SAT Math: Evaluating statistical claims

Evaluating statistical claims: observational studies and experiments.

Practise evaluating statistical claims →Adaptive SAT module

What the test covers

Key ideas

Common mistakes

Do it in Desmos

Ask two questions: was there random assignment, and was there random sampling?

Worked example

Worked example

A researcher asked for volunteers at a gym. The 120 volunteers were randomly assigned to follow either a new stretching routine or their usual routine for 8 weeks, and the new-routine group showed a greater gain in flexibility. Which conclusion is best supported?

  1. The new routine causes greater flexibility gains for all gym members.
  2. The new routine causes greater flexibility gains for people like these volunteers, but the result cannot be generalized to all gym members.
  3. No conclusion can be drawn because the sample was smaller than 200.
  4. The new routine is associated with flexibility gains, but no cause-and-effect conclusion can be drawn.

Answer: B: The new routine causes greater flexibility gains for people like these volunteers, but the result cannot be generalized to all gym members.

Random assignment to the two routines supports a cause-and-effect conclusion. The participants were volunteers, not a random sample of gym members, so the result applies only to people like the volunteers.

Practice questions

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Question 1

A researcher studied volunteers from employees of a company. The participants chose whether to use a sleep routine or not, and the group using a sleep routine showed a greater improvement in reaction time. Which conclusion is best supported?

  1. Using a sleep routine causes greater improvement in reaction time for all employees of the company.
  2. Using a sleep routine causes greater improvement in reaction time for people like the participants, but the result cannot be generalized to all employees of the company.
  3. Using a sleep routine is associated with greater improvement in reaction time among the participants only; neither cause nor generalization is supported.
  4. Using a sleep routine is associated with greater improvement in reaction time among employees of the company, but cause and effect cannot be concluded.
Show the answer and solution

Answer: C: Using a sleep routine is associated with greater improvement in reaction time among the participants only; neither cause nor generalization is supported.

Random assignment supports cause and effect; random sampling supports generalizing to the population. This study did not use random assignment and did not use a random sample, so: Using a sleep routine is associated with greater improvement in reaction time among the participants only; neither cause nor generalization is supported.

Question 2

A researcher studied a random sample from members of a gym. The participants were randomly assigned to use a new exercise plan or not, and the group using a new exercise plan showed a greater improvement in resting heart rate. Which conclusion is best supported?

  1. Using a new exercise plan causes greater improvement in resting heart rate for people like the participants, but the result cannot be generalized to all members of the gym.
  2. Using a new exercise plan causes greater improvement in resting heart rate for all members of the gym.
  3. Using a new exercise plan is associated with greater improvement in resting heart rate among members of the gym, but cause and effect cannot be concluded.
  4. No conclusion about resting heart rate can be drawn from this study.
Show the answer and solution

Answer: B: Using a new exercise plan causes greater improvement in resting heart rate for all members of the gym.

Random assignment supports cause and effect; random sampling supports generalizing to the population. This study used random assignment and used a random sample, so: Using a new exercise plan causes greater improvement in resting heart rate for all members of the gym.

Question 3

A researcher studied volunteers from members of a gym. The participants chose whether to use a new exercise plan or not, and the group using a new exercise plan showed a greater improvement in resting heart rate. Which conclusion is best supported?

  1. Using a new exercise plan causes greater improvement in resting heart rate for people like the participants, but the result cannot be generalized to all members of the gym.
  2. Using a new exercise plan is associated with greater improvement in resting heart rate among members of the gym, but cause and effect cannot be concluded.
  3. Using a new exercise plan is associated with greater improvement in resting heart rate among the participants only; neither cause nor generalization is supported.
  4. Using a new exercise plan causes greater improvement in resting heart rate for all members of the gym.
Show the answer and solution

Answer: C: Using a new exercise plan is associated with greater improvement in resting heart rate among the participants only; neither cause nor generalization is supported.

Random assignment supports cause and effect; random sampling supports generalizing to the population. This study did not use random assignment and did not use a random sample, so: Using a new exercise plan is associated with greater improvement in resting heart rate among the participants only; neither cause nor generalization is supported.

Question 4

A researcher studied a random sample from pupils in a school district. The participants chose whether to use a reading program or not, and the group using a reading program showed a greater improvement in reading speed. Which conclusion is best supported?

  1. Using a reading program causes greater improvement in reading speed for people like the participants, but the result cannot be generalized to all pupils in the district.
  2. Using a reading program is associated with greater improvement in reading speed among pupils in the district, but cause and effect cannot be concluded.
  3. Using a reading program causes greater improvement in reading speed for all pupils in the district.
  4. No conclusion about reading speed can be drawn from this study.
Show the answer and solution

Answer: B: Using a reading program is associated with greater improvement in reading speed among pupils in the district, but cause and effect cannot be concluded.

Random assignment supports cause and effect; random sampling supports generalizing to the population. This study did not use random assignment and used a random sample, so: Using a reading program is associated with greater improvement in reading speed among pupils in the district, but cause and effect cannot be concluded.

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