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 difícil≈ 1 min
A fitness magazine wanted to estimate how many days per week adults in a city exercise. A reporter surveyed $250$ people as they left the city's largest gym, and the mean response was $4.6$ days per week. Which of the following best describes a problem with using this result to estimate the mean for all adults in the city?
AA. The sample size of $250$ is too small to give any information about the city.
BB. The mean should have been reported as a median instead.
CC. The reporter should have surveyed people as they entered the gym instead.
DD. The sample is not representative, so the result likely overestimates the mean for all adults in the city.
Ver respuesta y explicación
Respuesta correcta: D. The sample is not representative, so the result likely overestimates the mean for all adults in the city.
Explicación
People leaving a gym are more likely to exercise often than adults in general, so the sample is biased and the estimate is probably too high. A random sample from all adults in the city would fix this.
A sample of $250$ can be informative if it is selected at random. Reporting a median would not remove the bias. Surveying people entering the gym has the same problem.