school students in the state, eating breakfast every day is associated with higher grades.
Explicación
The students were randomly selected, so the results can be generalized to high school students in the state. But the study only observed the students; no one was assigned to eat breakfast. So it shows an association, not cause and effect.
Both causal statements go beyond an observational study. The sample came from one state, so the conclusion cannot be extended to the whole country.
Pregunta 2
Dificultad media≈ 1 min
To estimate the average amount customers spend per visit, a grocery chain randomly selected $500$ receipts from its store in Denver during one month. The mean amount spent was \$46. To which group can the result most appropriately be generalized?
AA. All customers of every grocery store in Denver
BB. All customers of every store in the grocery chain
CC. All shoppers in the United States
DD. Customer visits to the chain's Denver store during that month
Ver respuesta y explicación
Respuesta correcta: D. Customer visits to the chain's Denver store during that month
Explicación
The receipts were selected at random only from the chain's Denver store during one month, so the estimate applies to customer visits to that store during that month.
Other stores in the chain, other grocery stores in Denver, and shoppers in general were not sampled, so the result cannot be generalized to them.
Pregunta 3
Dificultad media≈ 2 min
A survey of 1,000 randomly selected adults in a country found that adults who reported eating breakfast every day had lower average stress scores than adults who did not. Which conclusion is most appropriate?
AA. Eating breakfast every day reduces the stress scores of adults throughout the country.
BB. Being stressed causes adults in the country to skip breakfast more often.
CC. The association applies only to the 1,000 adults who were surveyed.
DD. Among the country’s adults, daily breakfast is associated with lower stress scores.
Ver respuesta y explicación
Respuesta correcta: D. Among the country’s adults, daily breakfast is associated with lower stress scores.
Explicación
This is an observational study (no one was assigned to eat breakfast), so it can show an association but not cause and effect in either direction. Because the sample was random, the association can be generalized to adults in the country.
The choices saying breakfast reduces stress or stress causes skipping breakfast both claim causation. The choice limiting the result to the 1,000 surveyed adults ignores that a random sample represents the population.