Lesson Worksheet: Surveys, Experiments, and Observational Studies Mathematics

In this worksheet, we will practice recognizing the difference between surveys and observational studies and between correlation and causation.


Which of the following statements is NOT true?

  • AWell-designed experiments allow cause and effect to be established.
  • BIn an experiment, the variables are controlled.
  • CObservational studies most often allow cause and effect to be established.
  • DIn an observational study, the variables are observed and recorded.
  • EIn an experiment, a treatment is performed on subjects to measure its effect.


A restaurant owner wants to conduct a survey about whether the residents of a town prefer his restaurant over others or not. His plan is to ask a random sample of the restaurant customers to fill in a questionnaire. Which of the following would most likely be the reason the sample is biased?

  • AThe restaurant customers will not want to spend time filling in the questionnaire.
  • BThe number of customers in the chosen sample is not large enough.
  • CThe restaurant customers are likely to prefer his restaurant.
  • DWe do not know how he will ensure that the sample is random.


A church organization wants to poll citizens on their opinion of religious education in schools. They send a survey to all their members around the country. Is their sample biased?

  • ANo
  • BYes


A student wants to research the number of students in his middle school who ride the school bus. Which of the following is the best method to obtain an unbiased sample?

  • AAsking all of the students in the library on Thursday if they ride the school bus
  • BAsking a random sample of 100 students during lunchtime if they ride the school bus
  • CAsking a random sample of 50 students from his grade if they ride the school bus
  • DAsking all of the students in the gymnastics team if they ride the school bus
  • EAsking a random sample of 5 students in the hallway if they ride the school bus


A student conducts a survey about the number of hours that the students in his school study per day. Which of the following is an unbiased sample?

  • AA random sample taken from primary students
  • BA random sample taken from secondary students
  • CA random sample taken from his class
  • DA random sample taken from the school students
  • EA random sample taken from girls in the school


Which of the following survey questions is least biased?

  • ADrinking sodas during a high-protein meal has been shown to decrease metabolic efficiency, which may prompt the body to store more fat. How often do you drink sodas during meals?
  • BHow often do you manage to drink water rather than sodas during meals?
  • CFor each of the beverages given, indicate how often you drink them during meals.
  • DOn a scale from 1 to 10, how do you rate the frequency and quantity of sodas you drink during meals?


A school principal wants to find out what the students think about the teaching quality in the school. Which of these samples is unbiased?

  • AA list of female students to interview is randomly generated.
  • BA list of students to interview is randomly generated.
  • CA questionnaire is available at the library for anyone who wants to take part in the survey.
  • DA list of male students to interview is randomly generated.
  • EAll ninth grade students are interviewed.


Abdulrahman wants to find out the proportion of seventh grade students who have already been abroad. There are 250 seventh grade students in his school. He decides to number all of them from 1 to 250, generate a random list of 40 numbers between 1 and 250, and then interview the corresponding students. Is his sample biased?

  • ANo
  • BYes


Joud is doing a research project on whether or not students in her school eat healthy food. She decides to interview her friends who do gymnastics with her. Is her sample biased?

  • ANo
  • BYes


Which of the following survey questions is least biased?

  • AAre nurses salaries too high, about right, or too low?
  • BThere is a concern in the country about the nurse shortage. Do you think nurses should be paid more?
  • CShould nurses be paid more?
  • DDo you believe the salaries of nurses and surgeons are appropriate?

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