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Observational studies and experiments worksheet

In an experiment the researcher assigns the treatment, ideally at random. In an observational study the researcher only records what people already do. Only an experiment can show cause and effect.

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Name

Studies and Experiments

Date Period

Answer each question.

  1. A sports scientist compares the injury rates of runners who wear minimalist shoes with those of runners who wear cushioned shoes. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?
  2. Researchers randomly assign 130 volunteers to take either a new sleep aid or a placebo, then record hours of sleep. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?
  3. A biologist records the snow depth and the number of deer seen in 40 areas of a forest. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?
  4. A chain randomly assigns 32 of its stores to play slow or fast music and compares daily sales. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?
  5. A company compares the sales of its stores that stay open late with the sales of stores that close early. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?
  6. Researchers randomly assign 160 volunteers to a 10-minute meditation or a 10-minute walk and measure their stress levels afterward. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?
  7. A physical therapist randomly assigns 40 patients with knee injuries to ice or heat treatment and measures their pain levels. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?
  8. A district randomly assigns its 28 high schools, half to start at 8:00 and half at 8:45, and compares attendance. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?
  9. A bakery randomly assigns 22 batches of dough to rise for one hour or two hours and measures the height of each loaf. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?
  10. A teacher randomly assigns her 52 students to get written comments or only a grade on a draft and compares how much their essays improve. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?
  11. A chef randomly assigns 36 taste testers to try a soup made with or without extra salt and records their ratings. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?
  12. Doctors review the records of 2,500 patients to compare coffee drinking with blood pressure. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?
  13. A city compares the crime rates of neighborhoods that have streetlights with those that do not. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?
  14. A city compares its 26 districts to see whether districts with more police officers have fewer crimes. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?
  15. A study compares the test scores of students who ride the bus with those who are driven to school. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?
  16. A school compares the attendance of students who eat the free breakfast with that of students who do not. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?
  17. A sleep lab randomly assigns 60 volunteers to use a phone or read a paper book before bed and records how long each takes to fall asleep. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?
  18. A city records the number of trees on each street and the average summer temperature there. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?
  19. A car company looks back at repair records to compare how often cars in cold states and in warm states need new batteries. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?
  20. A researcher randomly assigns 100 students to take a quiz with music playing or in silence and compares their scores. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Studies and ExperimentsAnswer keyVersion 1

Date Period

Answer each question.

  1. A sports scientist compares the injury rates of runners who wear minimalist shoes with those of runners who wear cushioned shoes. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?Observational study; explanatory: type of shoe; response: injury rateCause and effect: no, because nothing was assigned and other variables may explain the link
  2. Researchers randomly assign 130 volunteers to take either a new sleep aid or a placebo, then record hours of sleep. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?Experiment; explanatory: which pill a volunteer takes; response: hours of sleepCause and effect: yes, because the treatments were randomly assigned
  3. A biologist records the snow depth and the number of deer seen in 40 areas of a forest. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?Observational study; explanatory: snow depth; response: number of deerCause and effect: no, because nothing was assigned and other variables may explain the link
  4. A chain randomly assigns 32 of its stores to play slow or fast music and compares daily sales. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?Experiment; explanatory: the music tempo; response: daily salesCause and effect: yes, because the treatments were randomly assigned
  5. A company compares the sales of its stores that stay open late with the sales of stores that close early. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?Observational study; explanatory: store hours; response: salesCause and effect: no, because nothing was assigned and other variables may explain the link
  6. Researchers randomly assign 160 volunteers to a 10-minute meditation or a 10-minute walk and measure their stress levels afterward. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?Experiment; explanatory: the activity; response: stress levelCause and effect: yes, because the treatments were randomly assigned
  7. A physical therapist randomly assigns 40 patients with knee injuries to ice or heat treatment and measures their pain levels. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?Experiment; explanatory: ice or heat; response: pain levelCause and effect: yes, because the treatments were randomly assigned
  8. A district randomly assigns its 28 high schools, half to start at 8:00 and half at 8:45, and compares attendance. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?Experiment; explanatory: the start time; response: attendanceCause and effect: yes, because the treatments were randomly assigned
  9. A bakery randomly assigns 22 batches of dough to rise for one hour or two hours and measures the height of each loaf. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?Experiment; explanatory: rising time; response: loaf heightCause and effect: yes, because the treatments were randomly assigned
  10. A teacher randomly assigns her 52 students to get written comments or only a grade on a draft and compares how much their essays improve. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?Experiment; explanatory: the type of feedback; response: essay improvementCause and effect: yes, because the treatments were randomly assigned
  11. A chef randomly assigns 36 taste testers to try a soup made with or without extra salt and records their ratings. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?Experiment; explanatory: the amount of salt; response: taste ratingCause and effect: yes, because the treatments were randomly assigned
  12. Doctors review the records of 2,500 patients to compare coffee drinking with blood pressure. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?Observational study; explanatory: coffee drinking; response: blood pressureCause and effect: no, because nothing was assigned and other variables may explain the link
  13. A city compares the crime rates of neighborhoods that have streetlights with those that do not. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?Observational study; explanatory: streetlights; response: crime rateCause and effect: no, because nothing was assigned and other variables may explain the link
  14. A city compares its 26 districts to see whether districts with more police officers have fewer crimes. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?Observational study; explanatory: number of police officers; response: number of crimesCause and effect: no, because nothing was assigned and other variables may explain the link
  15. A study compares the test scores of students who ride the bus with those who are driven to school. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?Observational study; explanatory: how the student gets to school; response: test scoreCause and effect: no, because nothing was assigned and other variables may explain the link
  16. A school compares the attendance of students who eat the free breakfast with that of students who do not. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?Observational study; explanatory: eating the free breakfast; response: attendanceCause and effect: no, because nothing was assigned and other variables may explain the link
  17. A sleep lab randomly assigns 60 volunteers to use a phone or read a paper book before bed and records how long each takes to fall asleep. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?Experiment; explanatory: phone or book; response: time to fall asleepCause and effect: yes, because the treatments were randomly assigned
  18. A city records the number of trees on each street and the average summer temperature there. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?Observational study; explanatory: number of trees; response: average summer temperatureCause and effect: no, because nothing was assigned and other variables may explain the link
  19. A car company looks back at repair records to compare how often cars in cold states and in warm states need new batteries. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?Observational study; explanatory: the climate; response: how often batteries are replacedCause and effect: no, because nothing was assigned and other variables may explain the link
  20. A researcher randomly assigns 100 students to take a quiz with music playing or in silence and compares their scores. Is this an observational study or an experiment? Name the explanatory and response variables. Can it show cause and effect?Experiment; explanatory: whether music is playing; response: quiz scoreCause and effect: yes, because the treatments were randomly assigned

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

A researcher records how many hours of TV 500 children watch and their reading scores.

  1. Nobody is told how much TV to watch; the researcher only records it.
  2. TV is what might explain the scores, and the reading score is what is measured.

The answer is Observational study; explanatory: hours of TV; response: reading score.

Where students go wrong

Concluding cause from an observational study. Children who watch more TV may differ in many other ways, and any of them could explain the scores.

Also called observational study vs experiment or explanatory and response variables.

Questions about these worksheets

Yes. Every observational studies and experiments sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Statistics is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the observational studies and experiments questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

Concluding cause from an observational study. Children who watch more TV may differ in many other ways, and any of them could explain the scores.